diff options
| author |  Gael Guennebaud <g.gael@free.fr> | 2010-11-22 18:05:09 +0100 |
|---|---|---|
| committer | Gael Guennebaud <g.gael@free.fr> | 2010-11-22 18:05:09 +0100 |
| commit | a6f483e86b0c4c1d82622eec99fb051c804bf13d (patch) | |
| tree | ade493273b163904264c03585e749cfd24ab1a38 /blas | |
| parent | 7213dd1e6bbdcc0991be095deb85387d3c57dd17 (diff) | |
import reference BLAS routines which are not already implemented in Eigen : modified givens rotations, and packed and banded storages
Diffstat (limited to 'blas')
| -rw-r--r-- | blas/CMakeLists.txt | 5 | ||||
| -rw-r--r-- | blas/cgbmv.f | 322 | ||||
| -rw-r--r-- | blas/chbmv.f | 310 | ||||
| -rw-r--r-- | blas/chpmv.f | 272 | ||||
| -rw-r--r-- | blas/chpr.f | 220 | ||||
| -rw-r--r-- | blas/chpr2.f | 255 | ||||
| -rw-r--r-- | blas/ctbmv.f | 366 | ||||
| -rw-r--r-- | blas/ctbsv.f | 370 | ||||
| -rw-r--r-- | blas/ctpmv.f | 329 | ||||
| -rw-r--r-- | blas/ctpsv.f | 332 | ||||
| -rw-r--r-- | blas/dgbmv.f | 301 | ||||
| -rw-r--r-- | blas/drotm.f | 147 | ||||
| -rw-r--r-- | blas/drotmg.f | 206 | ||||
| -rw-r--r-- | blas/dsbmv.f | 304 | ||||
| -rw-r--r-- | blas/dspmv.f | 265 | ||||
| -rw-r--r-- | blas/dspr.f | 202 | ||||
| -rw-r--r-- | blas/dspr2.f | 233 | ||||
| -rw-r--r-- | blas/dtbmv.f | 335 | ||||
| -rw-r--r-- | blas/dtbsv.f | 339 | ||||
| -rw-r--r-- | blas/dtpmv.f | 293 | ||||
| -rw-r--r-- | blas/dtpsv.f | 296 | ||||
| -rw-r--r-- | blas/lsame.f | 85 | ||||
| -rw-r--r-- | blas/sgbmv.f | 301 | ||||
| -rw-r--r-- | blas/srotm.f | 148 | ||||
| -rw-r--r-- | blas/srotmg.f | 208 | ||||
| -rw-r--r-- | blas/ssbmv.f | 306 | ||||
| -rw-r--r-- | blas/sspmv.f | 265 | ||||
| -rw-r--r-- | blas/sspr.f | 202 | ||||
| -rw-r--r-- | blas/sspr2.f | 233 | ||||
| -rw-r--r-- | blas/stbmv.f | 335 | ||||
| -rw-r--r-- | blas/stbsv.f | 339 | ||||
| -rw-r--r-- | blas/stpmv.f | 293 | ||||
| -rw-r--r-- | blas/stpsv.f | 296 | ||||
| -rw-r--r-- | blas/zgbmv.f | 322 | ||||
| -rw-r--r-- | blas/zhbmv.f | 310 | ||||
| -rw-r--r-- | blas/zhpmv.f | 272 | ||||
| -rw-r--r-- | blas/zhpr.f | 220 | ||||
| -rw-r--r-- | blas/zhpr2.f | 255 | ||||
| -rw-r--r-- | blas/ztbmv.f | 366 | ||||
| -rw-r--r-- | blas/ztbsv.f | 370 | ||||
| -rw-r--r-- | blas/ztpmv.f | 329 | ||||
| -rw-r--r-- | blas/ztpsv.f | 332 |
42 files changed, 11488 insertions, 1 deletions
diff --git a/blas/CMakeLists.txt b/blas/CMakeLists.txt index 8c8034294..78b5f496c 100644 --- a/blas/CMakeLists.txt +++ b/blas/CMakeLists.txt @@ -15,7 +15,10 @@ endif() add_custom_target(blas) -set(EigenBlas_SRCS single.cpp double.cpp complex_single.cpp complex_double.cpp xerbla.cpp) +set(EigenBlas_SRCS single.cpp double.cpp complex_single.cpp complex_double.cpp xerbla.cpp + srotm.f srotmg.f drotm.f drotmg.f + lsame.f cgbmv.f chpr2.f ctbsv.f dspmv.f dtbmv.f dtpsv.f ssbmv.f sspr.f stpmv.f zgbmv.f zhpr2.f ztbsv.f chbmv.f chpr.f ctpmv.f dgbmv.f dspr2.f dtbsv.f sspmv.f stbmv.f stpsv.f zhbmv.f zhpr.f ztpmv.f chpmv.f ctbmv.f ctpsv.f dsbmv.f dspr.f dtpmv.f sgbmv.f sspr2.f stbsv.f zhpmv.f ztbmv.f ztpsv.f +) add_library(eigen_blas_static ${EigenBlas_SRCS}) add_library(eigen_blas SHARED ${EigenBlas_SRCS}) diff --git a/blas/cgbmv.f b/blas/cgbmv.f new file mode 100644 index 000000000..2a837dba3 --- /dev/null +++ b/blas/cgbmv.f @@ -0,0 +1,322 @@ + SUBROUTINE CGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER INCX,INCY,KL,KU,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* CGBMV performs one of the matrix-vector operations +* +* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or +* +* y := alpha*conjg( A' )*x + beta*y, +* +* where alpha and beta are scalars, x and y are vectors and A is an +* m by n band matrix, with kl sub-diagonals and ku super-diagonals. +* +* Arguments +* ========== +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +* +* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. +* +* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. +* +* Unchanged on exit. +* +* M - INTEGER. +* On entry, M specifies the number of rows of the matrix A. +* M must be at least zero. +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the number of columns of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* KL - INTEGER. +* On entry, KL specifies the number of sub-diagonals of the +* matrix A. KL must satisfy 0 .le. KL. +* Unchanged on exit. +* +* KU - INTEGER. +* On entry, KU specifies the number of super-diagonals of the +* matrix A. KU must satisfy 0 .le. KU. +* Unchanged on exit. +* +* ALPHA - COMPLEX . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - COMPLEX array of DIMENSION ( LDA, n ). +* Before entry, the leading ( kl + ku + 1 ) by n part of the +* array A must contain the matrix of coefficients, supplied +* column by column, with the leading diagonal of the matrix in +* row ( ku + 1 ) of the array, the first super-diagonal +* starting at position 2 in row ku, the first sub-diagonal +* starting at position 1 in row ( ku + 2 ), and so on. +* Elements in the array A that do not correspond to elements +* in the band matrix (such as the top left ku by ku triangle) +* are not referenced. +* The following program segment will transfer a band matrix +* from conventional full matrix storage to band storage: +* +* DO 20, J = 1, N +* K = KU + 1 - J +* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) +* A( K + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( kl + ku + 1 ). +* Unchanged on exit. +* +* X - COMPLEX array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +* and at least +* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +* Before entry, the incremented array X must contain the +* vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - COMPLEX . +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then Y need not be set on input. +* Unchanged on exit. +* +* Y - COMPLEX array of DIMENSION at least +* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +* and at least +* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +* Before entry, the incremented array Y must contain the +* vector y. On exit, Y is overwritten by the updated vector y. +* +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE + PARAMETER (ONE= (1.0E+0,0.0E+0)) + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP + INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY + LOGICAL NOCONJ +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG,MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 1 + ELSE IF (M.LT.0) THEN + INFO = 2 + ELSE IF (N.LT.0) THEN + INFO = 3 + ELSE IF (KL.LT.0) THEN + INFO = 4 + ELSE IF (KU.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (KL+KU+1)) THEN + INFO = 8 + ELSE IF (INCX.EQ.0) THEN + INFO = 10 + ELSE IF (INCY.EQ.0) THEN + INFO = 13 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CGBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* + NOCONJ = LSAME(TRANS,'T') +* +* Set LENX and LENY, the lengths of the vectors x and y, and set +* up the start points in X and Y. +* + IF (LSAME(TRANS,'N')) THEN + LENX = N + LENY = M + ELSE + LENX = M + LENY = N + END IF + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (LENX-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (LENY-1)*INCY + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through the band part of A. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,LENY + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,LENY + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,LENY + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,LENY + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + KUP1 = KU + 1 + IF (LSAME(TRANS,'N')) THEN +* +* Form y := alpha*A*x + y. +* + JX = KX + IF (INCY.EQ.1) THEN + DO 60 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + K = KUP1 - J + DO 50 I = MAX(1,J-KU),MIN(M,J+KL) + Y(I) = Y(I) + TEMP*A(K+I,J) + 50 CONTINUE + END IF + JX = JX + INCX + 60 CONTINUE + ELSE + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + IY = KY + K = KUP1 - J + DO 70 I = MAX(1,J-KU),MIN(M,J+KL) + Y(IY) = Y(IY) + TEMP*A(K+I,J) + IY = IY + INCY + 70 CONTINUE + END IF + JX = JX + INCX + IF (J.GT.KU) KY = KY + INCY + 80 CONTINUE + END IF + ELSE +* +* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. +* + JY = KY + IF (INCX.EQ.1) THEN + DO 110 J = 1,N + TEMP = ZERO + K = KUP1 - J + IF (NOCONJ) THEN + DO 90 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + A(K+I,J)*X(I) + 90 CONTINUE + ELSE + DO 100 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + CONJG(A(K+I,J))*X(I) + 100 CONTINUE + END IF + Y(JY) = Y(JY) + ALPHA*TEMP + JY = JY + INCY + 110 CONTINUE + ELSE + DO 140 J = 1,N + TEMP = ZERO + IX = KX + K = KUP1 - J + IF (NOCONJ) THEN + DO 120 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + A(K+I,J)*X(IX) + IX = IX + INCX + 120 CONTINUE + ELSE + DO 130 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + CONJG(A(K+I,J))*X(IX) + IX = IX + INCX + 130 CONTINUE + END IF + Y(JY) = Y(JY) + ALPHA*TEMP + JY = JY + INCY + IF (J.GT.KU) KX = KX + INCX + 140 CONTINUE + END IF + END IF +* + RETURN +* +* End of CGBMV . +* + END diff --git a/blas/chbmv.f b/blas/chbmv.f new file mode 100644 index 000000000..1b1c330ea --- /dev/null +++ b/blas/chbmv.f @@ -0,0 +1,310 @@ + SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER INCX,INCY,K,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* CHBMV performs the matrix-vector operation +* +* y := alpha*A*x + beta*y, +* +* where alpha and beta are scalars, x and y are n element vectors and +* A is an n by n hermitian band matrix, with k super-diagonals. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the band matrix A is being supplied as +* follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* being supplied. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* being supplied. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry, K specifies the number of super-diagonals of the +* matrix A. K must satisfy 0 .le. K. +* Unchanged on exit. +* +* ALPHA - COMPLEX . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - COMPLEX array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the hermitian matrix, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer the upper +* triangular part of a hermitian band matrix from conventional +* full matrix storage to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the hermitian matrix, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer the lower +* triangular part of a hermitian band matrix from conventional +* full matrix storage to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that the imaginary parts of the diagonal elements need +* not be set and are assumed to be zero. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - COMPLEX array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the +* vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - COMPLEX . +* On entry, BETA specifies the scalar beta. +* Unchanged on exit. +* +* Y - COMPLEX array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the +* vector y. On exit, Y is overwritten by the updated vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE + PARAMETER (ONE= (1.0E+0,0.0E+0)) + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG,MAX,MIN,REAL +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (K.LT.0) THEN + INFO = 3 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 6 + ELSE IF (INCX.EQ.0) THEN + INFO = 8 + ELSE IF (INCY.EQ.0) THEN + INFO = 11 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CHBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set up the start points in X and Y. +* + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF +* +* Start the operations. In this version the elements of the array A +* are accessed sequentially with one pass through A. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,N + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,N + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,N + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,N + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + IF (LSAME(UPLO,'U')) THEN +* +* Form y when upper triangle of A is stored. +* + KPLUS1 = K + 1 + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + L = KPLUS1 - J + DO 50 I = MAX(1,J-K),J - 1 + Y(I) = Y(I) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(I) + 50 CONTINUE + Y(J) = Y(J) + TEMP1*REAL(A(KPLUS1,J)) + ALPHA*TEMP2 + 60 CONTINUE + ELSE + JX = KX + JY = KY + DO 80 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + IX = KX + IY = KY + L = KPLUS1 - J + DO 70 I = MAX(1,J-K),J - 1 + Y(IY) = Y(IY) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(IX) + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + Y(JY) = Y(JY) + TEMP1*REAL(A(KPLUS1,J)) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + IF (J.GT.K) THEN + KX = KX + INCX + KY = KY + INCY + END IF + 80 CONTINUE + END IF + ELSE +* +* Form y when lower triangle of A is stored. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 100 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + Y(J) = Y(J) + TEMP1*REAL(A(1,J)) + L = 1 - J + DO 90 I = J + 1,MIN(N,J+K) + Y(I) = Y(I) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(I) + 90 CONTINUE + Y(J) = Y(J) + ALPHA*TEMP2 + 100 CONTINUE + ELSE + JX = KX + JY = KY + DO 120 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + Y(JY) = Y(JY) + TEMP1*REAL(A(1,J)) + L = 1 - J + IX = JX + IY = JY + DO 110 I = J + 1,MIN(N,J+K) + IX = IX + INCX + IY = IY + INCY + Y(IY) = Y(IY) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(IX) + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of CHBMV . +* + END diff --git a/blas/chpmv.f b/blas/chpmv.f new file mode 100644 index 000000000..158be5a7b --- /dev/null +++ b/blas/chpmv.f @@ -0,0 +1,272 @@ + SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* CHPMV performs the matrix-vector operation +* +* y := alpha*A*x + beta*y, +* +* where alpha and beta are scalars, x and y are n element vectors and +* A is an n by n hermitian matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - COMPLEX . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* AP - COMPLEX array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. +* Note that the imaginary parts of the diagonal elements need +* not be set and are assumed to be zero. +* Unchanged on exit. +* +* X - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - COMPLEX . +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then Y need not be set on input. +* Unchanged on exit. +* +* Y - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. On exit, Y is overwritten by the updated +* vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE + PARAMETER (ONE= (1.0E+0,0.0E+0)) + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG,REAL +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 6 + ELSE IF (INCY.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CHPMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set up the start points in X and Y. +* + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,N + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,N + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,N + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,N + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form y when AP contains the upper triangle. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + K = KK + DO 50 I = 1,J - 1 + Y(I) = Y(I) + TEMP1*AP(K) + TEMP2 = TEMP2 + CONJG(AP(K))*X(I) + K = K + 1 + 50 CONTINUE + Y(J) = Y(J) + TEMP1*REAL(AP(KK+J-1)) + ALPHA*TEMP2 + KK = KK + J + 60 CONTINUE + ELSE + JX = KX + JY = KY + DO 80 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + IX = KX + IY = KY + DO 70 K = KK,KK + J - 2 + Y(IY) = Y(IY) + TEMP1*AP(K) + TEMP2 = TEMP2 + CONJG(AP(K))*X(IX) + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + Y(JY) = Y(JY) + TEMP1*REAL(AP(KK+J-1)) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + KK = KK + J + 80 CONTINUE + END IF + ELSE +* +* Form y when AP contains the lower triangle. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 100 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + Y(J) = Y(J) + TEMP1*REAL(AP(KK)) + K = KK + 1 + DO 90 I = J + 1,N + Y(I) = Y(I) + TEMP1*AP(K) + TEMP2 = TEMP2 + CONJG(AP(K))*X(I) + K = K + 1 + 90 CONTINUE + Y(J) = Y(J) + ALPHA*TEMP2 + KK = KK + (N-J+1) + 100 CONTINUE + ELSE + JX = KX + JY = KY + DO 120 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + Y(JY) = Y(JY) + TEMP1*REAL(AP(KK)) + IX = JX + IY = JY + DO 110 K = KK + 1,KK + N - J + IX = IX + INCX + IY = IY + INCY + Y(IY) = Y(IY) + TEMP1*AP(K) + TEMP2 = TEMP2 + CONJG(AP(K))*X(IX) + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + KK = KK + (N-J+1) + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of CHPMV . +* + END diff --git a/blas/chpr.f b/blas/chpr.f new file mode 100644 index 000000000..11bd5c6ee --- /dev/null +++ b/blas/chpr.f @@ -0,0 +1,220 @@ + SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP) +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* CHPR performs the hermitian rank 1 operation +* +* A := alpha*x*conjg( x' ) + A, +* +* where alpha is a real scalar, x is an n element vector and A is an +* n by n hermitian matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - REAL . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* AP - COMPLEX array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. On exit, the array +* AP is overwritten by the upper triangular part of the +* updated matrix. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. On exit, the array +* AP is overwritten by the lower triangular part of the +* updated matrix. +* Note that the imaginary parts of the diagonal elements need +* not be set, they are assumed to be zero, and on exit they +* are set to zero. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG,REAL +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CHPR ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN +* +* Set the start point in X if the increment is not unity. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form A when upper triangle is stored in AP. +* + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = ALPHA*CONJG(X(J)) + K = KK + DO 10 I = 1,J - 1 + AP(K) = AP(K) + X(I)*TEMP + K = K + 1 + 10 CONTINUE + AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP) + ELSE + AP(KK+J-1) = REAL(AP(KK+J-1)) + END IF + KK = KK + J + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*CONJG(X(JX)) + IX = KX + DO 30 K = KK,KK + J - 2 + AP(K) = AP(K) + X(IX)*TEMP + IX = IX + INCX + 30 CONTINUE + AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP) + ELSE + AP(KK+J-1) = REAL(AP(KK+J-1)) + END IF + JX = JX + INCX + KK = KK + J + 40 CONTINUE + END IF + ELSE +* +* Form A when lower triangle is stored in AP. +* + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = ALPHA*CONJG(X(J)) + AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(J)) + K = KK + 1 + DO 50 I = J + 1,N + AP(K) = AP(K) + X(I)*TEMP + K = K + 1 + 50 CONTINUE + ELSE + AP(KK) = REAL(AP(KK)) + END IF + KK = KK + N - J + 1 + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*CONJG(X(JX)) + AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(JX)) + IX = JX + DO 70 K = KK + 1,KK + N - J + IX = IX + INCX + AP(K) = AP(K) + X(IX)*TEMP + 70 CONTINUE + ELSE + AP(KK) = REAL(AP(KK)) + END IF + JX = JX + INCX + KK = KK + N - J + 1 + 80 CONTINUE + END IF + END IF +* + RETURN +* +* End of CHPR . +* + END diff --git a/blas/chpr2.f b/blas/chpr2.f new file mode 100644 index 000000000..a0020ef3e --- /dev/null +++ b/blas/chpr2.f @@ -0,0 +1,255 @@ + SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) +* .. Scalar Arguments .. + COMPLEX ALPHA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* CHPR2 performs the hermitian rank 2 operation +* +* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, +* +* where alpha is a scalar, x and y are n element vectors and A is an +* n by n hermitian matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - COMPLEX . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Y - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. +* Unchanged on exit. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* AP - COMPLEX array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. On exit, the array +* AP is overwritten by the upper triangular part of the +* updated matrix. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. On exit, the array +* AP is overwritten by the lower triangular part of the +* updated matrix. +* Note that the imaginary parts of the diagonal elements need +* not be set, they are assumed to be zero, and on exit they +* are set to zero. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG,REAL +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + ELSE IF (INCY.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CHPR2 ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN +* +* Set up the start points in X and Y if the increments are not both +* unity. +* + IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF + JX = KX + JY = KY + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form A when upper triangle is stored in AP. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 20 J = 1,N + IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN + TEMP1 = ALPHA*CONJG(Y(J)) + TEMP2 = CONJG(ALPHA*X(J)) + K = KK + DO 10 I = 1,J - 1 + AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 + K = K + 1 + 10 CONTINUE + AP(KK+J-1) = REAL(AP(KK+J-1)) + + + REAL(X(J)*TEMP1+Y(J)*TEMP2) + ELSE + AP(KK+J-1) = REAL(AP(KK+J-1)) + END IF + KK = KK + J + 20 CONTINUE + ELSE + DO 40 J = 1,N + IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN + TEMP1 = ALPHA*CONJG(Y(JY)) + TEMP2 = CONJG(ALPHA*X(JX)) + IX = KX + IY = KY + DO 30 K = KK,KK + J - 2 + AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 + IX = IX + INCX + IY = IY + INCY + 30 CONTINUE + AP(KK+J-1) = REAL(AP(KK+J-1)) + + + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) + ELSE + AP(KK+J-1) = REAL(AP(KK+J-1)) + END IF + JX = JX + INCX + JY = JY + INCY + KK = KK + J + 40 CONTINUE + END IF + ELSE +* +* Form A when lower triangle is stored in AP. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN + TEMP1 = ALPHA*CONJG(Y(J)) + TEMP2 = CONJG(ALPHA*X(J)) + AP(KK) = REAL(AP(KK)) + + + REAL(X(J)*TEMP1+Y(J)*TEMP2) + K = KK + 1 + DO 50 I = J + 1,N + AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 + K = K + 1 + 50 CONTINUE + ELSE + AP(KK) = REAL(AP(KK)) + END IF + KK = KK + N - J + 1 + 60 CONTINUE + ELSE + DO 80 J = 1,N + IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN + TEMP1 = ALPHA*CONJG(Y(JY)) + TEMP2 = CONJG(ALPHA*X(JX)) + AP(KK) = REAL(AP(KK)) + + + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) + IX = JX + IY = JY + DO 70 K = KK + 1,KK + N - J + IX = IX + INCX + IY = IY + INCY + AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 + 70 CONTINUE + ELSE + AP(KK) = REAL(AP(KK)) + END IF + JX = JX + INCX + JY = JY + INCY + KK = KK + N - J + 1 + 80 CONTINUE + END IF + END IF +* + RETURN +* +* End of CHPR2 . +* + END diff --git a/blas/ctbmv.f b/blas/ctbmv.f new file mode 100644 index 000000000..5a879fa01 --- /dev/null +++ b/blas/ctbmv.f @@ -0,0 +1,366 @@ + SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* CTBMV performs one of the matrix-vector operations +* +* x := A*x, or x := A'*x, or x := conjg( A' )*x, +* +* where x is an n element vector and A is an n by n unit, or non-unit, +* upper or lower triangular band matrix, with ( k + 1 ) diagonals. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' x := A*x. +* +* TRANS = 'T' or 't' x := A'*x. +* +* TRANS = 'C' or 'c' x := conjg( A' )*x. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry with UPLO = 'U' or 'u', K specifies the number of +* super-diagonals of the matrix A. +* On entry with UPLO = 'L' or 'l', K specifies the number of +* sub-diagonals of the matrix A. +* K must satisfy 0 .le. K. +* Unchanged on exit. +* +* A - COMPLEX array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer an upper +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer a lower +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that when DIAG = 'U' or 'u' the elements of the array A +* corresponding to the diagonal elements of the matrix are not +* referenced, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. On exit, X is overwritten with the +* tranformed vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG,MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 7 + ELSE IF (INCX.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CTBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := A*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + L = KPLUS1 - J + DO 10 I = MAX(1,J-K),J - 1 + X(I) = X(I) + TEMP*A(L+I,J) + 10 CONTINUE + IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) + END IF + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + L = KPLUS1 - J + DO 30 I = MAX(1,J-K),J - 1 + X(IX) = X(IX) + TEMP*A(L+I,J) + IX = IX + INCX + 30 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) + END IF + JX = JX + INCX + IF (J.GT.K) KX = KX + INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + L = 1 - J + DO 50 I = MIN(N,J+K),J + 1,-1 + X(I) = X(I) + TEMP*A(L+I,J) + 50 CONTINUE + IF (NOUNIT) X(J) = X(J)*A(1,J) + END IF + 60 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 80 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + L = 1 - J + DO 70 I = MIN(N,J+K),J + 1,-1 + X(IX) = X(IX) + TEMP*A(L+I,J) + IX = IX - INCX + 70 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*A(1,J) + END IF + JX = JX - INCX + IF ((N-J).GE.K) KX = KX - INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := A'*x or x := conjg( A' )*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 110 J = N,1,-1 + TEMP = X(J) + L = KPLUS1 - J + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) + DO 90 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + A(L+I,J)*X(I) + 90 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*CONJG(A(KPLUS1,J)) + DO 100 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + CONJG(A(L+I,J))*X(I) + 100 CONTINUE + END IF + X(J) = TEMP + 110 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 140 J = N,1,-1 + TEMP = X(JX) + KX = KX - INCX + IX = KX + L = KPLUS1 - J + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) + DO 120 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + A(L+I,J)*X(IX) + IX = IX - INCX + 120 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*CONJG(A(KPLUS1,J)) + DO 130 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + CONJG(A(L+I,J))*X(IX) + IX = IX - INCX + 130 CONTINUE + END IF + X(JX) = TEMP + JX = JX - INCX + 140 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 170 J = 1,N + TEMP = X(J) + L = 1 - J + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*A(1,J) + DO 150 I = J + 1,MIN(N,J+K) + TEMP = TEMP + A(L+I,J)*X(I) + 150 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*CONJG(A(1,J)) + DO 160 I = J + 1,MIN(N,J+K) + TEMP = TEMP + CONJG(A(L+I,J))*X(I) + 160 CONTINUE + END IF + X(J) = TEMP + 170 CONTINUE + ELSE + JX = KX + DO 200 J = 1,N + TEMP = X(JX) + KX = KX + INCX + IX = KX + L = 1 - J + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*A(1,J) + DO 180 I = J + 1,MIN(N,J+K) + TEMP = TEMP + A(L+I,J)*X(IX) + IX = IX + INCX + 180 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*CONJG(A(1,J)) + DO 190 I = J + 1,MIN(N,J+K) + TEMP = TEMP + CONJG(A(L+I,J))*X(IX) + IX = IX + INCX + 190 CONTINUE + END IF + X(JX) = TEMP + JX = JX + INCX + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of CTBMV . +* + END diff --git a/blas/ctbsv.f b/blas/ctbsv.f new file mode 100644 index 000000000..853b9d75e --- /dev/null +++ b/blas/ctbsv.f @@ -0,0 +1,370 @@ + SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* CTBSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, or conjg( A' )*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular band matrix, with ( k + 1 ) +* diagonals. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' conjg( A' )*x = b. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry with UPLO = 'U' or 'u', K specifies the number of +* super-diagonals of the matrix A. +* On entry with UPLO = 'L' or 'l', K specifies the number of +* sub-diagonals of the matrix A. +* K must satisfy 0 .le. K. +* Unchanged on exit. +* +* A - COMPLEX array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer an upper +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer a lower +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that when DIAG = 'U' or 'u' the elements of the array A +* corresponding to the diagonal elements of the matrix are not +* referenced, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG,MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 7 + ELSE IF (INCX.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CTBSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed by sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + L = KPLUS1 - J + IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J) + TEMP = X(J) + DO 10 I = J - 1,MAX(1,J-K),-1 + X(I) = X(I) - TEMP*A(L+I,J) + 10 CONTINUE + END IF + 20 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 40 J = N,1,-1 + KX = KX - INCX + IF (X(JX).NE.ZERO) THEN + IX = KX + L = KPLUS1 - J + IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J) + TEMP = X(JX) + DO 30 I = J - 1,MAX(1,J-K),-1 + X(IX) = X(IX) - TEMP*A(L+I,J) + IX = IX - INCX + 30 CONTINUE + END IF + JX = JX - INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + L = 1 - J + IF (NOUNIT) X(J) = X(J)/A(1,J) + TEMP = X(J) + DO 50 I = J + 1,MIN(N,J+K) + X(I) = X(I) - TEMP*A(L+I,J) + 50 CONTINUE + END IF + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + KX = KX + INCX + IF (X(JX).NE.ZERO) THEN + IX = KX + L = 1 - J + IF (NOUNIT) X(JX) = X(JX)/A(1,J) + TEMP = X(JX) + DO 70 I = J + 1,MIN(N,J+K) + X(IX) = X(IX) - TEMP*A(L+I,J) + IX = IX + INCX + 70 CONTINUE + END IF + JX = JX + INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A' )*x or x := inv( conjg( A') )*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 110 J = 1,N + TEMP = X(J) + L = KPLUS1 - J + IF (NOCONJ) THEN + DO 90 I = MAX(1,J-K),J - 1 + TEMP = TEMP - A(L+I,J)*X(I) + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) + ELSE + DO 100 I = MAX(1,J-K),J - 1 + TEMP = TEMP - CONJG(A(L+I,J))*X(I) + 100 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J)) + END IF + X(J) = TEMP + 110 CONTINUE + ELSE + JX = KX + DO 140 J = 1,N + TEMP = X(JX) + IX = KX + L = KPLUS1 - J + IF (NOCONJ) THEN + DO 120 I = MAX(1,J-K),J - 1 + TEMP = TEMP - A(L+I,J)*X(IX) + IX = IX + INCX + 120 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) + ELSE + DO 130 I = MAX(1,J-K),J - 1 + TEMP = TEMP - CONJG(A(L+I,J))*X(IX) + IX = IX + INCX + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J)) + END IF + X(JX) = TEMP + JX = JX + INCX + IF (J.GT.K) KX = KX + INCX + 140 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 170 J = N,1,-1 + TEMP = X(J) + L = 1 - J + IF (NOCONJ) THEN + DO 150 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - A(L+I,J)*X(I) + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(1,J) + ELSE + DO 160 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - CONJG(A(L+I,J))*X(I) + 160 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J)) + END IF + X(J) = TEMP + 170 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 200 J = N,1,-1 + TEMP = X(JX) + IX = KX + L = 1 - J + IF (NOCONJ) THEN + DO 180 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - A(L+I,J)*X(IX) + IX = IX - INCX + 180 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(1,J) + ELSE + DO 190 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - CONJG(A(L+I,J))*X(IX) + IX = IX - INCX + 190 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J)) + END IF + X(JX) = TEMP + JX = JX - INCX + IF ((N-J).GE.K) KX = KX - INCX + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of CTBSV . +* + END diff --git a/blas/ctpmv.f b/blas/ctpmv.f new file mode 100644 index 000000000..b63742ccb --- /dev/null +++ b/blas/ctpmv.f @@ -0,0 +1,329 @@ + SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* CTPMV performs one of the matrix-vector operations +* +* x := A*x, or x := A'*x, or x := conjg( A' )*x, +* +* where x is an n element vector and A is an n by n unit, or non-unit, +* upper or lower triangular matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' x := A*x. +* +* TRANS = 'T' or 't' x := A'*x. +* +* TRANS = 'C' or 'c' x := conjg( A' )*x. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* AP - COMPLEX array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +* respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +* respectively, and so on. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced, but are assumed to be unity. +* Unchanged on exit. +* +* X - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. On exit, X is overwritten with the +* tranformed vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (INCX.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CTPMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of AP are +* accessed sequentially with one pass through AP. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x:= A*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = 1 + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + K = KK + DO 10 I = 1,J - 1 + X(I) = X(I) + TEMP*AP(K) + K = K + 1 + 10 CONTINUE + IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) + END IF + KK = KK + J + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + DO 30 K = KK,KK + J - 2 + X(IX) = X(IX) + TEMP*AP(K) + IX = IX + INCX + 30 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) + END IF + JX = JX + INCX + KK = KK + J + 40 CONTINUE + END IF + ELSE + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 60 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + K = KK + DO 50 I = N,J + 1,-1 + X(I) = X(I) + TEMP*AP(K) + K = K - 1 + 50 CONTINUE + IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) + END IF + KK = KK - (N-J+1) + 60 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 80 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + DO 70 K = KK,KK - (N- (J+1)),-1 + X(IX) = X(IX) + TEMP*AP(K) + IX = IX - INCX + 70 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) + END IF + JX = JX - INCX + KK = KK - (N-J+1) + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := A'*x or x := conjg( A' )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 110 J = N,1,-1 + TEMP = X(J) + K = KK - 1 + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 90 I = J - 1,1,-1 + TEMP = TEMP + AP(K)*X(I) + K = K - 1 + 90 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) + DO 100 I = J - 1,1,-1 + TEMP = TEMP + CONJG(AP(K))*X(I) + K = K - 1 + 100 CONTINUE + END IF + X(J) = TEMP + KK = KK - J + 110 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 140 J = N,1,-1 + TEMP = X(JX) + IX = JX + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 120 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + TEMP = TEMP + AP(K)*X(IX) + 120 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) + DO 130 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + TEMP = TEMP + CONJG(AP(K))*X(IX) + 130 CONTINUE + END IF + X(JX) = TEMP + JX = JX - INCX + KK = KK - J + 140 CONTINUE + END IF + ELSE + KK = 1 + IF (INCX.EQ.1) THEN + DO 170 J = 1,N + TEMP = X(J) + K = KK + 1 + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 150 I = J + 1,N + TEMP = TEMP + AP(K)*X(I) + K = K + 1 + 150 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) + DO 160 I = J + 1,N + TEMP = TEMP + CONJG(AP(K))*X(I) + K = K + 1 + 160 CONTINUE + END IF + X(J) = TEMP + KK = KK + (N-J+1) + 170 CONTINUE + ELSE + JX = KX + DO 200 J = 1,N + TEMP = X(JX) + IX = JX + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 180 K = KK + 1,KK + N - J + IX = IX + INCX + TEMP = TEMP + AP(K)*X(IX) + 180 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) + DO 190 K = KK + 1,KK + N - J + IX = IX + INCX + TEMP = TEMP + CONJG(AP(K))*X(IX) + 190 CONTINUE + END IF + X(JX) = TEMP + JX = JX + INCX + KK = KK + (N-J+1) + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of CTPMV . +* + END diff --git a/blas/ctpsv.f b/blas/ctpsv.f new file mode 100644 index 000000000..1804797ea --- /dev/null +++ b/blas/ctpsv.f @@ -0,0 +1,332 @@ + SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* CTPSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, or conjg( A' )*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular matrix, supplied in packed form. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' conjg( A' )*x = b. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* AP - COMPLEX array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +* respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +* respectively, and so on. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced, but are assumed to be unity. +* Unchanged on exit. +* +* X - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (INCX.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CTPSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of AP are +* accessed sequentially with one pass through AP. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/AP(KK) + TEMP = X(J) + K = KK - 1 + DO 10 I = J - 1,1,-1 + X(I) = X(I) - TEMP*AP(K) + K = K - 1 + 10 CONTINUE + END IF + KK = KK - J + 20 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 40 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/AP(KK) + TEMP = X(JX) + IX = JX + DO 30 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + X(IX) = X(IX) - TEMP*AP(K) + 30 CONTINUE + END IF + JX = JX - INCX + KK = KK - J + 40 CONTINUE + END IF + ELSE + KK = 1 + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/AP(KK) + TEMP = X(J) + K = KK + 1 + DO 50 I = J + 1,N + X(I) = X(I) - TEMP*AP(K) + K = K + 1 + 50 CONTINUE + END IF + KK = KK + (N-J+1) + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/AP(KK) + TEMP = X(JX) + IX = JX + DO 70 K = KK + 1,KK + N - J + IX = IX + INCX + X(IX) = X(IX) - TEMP*AP(K) + 70 CONTINUE + END IF + JX = JX + INCX + KK = KK + (N-J+1) + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = 1 + IF (INCX.EQ.1) THEN + DO 110 J = 1,N + TEMP = X(J) + K = KK + IF (NOCONJ) THEN + DO 90 I = 1,J - 1 + TEMP = TEMP - AP(K)*X(I) + K = K + 1 + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) + ELSE + DO 100 I = 1,J - 1 + TEMP = TEMP - CONJG(AP(K))*X(I) + K = K + 1 + 100 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) + END IF + X(J) = TEMP + KK = KK + J + 110 CONTINUE + ELSE + JX = KX + DO 140 J = 1,N + TEMP = X(JX) + IX = KX + IF (NOCONJ) THEN + DO 120 K = KK,KK + J - 2 + TEMP = TEMP - AP(K)*X(IX) + IX = IX + INCX + 120 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) + ELSE + DO 130 K = KK,KK + J - 2 + TEMP = TEMP - CONJG(AP(K))*X(IX) + IX = IX + INCX + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) + END IF + X(JX) = TEMP + JX = JX + INCX + KK = KK + J + 140 CONTINUE + END IF + ELSE + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 170 J = N,1,-1 + TEMP = X(J) + K = KK + IF (NOCONJ) THEN + DO 150 I = N,J + 1,-1 + TEMP = TEMP - AP(K)*X(I) + K = K - 1 + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) + ELSE + DO 160 I = N,J + 1,-1 + TEMP = TEMP - CONJG(AP(K))*X(I) + K = K - 1 + 160 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) + END IF + X(J) = TEMP + KK = KK - (N-J+1) + 170 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 200 J = N,1,-1 + TEMP = X(JX) + IX = KX + IF (NOCONJ) THEN + DO 180 K = KK,KK - (N- (J+1)),-1 + TEMP = TEMP - AP(K)*X(IX) + IX = IX - INCX + 180 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) + ELSE + DO 190 K = KK,KK - (N- (J+1)),-1 + TEMP = TEMP - CONJG(AP(K))*X(IX) + IX = IX - INCX + 190 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) + END IF + X(JX) = TEMP + JX = JX - INCX + KK = KK - (N-J+1) + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of CTPSV . +* + END diff --git a/blas/dgbmv.f b/blas/dgbmv.f new file mode 100644 index 000000000..c3dc64aa3 --- /dev/null +++ b/blas/dgbmv.f @@ -0,0 +1,301 @@ + SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER INCX,INCY,KL,KU,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* DGBMV performs one of the matrix-vector operations +* +* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, +* +* where alpha and beta are scalars, x and y are vectors and A is an +* m by n band matrix, with kl sub-diagonals and ku super-diagonals. +* +* Arguments +* ========== +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +* +* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. +* +* TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. +* +* Unchanged on exit. +* +* M - INTEGER. +* On entry, M specifies the number of rows of the matrix A. +* M must be at least zero. +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the number of columns of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* KL - INTEGER. +* On entry, KL specifies the number of sub-diagonals of the +* matrix A. KL must satisfy 0 .le. KL. +* Unchanged on exit. +* +* KU - INTEGER. +* On entry, KU specifies the number of super-diagonals of the +* matrix A. KU must satisfy 0 .le. KU. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). +* Before entry, the leading ( kl + ku + 1 ) by n part of the +* array A must contain the matrix of coefficients, supplied +* column by column, with the leading diagonal of the matrix in +* row ( ku + 1 ) of the array, the first super-diagonal +* starting at position 2 in row ku, the first sub-diagonal +* starting at position 1 in row ( ku + 2 ), and so on. +* Elements in the array A that do not correspond to elements +* in the band matrix (such as the top left ku by ku triangle) +* are not referenced. +* The following program segment will transfer a band matrix +* from conventional full matrix storage to band storage: +* +* DO 20, J = 1, N +* K = KU + 1 - J +* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) +* A( K + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( kl + ku + 1 ). +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +* and at least +* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +* Before entry, the incremented array X must contain the +* vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - DOUBLE PRECISION. +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then Y need not be set on input. +* Unchanged on exit. +* +* Y - DOUBLE PRECISION array of DIMENSION at least +* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +* and at least +* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +* Before entry, the incremented array Y must contain the +* vector y. On exit, Y is overwritten by the updated vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE,ZERO + PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 1 + ELSE IF (M.LT.0) THEN + INFO = 2 + ELSE IF (N.LT.0) THEN + INFO = 3 + ELSE IF (KL.LT.0) THEN + INFO = 4 + ELSE IF (KU.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (KL+KU+1)) THEN + INFO = 8 + ELSE IF (INCX.EQ.0) THEN + INFO = 10 + ELSE IF (INCY.EQ.0) THEN + INFO = 13 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DGBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set LENX and LENY, the lengths of the vectors x and y, and set +* up the start points in X and Y. +* + IF (LSAME(TRANS,'N')) THEN + LENX = N + LENY = M + ELSE + LENX = M + LENY = N + END IF + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (LENX-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (LENY-1)*INCY + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through the band part of A. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,LENY + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,LENY + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,LENY + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,LENY + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + KUP1 = KU + 1 + IF (LSAME(TRANS,'N')) THEN +* +* Form y := alpha*A*x + y. +* + JX = KX + IF (INCY.EQ.1) THEN + DO 60 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + K = KUP1 - J + DO 50 I = MAX(1,J-KU),MIN(M,J+KL) + Y(I) = Y(I) + TEMP*A(K+I,J) + 50 CONTINUE + END IF + JX = JX + INCX + 60 CONTINUE + ELSE + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + IY = KY + K = KUP1 - J + DO 70 I = MAX(1,J-KU),MIN(M,J+KL) + Y(IY) = Y(IY) + TEMP*A(K+I,J) + IY = IY + INCY + 70 CONTINUE + END IF + JX = JX + INCX + IF (J.GT.KU) KY = KY + INCY + 80 CONTINUE + END IF + ELSE +* +* Form y := alpha*A'*x + y. +* + JY = KY + IF (INCX.EQ.1) THEN + DO 100 J = 1,N + TEMP = ZERO + K = KUP1 - J + DO 90 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + A(K+I,J)*X(I) + 90 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP + JY = JY + INCY + 100 CONTINUE + ELSE + DO 120 J = 1,N + TEMP = ZERO + IX = KX + K = KUP1 - J + DO 110 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + A(K+I,J)*X(IX) + IX = IX + INCX + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP + JY = JY + INCY + IF (J.GT.KU) KX = KX + INCX + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of DGBMV . +* + END diff --git a/blas/drotm.f b/blas/drotm.f new file mode 100644 index 000000000..63a3b1134 --- /dev/null +++ b/blas/drotm.f @@ -0,0 +1,147 @@ + SUBROUTINE DROTM(N,DX,INCX,DY,INCY,DPARAM) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DPARAM(5),DX(*),DY(*) +* .. +* +* Purpose +* ======= +* +* APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX +* +* (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN +* (DY**T) +* +* DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE +* LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY. +* WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +* +* DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 +* +* (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) +* H=( ) ( ) ( ) ( ) +* (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). +* SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM. +* +* Arguments +* ========= +* +* N (input) INTEGER +* number of elements in input vector(s) +* +* DX (input/output) DOUBLE PRECISION array, dimension N +* double precision vector with N elements +* +* INCX (input) INTEGER +* storage spacing between elements of DX +* +* DY (input/output) DOUBLE PRECISION array, dimension N +* double precision vector with N elements +* +* INCY (input) INTEGER +* storage spacing between elements of DY +* +* DPARAM (input/output) DOUBLE PRECISION array, dimension 5 +* DPARAM(1)=DFLAG +* DPARAM(2)=DH11 +* DPARAM(3)=DH21 +* DPARAM(4)=DH12 +* DPARAM(5)=DH22 +* +* ===================================================================== +* +* .. Local Scalars .. + DOUBLE PRECISION DFLAG,DH11,DH12,DH21,DH22,TWO,W,Z,ZERO + INTEGER I,KX,KY,NSTEPS +* .. +* .. Data statements .. + DATA ZERO,TWO/0.D0,2.D0/ +* .. +* + DFLAG = DPARAM(1) + IF (N.LE.0 .OR. (DFLAG+TWO.EQ.ZERO)) GO TO 140 + IF (.NOT. (INCX.EQ.INCY.AND.INCX.GT.0)) GO TO 70 +* + NSTEPS = N*INCX + IF (DFLAG) 50,10,30 + 10 CONTINUE + DH12 = DPARAM(4) + DH21 = DPARAM(3) + DO 20 I = 1,NSTEPS,INCX + W = DX(I) + Z = DY(I) + DX(I) = W + Z*DH12 + DY(I) = W*DH21 + Z + 20 CONTINUE + GO TO 140 + 30 CONTINUE + DH11 = DPARAM(2) + DH22 = DPARAM(5) + DO 40 I = 1,NSTEPS,INCX + W = DX(I) + Z = DY(I) + DX(I) = W*DH11 + Z + DY(I) = -W + DH22*Z + 40 CONTINUE + GO TO 140 + 50 CONTINUE + DH11 = DPARAM(2) + DH12 = DPARAM(4) + DH21 = DPARAM(3) + DH22 = DPARAM(5) + DO 60 I = 1,NSTEPS,INCX + W = DX(I) + Z = DY(I) + DX(I) = W*DH11 + Z*DH12 + DY(I) = W*DH21 + Z*DH22 + 60 CONTINUE + GO TO 140 + 70 CONTINUE + KX = 1 + KY = 1 + IF (INCX.LT.0) KX = 1 + (1-N)*INCX + IF (INCY.LT.0) KY = 1 + (1-N)*INCY +* + IF (DFLAG) 120,80,100 + 80 CONTINUE + DH12 = DPARAM(4) + DH21 = DPARAM(3) + DO 90 I = 1,N + W = DX(KX) + Z = DY(KY) + DX(KX) = W + Z*DH12 + DY(KY) = W*DH21 + Z + KX = KX + INCX + KY = KY + INCY + 90 CONTINUE + GO TO 140 + 100 CONTINUE + DH11 = DPARAM(2) + DH22 = DPARAM(5) + DO 110 I = 1,N + W = DX(KX) + Z = DY(KY) + DX(KX) = W*DH11 + Z + DY(KY) = -W + DH22*Z + KX = KX + INCX + KY = KY + INCY + 110 CONTINUE + GO TO 140 + 120 CONTINUE + DH11 = DPARAM(2) + DH12 = DPARAM(4) + DH21 = DPARAM(3) + DH22 = DPARAM(5) + DO 130 I = 1,N + W = DX(KX) + Z = DY(KY) + DX(KX) = W*DH11 + Z*DH12 + DY(KY) = W*DH21 + Z*DH22 + KX = KX + INCX + KY = KY + INCY + 130 CONTINUE + 140 CONTINUE + RETURN + END diff --git a/blas/drotmg.f b/blas/drotmg.f new file mode 100644 index 000000000..3ae647b08 --- /dev/null +++ b/blas/drotmg.f @@ -0,0 +1,206 @@ + SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM) +* .. Scalar Arguments .. + DOUBLE PRECISION DD1,DD2,DX1,DY1 +* .. +* .. Array Arguments .. + DOUBLE PRECISION DPARAM(5) +* .. +* +* Purpose +* ======= +* +* CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS +* THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)* +* DY2)**T. +* WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +* +* DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 +* +* (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) +* H=( ) ( ) ( ) ( ) +* (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). +* LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22 +* RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE +* VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.) +* +* THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE +* INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE +* OF DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. +* +* +* Arguments +* ========= +* +* DD1 (input/output) DOUBLE PRECISION +* +* DD2 (input/output) DOUBLE PRECISION +* +* DX1 (input/output) DOUBLE PRECISION +* +* DY1 (input) DOUBLE PRECISION +* +* DPARAM (input/output) DOUBLE PRECISION array, dimension 5 +* DPARAM(1)=DFLAG +* DPARAM(2)=DH11 +* DPARAM(3)=DH21 +* DPARAM(4)=DH12 +* DPARAM(5)=DH22 +* +* ===================================================================== +* +* .. Local Scalars .. + DOUBLE PRECISION DFLAG,DH11,DH12,DH21,DH22,DP1,DP2,DQ1,DQ2,DTEMP, + + DU,GAM,GAMSQ,ONE,RGAMSQ,TWO,ZERO + INTEGER IGO +* .. +* .. Intrinsic Functions .. + INTRINSIC DABS +* .. +* .. Data statements .. +* + DATA ZERO,ONE,TWO/0.D0,1.D0,2.D0/ + DATA GAM,GAMSQ,RGAMSQ/4096.D0,16777216.D0,5.9604645D-8/ +* .. + + IF (.NOT.DD1.LT.ZERO) GO TO 10 +* GO ZERO-H-D-AND-DX1.. + GO TO 60 + 10 CONTINUE +* CASE-DD1-NONNEGATIVE + DP2 = DD2*DY1 + IF (.NOT.DP2.EQ.ZERO) GO TO 20 + DFLAG = -TWO + GO TO 260 +* REGULAR-CASE.. + 20 CONTINUE + DP1 = DD1*DX1 + DQ2 = DP2*DY1 + DQ1 = DP1*DX1 +* + IF (.NOT.DABS(DQ1).GT.DABS(DQ2)) GO TO 40 + DH21 = -DY1/DX1 + DH12 = DP2/DP1 +* + DU = ONE - DH12*DH21 +* + IF (.NOT.DU.LE.ZERO) GO TO 30 +* GO ZERO-H-D-AND-DX1.. + GO TO 60 + 30 CONTINUE + DFLAG = ZERO + DD1 = DD1/DU + DD2 = DD2/DU + DX1 = DX1*DU +* GO SCALE-CHECK.. + GO TO 100 + 40 CONTINUE + IF (.NOT.DQ2.LT.ZERO) GO TO 50 +* GO ZERO-H-D-AND-DX1.. + GO TO 60 + 50 CONTINUE + DFLAG = ONE + DH11 = DP1/DP2 + DH22 = DX1/DY1 + DU = ONE + DH11*DH22 + DTEMP = DD2/DU + DD2 = DD1/DU + DD1 = DTEMP + DX1 = DY1*DU +* GO SCALE-CHECK + GO TO 100 +* PROCEDURE..ZERO-H-D-AND-DX1.. + 60 CONTINUE + DFLAG = -ONE + DH11 = ZERO + DH12 = ZERO + DH21 = ZERO + DH22 = ZERO +* + DD1 = ZERO + DD2 = ZERO + DX1 = ZERO +* RETURN.. + GO TO 220 +* PROCEDURE..FIX-H.. + 70 CONTINUE + IF (.NOT.DFLAG.GE.ZERO) GO TO 90 +* + IF (.NOT.DFLAG.EQ.ZERO) GO TO 80 + DH11 = ONE + DH22 = ONE + DFLAG = -ONE + GO TO 90 + 80 CONTINUE + DH21 = -ONE + DH12 = ONE + DFLAG = -ONE + 90 CONTINUE + GO TO IGO(120,150,180,210) +* PROCEDURE..SCALE-CHECK + 100 CONTINUE + 110 CONTINUE + IF (.NOT.DD1.LE.RGAMSQ) GO TO 130 + IF (DD1.EQ.ZERO) GO TO 160 + ASSIGN 120 TO IGO +* FIX-H.. + GO TO 70 + 120 CONTINUE + DD1 = DD1*GAM**2 + DX1 = DX1/GAM + DH11 = DH11/GAM + DH12 = DH12/GAM + GO TO 110 + 130 CONTINUE + 140 CONTINUE + IF (.NOT.DD1.GE.GAMSQ) GO TO 160 + ASSIGN 150 TO IGO +* FIX-H.. + GO TO 70 + 150 CONTINUE + DD1 = DD1/GAM**2 + DX1 = DX1*GAM + DH11 = DH11*GAM + DH12 = DH12*GAM + GO TO 140 + 160 CONTINUE + 170 CONTINUE + IF (.NOT.DABS(DD2).LE.RGAMSQ) GO TO 190 + IF (DD2.EQ.ZERO) GO TO 220 + ASSIGN 180 TO IGO +* FIX-H.. + GO TO 70 + 180 CONTINUE + DD2 = DD2*GAM**2 + DH21 = DH21/GAM + DH22 = DH22/GAM + GO TO 170 + 190 CONTINUE + 200 CONTINUE + IF (.NOT.DABS(DD2).GE.GAMSQ) GO TO 220 + ASSIGN 210 TO IGO +* FIX-H.. + GO TO 70 + 210 CONTINUE + DD2 = DD2/GAM**2 + DH21 = DH21*GAM + DH22 = DH22*GAM + GO TO 200 + 220 CONTINUE + IF (DFLAG) 250,230,240 + 230 CONTINUE + DPARAM(3) = DH21 + DPARAM(4) = DH12 + GO TO 260 + 240 CONTINUE + DPARAM(2) = DH11 + DPARAM(5) = DH22 + GO TO 260 + 250 CONTINUE + DPARAM(2) = DH11 + DPARAM(3) = DH21 + DPARAM(4) = DH12 + DPARAM(5) = DH22 + 260 CONTINUE + DPARAM(1) = DFLAG + RETURN + END diff --git a/blas/dsbmv.f b/blas/dsbmv.f new file mode 100644 index 000000000..8c82d1fa1 --- /dev/null +++ b/blas/dsbmv.f @@ -0,0 +1,304 @@ + SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER INCX,INCY,K,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* DSBMV performs the matrix-vector operation +* +* y := alpha*A*x + beta*y, +* +* where alpha and beta are scalars, x and y are n element vectors and +* A is an n by n symmetric band matrix, with k super-diagonals. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the band matrix A is being supplied as +* follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* being supplied. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* being supplied. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry, K specifies the number of super-diagonals of the +* matrix A. K must satisfy 0 .le. K. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the symmetric matrix, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer the upper +* triangular part of a symmetric band matrix from conventional +* full matrix storage to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the symmetric matrix, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer the lower +* triangular part of a symmetric band matrix from conventional +* full matrix storage to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the +* vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - DOUBLE PRECISION. +* On entry, BETA specifies the scalar beta. +* Unchanged on exit. +* +* Y - DOUBLE PRECISION array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the +* vector y. On exit, Y is overwritten by the updated vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE,ZERO + PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (K.LT.0) THEN + INFO = 3 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 6 + ELSE IF (INCX.EQ.0) THEN + INFO = 8 + ELSE IF (INCY.EQ.0) THEN + INFO = 11 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DSBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set up the start points in X and Y. +* + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF +* +* Start the operations. In this version the elements of the array A +* are accessed sequentially with one pass through A. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,N + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,N + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,N + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,N + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + IF (LSAME(UPLO,'U')) THEN +* +* Form y when upper triangle of A is stored. +* + KPLUS1 = K + 1 + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + L = KPLUS1 - J + DO 50 I = MAX(1,J-K),J - 1 + Y(I) = Y(I) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + A(L+I,J)*X(I) + 50 CONTINUE + Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 + 60 CONTINUE + ELSE + JX = KX + JY = KY + DO 80 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + IX = KX + IY = KY + L = KPLUS1 - J + DO 70 I = MAX(1,J-K),J - 1 + Y(IY) = Y(IY) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + A(L+I,J)*X(IX) + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + IF (J.GT.K) THEN + KX = KX + INCX + KY = KY + INCY + END IF + 80 CONTINUE + END IF + ELSE +* +* Form y when lower triangle of A is stored. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 100 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + Y(J) = Y(J) + TEMP1*A(1,J) + L = 1 - J + DO 90 I = J + 1,MIN(N,J+K) + Y(I) = Y(I) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + A(L+I,J)*X(I) + 90 CONTINUE + Y(J) = Y(J) + ALPHA*TEMP2 + 100 CONTINUE + ELSE + JX = KX + JY = KY + DO 120 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + Y(JY) = Y(JY) + TEMP1*A(1,J) + L = 1 - J + IX = JX + IY = JY + DO 110 I = J + 1,MIN(N,J+K) + IX = IX + INCX + IY = IY + INCY + Y(IY) = Y(IY) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + A(L+I,J)*X(IX) + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of DSBMV . +* + END diff --git a/blas/dspmv.f b/blas/dspmv.f new file mode 100644 index 000000000..f6e121e76 --- /dev/null +++ b/blas/dspmv.f @@ -0,0 +1,265 @@ + SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* DSPMV performs the matrix-vector operation +* +* y := alpha*A*x + beta*y, +* +* where alpha and beta are scalars, x and y are n element vectors and +* A is an n by n symmetric matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* AP - DOUBLE PRECISION array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - DOUBLE PRECISION. +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then Y need not be set on input. +* Unchanged on exit. +* +* Y - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. On exit, Y is overwritten by the updated +* vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE,ZERO + PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 6 + ELSE IF (INCY.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DSPMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set up the start points in X and Y. +* + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,N + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,N + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,N + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,N + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form y when AP contains the upper triangle. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + K = KK + DO 50 I = 1,J - 1 + Y(I) = Y(I) + TEMP1*AP(K) + TEMP2 = TEMP2 + AP(K)*X(I) + K = K + 1 + 50 CONTINUE + Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 + KK = KK + J + 60 CONTINUE + ELSE + JX = KX + JY = KY + DO 80 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + IX = KX + IY = KY + DO 70 K = KK,KK + J - 2 + Y(IY) = Y(IY) + TEMP1*AP(K) + TEMP2 = TEMP2 + AP(K)*X(IX) + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + KK = KK + J + 80 CONTINUE + END IF + ELSE +* +* Form y when AP contains the lower triangle. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 100 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + Y(J) = Y(J) + TEMP1*AP(KK) + K = KK + 1 + DO 90 I = J + 1,N + Y(I) = Y(I) + TEMP1*AP(K) + TEMP2 = TEMP2 + AP(K)*X(I) + K = K + 1 + 90 CONTINUE + Y(J) = Y(J) + ALPHA*TEMP2 + KK = KK + (N-J+1) + 100 CONTINUE + ELSE + JX = KX + JY = KY + DO 120 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + Y(JY) = Y(JY) + TEMP1*AP(KK) + IX = JX + IY = JY + DO 110 K = KK + 1,KK + N - J + IX = IX + INCX + IY = IY + INCY + Y(IY) = Y(IY) + TEMP1*AP(K) + TEMP2 = TEMP2 + AP(K)*X(IX) + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + KK = KK + (N-J+1) + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of DSPMV . +* + END diff --git a/blas/dspr.f b/blas/dspr.f new file mode 100644 index 000000000..538e4f76b --- /dev/null +++ b/blas/dspr.f @@ -0,0 +1,202 @@ + SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* DSPR performs the symmetric rank 1 operation +* +* A := alpha*x*x' + A, +* +* where alpha is a real scalar, x is an n element vector and A is an +* n by n symmetric matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* AP - DOUBLE PRECISION array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. On exit, the array +* AP is overwritten by the upper triangular part of the +* updated matrix. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. On exit, the array +* AP is overwritten by the lower triangular part of the +* updated matrix. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER (ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DSPR ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN +* +* Set the start point in X if the increment is not unity. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form A when upper triangle is stored in AP. +* + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = ALPHA*X(J) + K = KK + DO 10 I = 1,J + AP(K) = AP(K) + X(I)*TEMP + K = K + 1 + 10 CONTINUE + END IF + KK = KK + J + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + IX = KX + DO 30 K = KK,KK + J - 1 + AP(K) = AP(K) + X(IX)*TEMP + IX = IX + INCX + 30 CONTINUE + END IF + JX = JX + INCX + KK = KK + J + 40 CONTINUE + END IF + ELSE +* +* Form A when lower triangle is stored in AP. +* + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = ALPHA*X(J) + K = KK + DO 50 I = J,N + AP(K) = AP(K) + X(I)*TEMP + K = K + 1 + 50 CONTINUE + END IF + KK = KK + N - J + 1 + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + IX = JX + DO 70 K = KK,KK + N - J + AP(K) = AP(K) + X(IX)*TEMP + IX = IX + INCX + 70 CONTINUE + END IF + JX = JX + INCX + KK = KK + N - J + 1 + 80 CONTINUE + END IF + END IF +* + RETURN +* +* End of DSPR . +* + END diff --git a/blas/dspr2.f b/blas/dspr2.f new file mode 100644 index 000000000..6f6b54a8c --- /dev/null +++ b/blas/dspr2.f @@ -0,0 +1,233 @@ + SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* DSPR2 performs the symmetric rank 2 operation +* +* A := alpha*x*y' + alpha*y*x' + A, +* +* where alpha is a scalar, x and y are n element vectors and A is an +* n by n symmetric matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Y - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. +* Unchanged on exit. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* AP - DOUBLE PRECISION array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. On exit, the array +* AP is overwritten by the upper triangular part of the +* updated matrix. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. On exit, the array +* AP is overwritten by the lower triangular part of the +* updated matrix. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER (ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + ELSE IF (INCY.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DSPR2 ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN +* +* Set up the start points in X and Y if the increments are not both +* unity. +* + IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF + JX = KX + JY = KY + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form A when upper triangle is stored in AP. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 20 J = 1,N + IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN + TEMP1 = ALPHA*Y(J) + TEMP2 = ALPHA*X(J) + K = KK + DO 10 I = 1,J + AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 + K = K + 1 + 10 CONTINUE + END IF + KK = KK + J + 20 CONTINUE + ELSE + DO 40 J = 1,N + IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN + TEMP1 = ALPHA*Y(JY) + TEMP2 = ALPHA*X(JX) + IX = KX + IY = KY + DO 30 K = KK,KK + J - 1 + AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 + IX = IX + INCX + IY = IY + INCY + 30 CONTINUE + END IF + JX = JX + INCX + JY = JY + INCY + KK = KK + J + 40 CONTINUE + END IF + ELSE +* +* Form A when lower triangle is stored in AP. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN + TEMP1 = ALPHA*Y(J) + TEMP2 = ALPHA*X(J) + K = KK + DO 50 I = J,N + AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 + K = K + 1 + 50 CONTINUE + END IF + KK = KK + N - J + 1 + 60 CONTINUE + ELSE + DO 80 J = 1,N + IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN + TEMP1 = ALPHA*Y(JY) + TEMP2 = ALPHA*X(JX) + IX = JX + IY = JY + DO 70 K = KK,KK + N - J + AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + END IF + JX = JX + INCX + JY = JY + INCY + KK = KK + N - J + 1 + 80 CONTINUE + END IF + END IF +* + RETURN +* +* End of DSPR2 . +* + END diff --git a/blas/dtbmv.f b/blas/dtbmv.f new file mode 100644 index 000000000..a87ffdeae --- /dev/null +++ b/blas/dtbmv.f @@ -0,0 +1,335 @@ + SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* DTBMV performs one of the matrix-vector operations +* +* x := A*x, or x := A'*x, +* +* where x is an n element vector and A is an n by n unit, or non-unit, +* upper or lower triangular band matrix, with ( k + 1 ) diagonals. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' x := A*x. +* +* TRANS = 'T' or 't' x := A'*x. +* +* TRANS = 'C' or 'c' x := A'*x. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry with UPLO = 'U' or 'u', K specifies the number of +* super-diagonals of the matrix A. +* On entry with UPLO = 'L' or 'l', K specifies the number of +* sub-diagonals of the matrix A. +* K must satisfy 0 .le. K. +* Unchanged on exit. +* +* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer an upper +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer a lower +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that when DIAG = 'U' or 'u' the elements of the array A +* corresponding to the diagonal elements of the matrix are not +* referenced, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. On exit, X is overwritten with the +* tranformed vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER (ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L + LOGICAL NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 7 + ELSE IF (INCX.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DTBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := A*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + L = KPLUS1 - J + DO 10 I = MAX(1,J-K),J - 1 + X(I) = X(I) + TEMP*A(L+I,J) + 10 CONTINUE + IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) + END IF + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + L = KPLUS1 - J + DO 30 I = MAX(1,J-K),J - 1 + X(IX) = X(IX) + TEMP*A(L+I,J) + IX = IX + INCX + 30 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) + END IF + JX = JX + INCX + IF (J.GT.K) KX = KX + INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + L = 1 - J + DO 50 I = MIN(N,J+K),J + 1,-1 + X(I) = X(I) + TEMP*A(L+I,J) + 50 CONTINUE + IF (NOUNIT) X(J) = X(J)*A(1,J) + END IF + 60 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 80 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + L = 1 - J + DO 70 I = MIN(N,J+K),J + 1,-1 + X(IX) = X(IX) + TEMP*A(L+I,J) + IX = IX - INCX + 70 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*A(1,J) + END IF + JX = JX - INCX + IF ((N-J).GE.K) KX = KX - INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := A'*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 100 J = N,1,-1 + TEMP = X(J) + L = KPLUS1 - J + IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) + DO 90 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + A(L+I,J)*X(I) + 90 CONTINUE + X(J) = TEMP + 100 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 120 J = N,1,-1 + TEMP = X(JX) + KX = KX - INCX + IX = KX + L = KPLUS1 - J + IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) + DO 110 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + A(L+I,J)*X(IX) + IX = IX - INCX + 110 CONTINUE + X(JX) = TEMP + JX = JX - INCX + 120 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 140 J = 1,N + TEMP = X(J) + L = 1 - J + IF (NOUNIT) TEMP = TEMP*A(1,J) + DO 130 I = J + 1,MIN(N,J+K) + TEMP = TEMP + A(L+I,J)*X(I) + 130 CONTINUE + X(J) = TEMP + 140 CONTINUE + ELSE + JX = KX + DO 160 J = 1,N + TEMP = X(JX) + KX = KX + INCX + IX = KX + L = 1 - J + IF (NOUNIT) TEMP = TEMP*A(1,J) + DO 150 I = J + 1,MIN(N,J+K) + TEMP = TEMP + A(L+I,J)*X(IX) + IX = IX + INCX + 150 CONTINUE + X(JX) = TEMP + JX = JX + INCX + 160 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of DTBMV . +* + END diff --git a/blas/dtbsv.f b/blas/dtbsv.f new file mode 100644 index 000000000..cfeb0b82b --- /dev/null +++ b/blas/dtbsv.f @@ -0,0 +1,339 @@ + SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* DTBSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular band matrix, with ( k + 1 ) +* diagonals. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' A'*x = b. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry with UPLO = 'U' or 'u', K specifies the number of +* super-diagonals of the matrix A. +* On entry with UPLO = 'L' or 'l', K specifies the number of +* sub-diagonals of the matrix A. +* K must satisfy 0 .le. K. +* Unchanged on exit. +* +* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer an upper +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer a lower +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that when DIAG = 'U' or 'u' the elements of the array A +* corresponding to the diagonal elements of the matrix are not +* referenced, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER (ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L + LOGICAL NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 7 + ELSE IF (INCX.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DTBSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed by sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + L = KPLUS1 - J + IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J) + TEMP = X(J) + DO 10 I = J - 1,MAX(1,J-K),-1 + X(I) = X(I) - TEMP*A(L+I,J) + 10 CONTINUE + END IF + 20 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 40 J = N,1,-1 + KX = KX - INCX + IF (X(JX).NE.ZERO) THEN + IX = KX + L = KPLUS1 - J + IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J) + TEMP = X(JX) + DO 30 I = J - 1,MAX(1,J-K),-1 + X(IX) = X(IX) - TEMP*A(L+I,J) + IX = IX - INCX + 30 CONTINUE + END IF + JX = JX - INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + L = 1 - J + IF (NOUNIT) X(J) = X(J)/A(1,J) + TEMP = X(J) + DO 50 I = J + 1,MIN(N,J+K) + X(I) = X(I) - TEMP*A(L+I,J) + 50 CONTINUE + END IF + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + KX = KX + INCX + IF (X(JX).NE.ZERO) THEN + IX = KX + L = 1 - J + IF (NOUNIT) X(JX) = X(JX)/A(1,J) + TEMP = X(JX) + DO 70 I = J + 1,MIN(N,J+K) + X(IX) = X(IX) - TEMP*A(L+I,J) + IX = IX + INCX + 70 CONTINUE + END IF + JX = JX + INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A')*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 100 J = 1,N + TEMP = X(J) + L = KPLUS1 - J + DO 90 I = MAX(1,J-K),J - 1 + TEMP = TEMP - A(L+I,J)*X(I) + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) + X(J) = TEMP + 100 CONTINUE + ELSE + JX = KX + DO 120 J = 1,N + TEMP = X(JX) + IX = KX + L = KPLUS1 - J + DO 110 I = MAX(1,J-K),J - 1 + TEMP = TEMP - A(L+I,J)*X(IX) + IX = IX + INCX + 110 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) + X(JX) = TEMP + JX = JX + INCX + IF (J.GT.K) KX = KX + INCX + 120 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 140 J = N,1,-1 + TEMP = X(J) + L = 1 - J + DO 130 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - A(L+I,J)*X(I) + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(1,J) + X(J) = TEMP + 140 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 160 J = N,1,-1 + TEMP = X(JX) + IX = KX + L = 1 - J + DO 150 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - A(L+I,J)*X(IX) + IX = IX - INCX + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(1,J) + X(JX) = TEMP + JX = JX - INCX + IF ((N-J).GE.K) KX = KX - INCX + 160 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of DTBSV . +* + END diff --git a/blas/dtpmv.f b/blas/dtpmv.f new file mode 100644 index 000000000..c5bc112dc --- /dev/null +++ b/blas/dtpmv.f @@ -0,0 +1,293 @@ + SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* DTPMV performs one of the matrix-vector operations +* +* x := A*x, or x := A'*x, +* +* where x is an n element vector and A is an n by n unit, or non-unit, +* upper or lower triangular matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' x := A*x. +* +* TRANS = 'T' or 't' x := A'*x. +* +* TRANS = 'C' or 'c' x := A'*x. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* AP - DOUBLE PRECISION array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +* respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +* respectively, and so on. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced, but are assumed to be unity. +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. On exit, X is overwritten with the +* tranformed vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER (ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX + LOGICAL NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (INCX.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DTPMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of AP are +* accessed sequentially with one pass through AP. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x:= A*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = 1 + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + K = KK + DO 10 I = 1,J - 1 + X(I) = X(I) + TEMP*AP(K) + K = K + 1 + 10 CONTINUE + IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) + END IF + KK = KK + J + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + DO 30 K = KK,KK + J - 2 + X(IX) = X(IX) + TEMP*AP(K) + IX = IX + INCX + 30 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) + END IF + JX = JX + INCX + KK = KK + J + 40 CONTINUE + END IF + ELSE + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 60 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + K = KK + DO 50 I = N,J + 1,-1 + X(I) = X(I) + TEMP*AP(K) + K = K - 1 + 50 CONTINUE + IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) + END IF + KK = KK - (N-J+1) + 60 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 80 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + DO 70 K = KK,KK - (N- (J+1)),-1 + X(IX) = X(IX) + TEMP*AP(K) + IX = IX - INCX + 70 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) + END IF + JX = JX - INCX + KK = KK - (N-J+1) + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := A'*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 100 J = N,1,-1 + TEMP = X(J) + IF (NOUNIT) TEMP = TEMP*AP(KK) + K = KK - 1 + DO 90 I = J - 1,1,-1 + TEMP = TEMP + AP(K)*X(I) + K = K - 1 + 90 CONTINUE + X(J) = TEMP + KK = KK - J + 100 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 120 J = N,1,-1 + TEMP = X(JX) + IX = JX + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 110 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + TEMP = TEMP + AP(K)*X(IX) + 110 CONTINUE + X(JX) = TEMP + JX = JX - INCX + KK = KK - J + 120 CONTINUE + END IF + ELSE + KK = 1 + IF (INCX.EQ.1) THEN + DO 140 J = 1,N + TEMP = X(J) + IF (NOUNIT) TEMP = TEMP*AP(KK) + K = KK + 1 + DO 130 I = J + 1,N + TEMP = TEMP + AP(K)*X(I) + K = K + 1 + 130 CONTINUE + X(J) = TEMP + KK = KK + (N-J+1) + 140 CONTINUE + ELSE + JX = KX + DO 160 J = 1,N + TEMP = X(JX) + IX = JX + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 150 K = KK + 1,KK + N - J + IX = IX + INCX + TEMP = TEMP + AP(K)*X(IX) + 150 CONTINUE + X(JX) = TEMP + JX = JX + INCX + KK = KK + (N-J+1) + 160 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of DTPMV . +* + END diff --git a/blas/dtpsv.f b/blas/dtpsv.f new file mode 100644 index 000000000..c7e58d32f --- /dev/null +++ b/blas/dtpsv.f @@ -0,0 +1,296 @@ + SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* DTPSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular matrix, supplied in packed form. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' A'*x = b. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* AP - DOUBLE PRECISION array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +* respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +* respectively, and so on. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced, but are assumed to be unity. +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER (ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX + LOGICAL NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (INCX.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DTPSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of AP are +* accessed sequentially with one pass through AP. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/AP(KK) + TEMP = X(J) + K = KK - 1 + DO 10 I = J - 1,1,-1 + X(I) = X(I) - TEMP*AP(K) + K = K - 1 + 10 CONTINUE + END IF + KK = KK - J + 20 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 40 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/AP(KK) + TEMP = X(JX) + IX = JX + DO 30 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + X(IX) = X(IX) - TEMP*AP(K) + 30 CONTINUE + END IF + JX = JX - INCX + KK = KK - J + 40 CONTINUE + END IF + ELSE + KK = 1 + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/AP(KK) + TEMP = X(J) + K = KK + 1 + DO 50 I = J + 1,N + X(I) = X(I) - TEMP*AP(K) + K = K + 1 + 50 CONTINUE + END IF + KK = KK + (N-J+1) + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/AP(KK) + TEMP = X(JX) + IX = JX + DO 70 K = KK + 1,KK + N - J + IX = IX + INCX + X(IX) = X(IX) - TEMP*AP(K) + 70 CONTINUE + END IF + JX = JX + INCX + KK = KK + (N-J+1) + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A' )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = 1 + IF (INCX.EQ.1) THEN + DO 100 J = 1,N + TEMP = X(J) + K = KK + DO 90 I = 1,J - 1 + TEMP = TEMP - AP(K)*X(I) + K = K + 1 + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) + X(J) = TEMP + KK = KK + J + 100 CONTINUE + ELSE + JX = KX + DO 120 J = 1,N + TEMP = X(JX) + IX = KX + DO 110 K = KK,KK + J - 2 + TEMP = TEMP - AP(K)*X(IX) + IX = IX + INCX + 110 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) + X(JX) = TEMP + JX = JX + INCX + KK = KK + J + 120 CONTINUE + END IF + ELSE + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 140 J = N,1,-1 + TEMP = X(J) + K = KK + DO 130 I = N,J + 1,-1 + TEMP = TEMP - AP(K)*X(I) + K = K - 1 + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) + X(J) = TEMP + KK = KK - (N-J+1) + 140 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 160 J = N,1,-1 + TEMP = X(JX) + IX = KX + DO 150 K = KK,KK - (N- (J+1)),-1 + TEMP = TEMP - AP(K)*X(IX) + IX = IX - INCX + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) + X(JX) = TEMP + JX = JX - INCX + KK = KK - (N-J+1) + 160 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of DTPSV . +* + END diff --git a/blas/lsame.f b/blas/lsame.f new file mode 100644 index 000000000..f53690268 --- /dev/null +++ b/blas/lsame.f @@ -0,0 +1,85 @@ + LOGICAL FUNCTION LSAME(CA,CB) +* +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER CA,CB +* .. +* +* Purpose +* ======= +* +* LSAME returns .TRUE. if CA is the same letter as CB regardless of +* case. +* +* Arguments +* ========= +* +* CA (input) CHARACTER*1 +* +* CB (input) CHARACTER*1 +* CA and CB specify the single characters to be compared. +* +* ===================================================================== +* +* .. Intrinsic Functions .. + INTRINSIC ICHAR +* .. +* .. Local Scalars .. + INTEGER INTA,INTB,ZCODE +* .. +* +* Test if the characters are equal +* + LSAME = CA .EQ. CB + IF (LSAME) RETURN +* +* Now test for equivalence if both characters are alphabetic. +* + ZCODE = ICHAR('Z') +* +* Use 'Z' rather than 'A' so that ASCII can be detected on Prime +* machines, on which ICHAR returns a value with bit 8 set. +* ICHAR('A') on Prime machines returns 193 which is the same as +* ICHAR('A') on an EBCDIC machine. +* + INTA = ICHAR(CA) + INTB = ICHAR(CB) +* + IF (ZCODE.EQ.90 .OR. ZCODE.EQ.122) THEN +* +* ASCII is assumed - ZCODE is the ASCII code of either lower or +* upper case 'Z'. +* + IF (INTA.GE.97 .AND. INTA.LE.122) INTA = INTA - 32 + IF (INTB.GE.97 .AND. INTB.LE.122) INTB = INTB - 32 +* + ELSE IF (ZCODE.EQ.233 .OR. ZCODE.EQ.169) THEN +* +* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or +* upper case 'Z'. +* + IF (INTA.GE.129 .AND. INTA.LE.137 .OR. + + INTA.GE.145 .AND. INTA.LE.153 .OR. + + INTA.GE.162 .AND. INTA.LE.169) INTA = INTA + 64 + IF (INTB.GE.129 .AND. INTB.LE.137 .OR. + + INTB.GE.145 .AND. INTB.LE.153 .OR. + + INTB.GE.162 .AND. INTB.LE.169) INTB = INTB + 64 +* + ELSE IF (ZCODE.EQ.218 .OR. ZCODE.EQ.250) THEN +* +* ASCII is assumed, on Prime machines - ZCODE is the ASCII code +* plus 128 of either lower or upper case 'Z'. +* + IF (INTA.GE.225 .AND. INTA.LE.250) INTA = INTA - 32 + IF (INTB.GE.225 .AND. INTB.LE.250) INTB = INTB - 32 + END IF + LSAME = INTA .EQ. INTB +* +* RETURN +* +* End of LSAME +* + END diff --git a/blas/sgbmv.f b/blas/sgbmv.f new file mode 100644 index 000000000..aaa8b1a17 --- /dev/null +++ b/blas/sgbmv.f @@ -0,0 +1,301 @@ + SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER INCX,INCY,KL,KU,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* SGBMV performs one of the matrix-vector operations +* +* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, +* +* where alpha and beta are scalars, x and y are vectors and A is an +* m by n band matrix, with kl sub-diagonals and ku super-diagonals. +* +* Arguments +* ========== +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +* +* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. +* +* TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. +* +* Unchanged on exit. +* +* M - INTEGER. +* On entry, M specifies the number of rows of the matrix A. +* M must be at least zero. +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the number of columns of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* KL - INTEGER. +* On entry, KL specifies the number of sub-diagonals of the +* matrix A. KL must satisfy 0 .le. KL. +* Unchanged on exit. +* +* KU - INTEGER. +* On entry, KU specifies the number of super-diagonals of the +* matrix A. KU must satisfy 0 .le. KU. +* Unchanged on exit. +* +* ALPHA - REAL . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - REAL array of DIMENSION ( LDA, n ). +* Before entry, the leading ( kl + ku + 1 ) by n part of the +* array A must contain the matrix of coefficients, supplied +* column by column, with the leading diagonal of the matrix in +* row ( ku + 1 ) of the array, the first super-diagonal +* starting at position 2 in row ku, the first sub-diagonal +* starting at position 1 in row ( ku + 2 ), and so on. +* Elements in the array A that do not correspond to elements +* in the band matrix (such as the top left ku by ku triangle) +* are not referenced. +* The following program segment will transfer a band matrix +* from conventional full matrix storage to band storage: +* +* DO 20, J = 1, N +* K = KU + 1 - J +* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) +* A( K + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( kl + ku + 1 ). +* Unchanged on exit. +* +* X - REAL array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +* and at least +* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +* Before entry, the incremented array X must contain the +* vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - REAL . +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then Y need not be set on input. +* Unchanged on exit. +* +* Y - REAL array of DIMENSION at least +* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +* and at least +* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +* Before entry, the incremented array Y must contain the +* vector y. On exit, Y is overwritten by the updated vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE,ZERO + PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP + INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 1 + ELSE IF (M.LT.0) THEN + INFO = 2 + ELSE IF (N.LT.0) THEN + INFO = 3 + ELSE IF (KL.LT.0) THEN + INFO = 4 + ELSE IF (KU.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (KL+KU+1)) THEN + INFO = 8 + ELSE IF (INCX.EQ.0) THEN + INFO = 10 + ELSE IF (INCY.EQ.0) THEN + INFO = 13 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('SGBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set LENX and LENY, the lengths of the vectors x and y, and set +* up the start points in X and Y. +* + IF (LSAME(TRANS,'N')) THEN + LENX = N + LENY = M + ELSE + LENX = M + LENY = N + END IF + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (LENX-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (LENY-1)*INCY + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through the band part of A. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,LENY + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,LENY + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,LENY + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,LENY + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + KUP1 = KU + 1 + IF (LSAME(TRANS,'N')) THEN +* +* Form y := alpha*A*x + y. +* + JX = KX + IF (INCY.EQ.1) THEN + DO 60 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + K = KUP1 - J + DO 50 I = MAX(1,J-KU),MIN(M,J+KL) + Y(I) = Y(I) + TEMP*A(K+I,J) + 50 CONTINUE + END IF + JX = JX + INCX + 60 CONTINUE + ELSE + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + IY = KY + K = KUP1 - J + DO 70 I = MAX(1,J-KU),MIN(M,J+KL) + Y(IY) = Y(IY) + TEMP*A(K+I,J) + IY = IY + INCY + 70 CONTINUE + END IF + JX = JX + INCX + IF (J.GT.KU) KY = KY + INCY + 80 CONTINUE + END IF + ELSE +* +* Form y := alpha*A'*x + y. +* + JY = KY + IF (INCX.EQ.1) THEN + DO 100 J = 1,N + TEMP = ZERO + K = KUP1 - J + DO 90 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + A(K+I,J)*X(I) + 90 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP + JY = JY + INCY + 100 CONTINUE + ELSE + DO 120 J = 1,N + TEMP = ZERO + IX = KX + K = KUP1 - J + DO 110 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + A(K+I,J)*X(IX) + IX = IX + INCX + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP + JY = JY + INCY + IF (J.GT.KU) KX = KX + INCX + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of SGBMV . +* + END diff --git a/blas/srotm.f b/blas/srotm.f new file mode 100644 index 000000000..fc5a59333 --- /dev/null +++ b/blas/srotm.f @@ -0,0 +1,148 @@ + SUBROUTINE SROTM(N,SX,INCX,SY,INCY,SPARAM) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + REAL SPARAM(5),SX(*),SY(*) +* .. +* +* Purpose +* ======= +* +* APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX +* +* (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN +* (DX**T) +* +* SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE +* LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY. +* WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +* +* SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 +* +* (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) +* H=( ) ( ) ( ) ( ) +* (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). +* SEE SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM. +* +* +* Arguments +* ========= +* +* N (input) INTEGER +* number of elements in input vector(s) +* +* SX (input/output) REAL array, dimension N +* double precision vector with N elements +* +* INCX (input) INTEGER +* storage spacing between elements of SX +* +* SY (input/output) REAL array, dimension N +* double precision vector with N elements +* +* INCY (input) INTEGER +* storage spacing between elements of SY +* +* SPARAM (input/output) REAL array, dimension 5 +* SPARAM(1)=SFLAG +* SPARAM(2)=SH11 +* SPARAM(3)=SH21 +* SPARAM(4)=SH12 +* SPARAM(5)=SH22 +* +* ===================================================================== +* +* .. Local Scalars .. + REAL SFLAG,SH11,SH12,SH21,SH22,TWO,W,Z,ZERO + INTEGER I,KX,KY,NSTEPS +* .. +* .. Data statements .. + DATA ZERO,TWO/0.E0,2.E0/ +* .. +* + SFLAG = SPARAM(1) + IF (N.LE.0 .OR. (SFLAG+TWO.EQ.ZERO)) GO TO 140 + IF (.NOT. (INCX.EQ.INCY.AND.INCX.GT.0)) GO TO 70 +* + NSTEPS = N*INCX + IF (SFLAG) 50,10,30 + 10 CONTINUE + SH12 = SPARAM(4) + SH21 = SPARAM(3) + DO 20 I = 1,NSTEPS,INCX + W = SX(I) + Z = SY(I) + SX(I) = W + Z*SH12 + SY(I) = W*SH21 + Z + 20 CONTINUE + GO TO 140 + 30 CONTINUE + SH11 = SPARAM(2) + SH22 = SPARAM(5) + DO 40 I = 1,NSTEPS,INCX + W = SX(I) + Z = SY(I) + SX(I) = W*SH11 + Z + SY(I) = -W + SH22*Z + 40 CONTINUE + GO TO 140 + 50 CONTINUE + SH11 = SPARAM(2) + SH12 = SPARAM(4) + SH21 = SPARAM(3) + SH22 = SPARAM(5) + DO 60 I = 1,NSTEPS,INCX + W = SX(I) + Z = SY(I) + SX(I) = W*SH11 + Z*SH12 + SY(I) = W*SH21 + Z*SH22 + 60 CONTINUE + GO TO 140 + 70 CONTINUE + KX = 1 + KY = 1 + IF (INCX.LT.0) KX = 1 + (1-N)*INCX + IF (INCY.LT.0) KY = 1 + (1-N)*INCY +* + IF (SFLAG) 120,80,100 + 80 CONTINUE + SH12 = SPARAM(4) + SH21 = SPARAM(3) + DO 90 I = 1,N + W = SX(KX) + Z = SY(KY) + SX(KX) = W + Z*SH12 + SY(KY) = W*SH21 + Z + KX = KX + INCX + KY = KY + INCY + 90 CONTINUE + GO TO 140 + 100 CONTINUE + SH11 = SPARAM(2) + SH22 = SPARAM(5) + DO 110 I = 1,N + W = SX(KX) + Z = SY(KY) + SX(KX) = W*SH11 + Z + SY(KY) = -W + SH22*Z + KX = KX + INCX + KY = KY + INCY + 110 CONTINUE + GO TO 140 + 120 CONTINUE + SH11 = SPARAM(2) + SH12 = SPARAM(4) + SH21 = SPARAM(3) + SH22 = SPARAM(5) + DO 130 I = 1,N + W = SX(KX) + Z = SY(KY) + SX(KX) = W*SH11 + Z*SH12 + SY(KY) = W*SH21 + Z*SH22 + KX = KX + INCX + KY = KY + INCY + 130 CONTINUE + 140 CONTINUE + RETURN + END diff --git a/blas/srotmg.f b/blas/srotmg.f new file mode 100644 index 000000000..7b3bd4272 --- /dev/null +++ b/blas/srotmg.f @@ -0,0 +1,208 @@ + SUBROUTINE SROTMG(SD1,SD2,SX1,SY1,SPARAM) +* .. Scalar Arguments .. + REAL SD1,SD2,SX1,SY1 +* .. +* .. Array Arguments .. + REAL SPARAM(5) +* .. +* +* Purpose +* ======= +* +* CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS +* THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)* +* SY2)**T. +* WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +* +* SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 +* +* (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) +* H=( ) ( ) ( ) ( ) +* (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). +* LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22 +* RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE +* VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.) +* +* THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE +* INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE +* OF SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. +* +* +* Arguments +* ========= +* +* +* SD1 (input/output) REAL +* +* SD2 (input/output) REAL +* +* SX1 (input/output) REAL +* +* SY1 (input) REAL +* +* +* SPARAM (input/output) REAL array, dimension 5 +* SPARAM(1)=SFLAG +* SPARAM(2)=SH11 +* SPARAM(3)=SH21 +* SPARAM(4)=SH12 +* SPARAM(5)=SH22 +* +* ===================================================================== +* +* .. Local Scalars .. + REAL GAM,GAMSQ,ONE,RGAMSQ,SFLAG,SH11,SH12,SH21,SH22,SP1,SP2,SQ1, + + SQ2,STEMP,SU,TWO,ZERO + INTEGER IGO +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Data statements .. +* + DATA ZERO,ONE,TWO/0.E0,1.E0,2.E0/ + DATA GAM,GAMSQ,RGAMSQ/4096.E0,1.67772E7,5.96046E-8/ +* .. + + IF (.NOT.SD1.LT.ZERO) GO TO 10 +* GO ZERO-H-D-AND-SX1.. + GO TO 60 + 10 CONTINUE +* CASE-SD1-NONNEGATIVE + SP2 = SD2*SY1 + IF (.NOT.SP2.EQ.ZERO) GO TO 20 + SFLAG = -TWO + GO TO 260 +* REGULAR-CASE.. + 20 CONTINUE + SP1 = SD1*SX1 + SQ2 = SP2*SY1 + SQ1 = SP1*SX1 +* + IF (.NOT.ABS(SQ1).GT.ABS(SQ2)) GO TO 40 + SH21 = -SY1/SX1 + SH12 = SP2/SP1 +* + SU = ONE - SH12*SH21 +* + IF (.NOT.SU.LE.ZERO) GO TO 30 +* GO ZERO-H-D-AND-SX1.. + GO TO 60 + 30 CONTINUE + SFLAG = ZERO + SD1 = SD1/SU + SD2 = SD2/SU + SX1 = SX1*SU +* GO SCALE-CHECK.. + GO TO 100 + 40 CONTINUE + IF (.NOT.SQ2.LT.ZERO) GO TO 50 +* GO ZERO-H-D-AND-SX1.. + GO TO 60 + 50 CONTINUE + SFLAG = ONE + SH11 = SP1/SP2 + SH22 = SX1/SY1 + SU = ONE + SH11*SH22 + STEMP = SD2/SU + SD2 = SD1/SU + SD1 = STEMP + SX1 = SY1*SU +* GO SCALE-CHECK + GO TO 100 +* PROCEDURE..ZERO-H-D-AND-SX1.. + 60 CONTINUE + SFLAG = -ONE + SH11 = ZERO + SH12 = ZERO + SH21 = ZERO + SH22 = ZERO +* + SD1 = ZERO + SD2 = ZERO + SX1 = ZERO +* RETURN.. + GO TO 220 +* PROCEDURE..FIX-H.. + 70 CONTINUE + IF (.NOT.SFLAG.GE.ZERO) GO TO 90 +* + IF (.NOT.SFLAG.EQ.ZERO) GO TO 80 + SH11 = ONE + SH22 = ONE + SFLAG = -ONE + GO TO 90 + 80 CONTINUE + SH21 = -ONE + SH12 = ONE + SFLAG = -ONE + 90 CONTINUE + GO TO IGO(120,150,180,210) +* PROCEDURE..SCALE-CHECK + 100 CONTINUE + 110 CONTINUE + IF (.NOT.SD1.LE.RGAMSQ) GO TO 130 + IF (SD1.EQ.ZERO) GO TO 160 + ASSIGN 120 TO IGO +* FIX-H.. + GO TO 70 + 120 CONTINUE + SD1 = SD1*GAM**2 + SX1 = SX1/GAM + SH11 = SH11/GAM + SH12 = SH12/GAM + GO TO 110 + 130 CONTINUE + 140 CONTINUE + IF (.NOT.SD1.GE.GAMSQ) GO TO 160 + ASSIGN 150 TO IGO +* FIX-H.. + GO TO 70 + 150 CONTINUE + SD1 = SD1/GAM**2 + SX1 = SX1*GAM + SH11 = SH11*GAM + SH12 = SH12*GAM + GO TO 140 + 160 CONTINUE + 170 CONTINUE + IF (.NOT.ABS(SD2).LE.RGAMSQ) GO TO 190 + IF (SD2.EQ.ZERO) GO TO 220 + ASSIGN 180 TO IGO +* FIX-H.. + GO TO 70 + 180 CONTINUE + SD2 = SD2*GAM**2 + SH21 = SH21/GAM + SH22 = SH22/GAM + GO TO 170 + 190 CONTINUE + 200 CONTINUE + IF (.NOT.ABS(SD2).GE.GAMSQ) GO TO 220 + ASSIGN 210 TO IGO +* FIX-H.. + GO TO 70 + 210 CONTINUE + SD2 = SD2/GAM**2 + SH21 = SH21*GAM + SH22 = SH22*GAM + GO TO 200 + 220 CONTINUE + IF (SFLAG) 250,230,240 + 230 CONTINUE + SPARAM(3) = SH21 + SPARAM(4) = SH12 + GO TO 260 + 240 CONTINUE + SPARAM(2) = SH11 + SPARAM(5) = SH22 + GO TO 260 + 250 CONTINUE + SPARAM(2) = SH11 + SPARAM(3) = SH21 + SPARAM(4) = SH12 + SPARAM(5) = SH22 + 260 CONTINUE + SPARAM(1) = SFLAG + RETURN + END diff --git a/blas/ssbmv.f b/blas/ssbmv.f new file mode 100644 index 000000000..16893a295 --- /dev/null +++ b/blas/ssbmv.f @@ -0,0 +1,306 @@ + SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER INCX,INCY,K,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* SSBMV performs the matrix-vector operation +* +* y := alpha*A*x + beta*y, +* +* where alpha and beta are scalars, x and y are n element vectors and +* A is an n by n symmetric band matrix, with k super-diagonals. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the band matrix A is being supplied as +* follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* being supplied. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* being supplied. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry, K specifies the number of super-diagonals of the +* matrix A. K must satisfy 0 .le. K. +* Unchanged on exit. +* +* ALPHA - REAL . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - REAL array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the symmetric matrix, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer the upper +* triangular part of a symmetric band matrix from conventional +* full matrix storage to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the symmetric matrix, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer the lower +* triangular part of a symmetric band matrix from conventional +* full matrix storage to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - REAL array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the +* vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - REAL . +* On entry, BETA specifies the scalar beta. +* Unchanged on exit. +* +* Y - REAL array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the +* vector y. On exit, Y is overwritten by the updated vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE,ZERO + PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (K.LT.0) THEN + INFO = 3 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 6 + ELSE IF (INCX.EQ.0) THEN + INFO = 8 + ELSE IF (INCY.EQ.0) THEN + INFO = 11 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('SSBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set up the start points in X and Y. +* + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF +* +* Start the operations. In this version the elements of the array A +* are accessed sequentially with one pass through A. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,N + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,N + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,N + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,N + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + IF (LSAME(UPLO,'U')) THEN +* +* Form y when upper triangle of A is stored. +* + KPLUS1 = K + 1 + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + L = KPLUS1 - J + DO 50 I = MAX(1,J-K),J - 1 + Y(I) = Y(I) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + A(L+I,J)*X(I) + 50 CONTINUE + Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 + 60 CONTINUE + ELSE + JX = KX + JY = KY + DO 80 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + IX = KX + IY = KY + L = KPLUS1 - J + DO 70 I = MAX(1,J-K),J - 1 + Y(IY) = Y(IY) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + A(L+I,J)*X(IX) + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + IF (J.GT.K) THEN + KX = KX + INCX + KY = KY + INCY + END IF + 80 CONTINUE + END IF + ELSE +* +* Form y when lower triangle of A is stored. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 100 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + Y(J) = Y(J) + TEMP1*A(1,J) + L = 1 - J + DO 90 I = J + 1,MIN(N,J+K) + Y(I) = Y(I) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + A(L+I,J)*X(I) + 90 CONTINUE + Y(J) = Y(J) + ALPHA*TEMP2 + 100 CONTINUE + ELSE + JX = KX + JY = KY + DO 120 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + Y(JY) = Y(JY) + TEMP1*A(1,J) + L = 1 - J + IX = JX + IY = JY + DO 110 I = J + 1,MIN(N,J+K) + IX = IX + INCX + IY = IY + INCY + Y(IY) = Y(IY) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + A(L+I,J)*X(IX) + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of SSBMV . +* + END diff --git a/blas/sspmv.f b/blas/sspmv.f new file mode 100644 index 000000000..0b8449824 --- /dev/null +++ b/blas/sspmv.f @@ -0,0 +1,265 @@ + SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* SSPMV performs the matrix-vector operation +* +* y := alpha*A*x + beta*y, +* +* where alpha and beta are scalars, x and y are n element vectors and +* A is an n by n symmetric matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - REAL . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* AP - REAL array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. +* Unchanged on exit. +* +* X - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - REAL . +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then Y need not be set on input. +* Unchanged on exit. +* +* Y - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. On exit, Y is overwritten by the updated +* vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE,ZERO + PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 6 + ELSE IF (INCY.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('SSPMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set up the start points in X and Y. +* + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,N + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,N + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,N + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,N + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form y when AP contains the upper triangle. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + K = KK + DO 50 I = 1,J - 1 + Y(I) = Y(I) + TEMP1*AP(K) + TEMP2 = TEMP2 + AP(K)*X(I) + K = K + 1 + 50 CONTINUE + Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 + KK = KK + J + 60 CONTINUE + ELSE + JX = KX + JY = KY + DO 80 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + IX = KX + IY = KY + DO 70 K = KK,KK + J - 2 + Y(IY) = Y(IY) + TEMP1*AP(K) + TEMP2 = TEMP2 + AP(K)*X(IX) + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + KK = KK + J + 80 CONTINUE + END IF + ELSE +* +* Form y when AP contains the lower triangle. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 100 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + Y(J) = Y(J) + TEMP1*AP(KK) + K = KK + 1 + DO 90 I = J + 1,N + Y(I) = Y(I) + TEMP1*AP(K) + TEMP2 = TEMP2 + AP(K)*X(I) + K = K + 1 + 90 CONTINUE + Y(J) = Y(J) + ALPHA*TEMP2 + KK = KK + (N-J+1) + 100 CONTINUE + ELSE + JX = KX + JY = KY + DO 120 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + Y(JY) = Y(JY) + TEMP1*AP(KK) + IX = JX + IY = JY + DO 110 K = KK + 1,KK + N - J + IX = IX + INCX + IY = IY + INCY + Y(IY) = Y(IY) + TEMP1*AP(K) + TEMP2 = TEMP2 + AP(K)*X(IX) + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + KK = KK + (N-J+1) + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of SSPMV . +* + END diff --git a/blas/sspr.f b/blas/sspr.f new file mode 100644 index 000000000..bae92612e --- /dev/null +++ b/blas/sspr.f @@ -0,0 +1,202 @@ + SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP) +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* SSPR performs the symmetric rank 1 operation +* +* A := alpha*x*x' + A, +* +* where alpha is a real scalar, x is an n element vector and A is an +* n by n symmetric matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - REAL . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* AP - REAL array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. On exit, the array +* AP is overwritten by the upper triangular part of the +* updated matrix. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. On exit, the array +* AP is overwritten by the lower triangular part of the +* updated matrix. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER (ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('SSPR ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN +* +* Set the start point in X if the increment is not unity. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form A when upper triangle is stored in AP. +* + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = ALPHA*X(J) + K = KK + DO 10 I = 1,J + AP(K) = AP(K) + X(I)*TEMP + K = K + 1 + 10 CONTINUE + END IF + KK = KK + J + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + IX = KX + DO 30 K = KK,KK + J - 1 + AP(K) = AP(K) + X(IX)*TEMP + IX = IX + INCX + 30 CONTINUE + END IF + JX = JX + INCX + KK = KK + J + 40 CONTINUE + END IF + ELSE +* +* Form A when lower triangle is stored in AP. +* + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = ALPHA*X(J) + K = KK + DO 50 I = J,N + AP(K) = AP(K) + X(I)*TEMP + K = K + 1 + 50 CONTINUE + END IF + KK = KK + N - J + 1 + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + IX = JX + DO 70 K = KK,KK + N - J + AP(K) = AP(K) + X(IX)*TEMP + IX = IX + INCX + 70 CONTINUE + END IF + JX = JX + INCX + KK = KK + N - J + 1 + 80 CONTINUE + END IF + END IF +* + RETURN +* +* End of SSPR . +* + END diff --git a/blas/sspr2.f b/blas/sspr2.f new file mode 100644 index 000000000..cd27c734b --- /dev/null +++ b/blas/sspr2.f @@ -0,0 +1,233 @@ + SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* SSPR2 performs the symmetric rank 2 operation +* +* A := alpha*x*y' + alpha*y*x' + A, +* +* where alpha is a scalar, x and y are n element vectors and A is an +* n by n symmetric matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - REAL . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Y - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. +* Unchanged on exit. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* AP - REAL array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. On exit, the array +* AP is overwritten by the upper triangular part of the +* updated matrix. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the symmetric matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. On exit, the array +* AP is overwritten by the lower triangular part of the +* updated matrix. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER (ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + ELSE IF (INCY.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('SSPR2 ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN +* +* Set up the start points in X and Y if the increments are not both +* unity. +* + IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF + JX = KX + JY = KY + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form A when upper triangle is stored in AP. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 20 J = 1,N + IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN + TEMP1 = ALPHA*Y(J) + TEMP2 = ALPHA*X(J) + K = KK + DO 10 I = 1,J + AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 + K = K + 1 + 10 CONTINUE + END IF + KK = KK + J + 20 CONTINUE + ELSE + DO 40 J = 1,N + IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN + TEMP1 = ALPHA*Y(JY) + TEMP2 = ALPHA*X(JX) + IX = KX + IY = KY + DO 30 K = KK,KK + J - 1 + AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 + IX = IX + INCX + IY = IY + INCY + 30 CONTINUE + END IF + JX = JX + INCX + JY = JY + INCY + KK = KK + J + 40 CONTINUE + END IF + ELSE +* +* Form A when lower triangle is stored in AP. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN + TEMP1 = ALPHA*Y(J) + TEMP2 = ALPHA*X(J) + K = KK + DO 50 I = J,N + AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 + K = K + 1 + 50 CONTINUE + END IF + KK = KK + N - J + 1 + 60 CONTINUE + ELSE + DO 80 J = 1,N + IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN + TEMP1 = ALPHA*Y(JY) + TEMP2 = ALPHA*X(JX) + IX = JX + IY = JY + DO 70 K = KK,KK + N - J + AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + END IF + JX = JX + INCX + JY = JY + INCY + KK = KK + N - J + 1 + 80 CONTINUE + END IF + END IF +* + RETURN +* +* End of SSPR2 . +* + END diff --git a/blas/stbmv.f b/blas/stbmv.f new file mode 100644 index 000000000..c0b8f1136 --- /dev/null +++ b/blas/stbmv.f @@ -0,0 +1,335 @@ + SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* STBMV performs one of the matrix-vector operations +* +* x := A*x, or x := A'*x, +* +* where x is an n element vector and A is an n by n unit, or non-unit, +* upper or lower triangular band matrix, with ( k + 1 ) diagonals. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' x := A*x. +* +* TRANS = 'T' or 't' x := A'*x. +* +* TRANS = 'C' or 'c' x := A'*x. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry with UPLO = 'U' or 'u', K specifies the number of +* super-diagonals of the matrix A. +* On entry with UPLO = 'L' or 'l', K specifies the number of +* sub-diagonals of the matrix A. +* K must satisfy 0 .le. K. +* Unchanged on exit. +* +* A - REAL array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer an upper +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer a lower +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that when DIAG = 'U' or 'u' the elements of the array A +* corresponding to the diagonal elements of the matrix are not +* referenced, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. On exit, X is overwritten with the +* tranformed vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER (ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP + INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L + LOGICAL NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 7 + ELSE IF (INCX.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('STBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := A*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + L = KPLUS1 - J + DO 10 I = MAX(1,J-K),J - 1 + X(I) = X(I) + TEMP*A(L+I,J) + 10 CONTINUE + IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) + END IF + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + L = KPLUS1 - J + DO 30 I = MAX(1,J-K),J - 1 + X(IX) = X(IX) + TEMP*A(L+I,J) + IX = IX + INCX + 30 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) + END IF + JX = JX + INCX + IF (J.GT.K) KX = KX + INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + L = 1 - J + DO 50 I = MIN(N,J+K),J + 1,-1 + X(I) = X(I) + TEMP*A(L+I,J) + 50 CONTINUE + IF (NOUNIT) X(J) = X(J)*A(1,J) + END IF + 60 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 80 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + L = 1 - J + DO 70 I = MIN(N,J+K),J + 1,-1 + X(IX) = X(IX) + TEMP*A(L+I,J) + IX = IX - INCX + 70 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*A(1,J) + END IF + JX = JX - INCX + IF ((N-J).GE.K) KX = KX - INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := A'*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 100 J = N,1,-1 + TEMP = X(J) + L = KPLUS1 - J + IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) + DO 90 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + A(L+I,J)*X(I) + 90 CONTINUE + X(J) = TEMP + 100 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 120 J = N,1,-1 + TEMP = X(JX) + KX = KX - INCX + IX = KX + L = KPLUS1 - J + IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) + DO 110 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + A(L+I,J)*X(IX) + IX = IX - INCX + 110 CONTINUE + X(JX) = TEMP + JX = JX - INCX + 120 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 140 J = 1,N + TEMP = X(J) + L = 1 - J + IF (NOUNIT) TEMP = TEMP*A(1,J) + DO 130 I = J + 1,MIN(N,J+K) + TEMP = TEMP + A(L+I,J)*X(I) + 130 CONTINUE + X(J) = TEMP + 140 CONTINUE + ELSE + JX = KX + DO 160 J = 1,N + TEMP = X(JX) + KX = KX + INCX + IX = KX + L = 1 - J + IF (NOUNIT) TEMP = TEMP*A(1,J) + DO 150 I = J + 1,MIN(N,J+K) + TEMP = TEMP + A(L+I,J)*X(IX) + IX = IX + INCX + 150 CONTINUE + X(JX) = TEMP + JX = JX + INCX + 160 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of STBMV . +* + END diff --git a/blas/stbsv.f b/blas/stbsv.f new file mode 100644 index 000000000..b846be85c --- /dev/null +++ b/blas/stbsv.f @@ -0,0 +1,339 @@ + SUBROUTINE STBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* STBSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular band matrix, with ( k + 1 ) +* diagonals. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' A'*x = b. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry with UPLO = 'U' or 'u', K specifies the number of +* super-diagonals of the matrix A. +* On entry with UPLO = 'L' or 'l', K specifies the number of +* sub-diagonals of the matrix A. +* K must satisfy 0 .le. K. +* Unchanged on exit. +* +* A - REAL array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer an upper +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer a lower +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that when DIAG = 'U' or 'u' the elements of the array A +* corresponding to the diagonal elements of the matrix are not +* referenced, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER (ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP + INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L + LOGICAL NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 7 + ELSE IF (INCX.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('STBSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed by sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + L = KPLUS1 - J + IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J) + TEMP = X(J) + DO 10 I = J - 1,MAX(1,J-K),-1 + X(I) = X(I) - TEMP*A(L+I,J) + 10 CONTINUE + END IF + 20 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 40 J = N,1,-1 + KX = KX - INCX + IF (X(JX).NE.ZERO) THEN + IX = KX + L = KPLUS1 - J + IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J) + TEMP = X(JX) + DO 30 I = J - 1,MAX(1,J-K),-1 + X(IX) = X(IX) - TEMP*A(L+I,J) + IX = IX - INCX + 30 CONTINUE + END IF + JX = JX - INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + L = 1 - J + IF (NOUNIT) X(J) = X(J)/A(1,J) + TEMP = X(J) + DO 50 I = J + 1,MIN(N,J+K) + X(I) = X(I) - TEMP*A(L+I,J) + 50 CONTINUE + END IF + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + KX = KX + INCX + IF (X(JX).NE.ZERO) THEN + IX = KX + L = 1 - J + IF (NOUNIT) X(JX) = X(JX)/A(1,J) + TEMP = X(JX) + DO 70 I = J + 1,MIN(N,J+K) + X(IX) = X(IX) - TEMP*A(L+I,J) + IX = IX + INCX + 70 CONTINUE + END IF + JX = JX + INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A')*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 100 J = 1,N + TEMP = X(J) + L = KPLUS1 - J + DO 90 I = MAX(1,J-K),J - 1 + TEMP = TEMP - A(L+I,J)*X(I) + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) + X(J) = TEMP + 100 CONTINUE + ELSE + JX = KX + DO 120 J = 1,N + TEMP = X(JX) + IX = KX + L = KPLUS1 - J + DO 110 I = MAX(1,J-K),J - 1 + TEMP = TEMP - A(L+I,J)*X(IX) + IX = IX + INCX + 110 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) + X(JX) = TEMP + JX = JX + INCX + IF (J.GT.K) KX = KX + INCX + 120 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 140 J = N,1,-1 + TEMP = X(J) + L = 1 - J + DO 130 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - A(L+I,J)*X(I) + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(1,J) + X(J) = TEMP + 140 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 160 J = N,1,-1 + TEMP = X(JX) + IX = KX + L = 1 - J + DO 150 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - A(L+I,J)*X(IX) + IX = IX - INCX + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(1,J) + X(JX) = TEMP + JX = JX - INCX + IF ((N-J).GE.K) KX = KX - INCX + 160 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of STBSV . +* + END diff --git a/blas/stpmv.f b/blas/stpmv.f new file mode 100644 index 000000000..71ea49a36 --- /dev/null +++ b/blas/stpmv.f @@ -0,0 +1,293 @@ + SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* STPMV performs one of the matrix-vector operations +* +* x := A*x, or x := A'*x, +* +* where x is an n element vector and A is an n by n unit, or non-unit, +* upper or lower triangular matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' x := A*x. +* +* TRANS = 'T' or 't' x := A'*x. +* +* TRANS = 'C' or 'c' x := A'*x. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* AP - REAL array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +* respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +* respectively, and so on. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced, but are assumed to be unity. +* Unchanged on exit. +* +* X - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. On exit, X is overwritten with the +* tranformed vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER (ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX + LOGICAL NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (INCX.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('STPMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of AP are +* accessed sequentially with one pass through AP. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x:= A*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = 1 + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + K = KK + DO 10 I = 1,J - 1 + X(I) = X(I) + TEMP*AP(K) + K = K + 1 + 10 CONTINUE + IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) + END IF + KK = KK + J + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + DO 30 K = KK,KK + J - 2 + X(IX) = X(IX) + TEMP*AP(K) + IX = IX + INCX + 30 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) + END IF + JX = JX + INCX + KK = KK + J + 40 CONTINUE + END IF + ELSE + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 60 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + K = KK + DO 50 I = N,J + 1,-1 + X(I) = X(I) + TEMP*AP(K) + K = K - 1 + 50 CONTINUE + IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) + END IF + KK = KK - (N-J+1) + 60 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 80 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + DO 70 K = KK,KK - (N- (J+1)),-1 + X(IX) = X(IX) + TEMP*AP(K) + IX = IX - INCX + 70 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) + END IF + JX = JX - INCX + KK = KK - (N-J+1) + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := A'*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 100 J = N,1,-1 + TEMP = X(J) + IF (NOUNIT) TEMP = TEMP*AP(KK) + K = KK - 1 + DO 90 I = J - 1,1,-1 + TEMP = TEMP + AP(K)*X(I) + K = K - 1 + 90 CONTINUE + X(J) = TEMP + KK = KK - J + 100 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 120 J = N,1,-1 + TEMP = X(JX) + IX = JX + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 110 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + TEMP = TEMP + AP(K)*X(IX) + 110 CONTINUE + X(JX) = TEMP + JX = JX - INCX + KK = KK - J + 120 CONTINUE + END IF + ELSE + KK = 1 + IF (INCX.EQ.1) THEN + DO 140 J = 1,N + TEMP = X(J) + IF (NOUNIT) TEMP = TEMP*AP(KK) + K = KK + 1 + DO 130 I = J + 1,N + TEMP = TEMP + AP(K)*X(I) + K = K + 1 + 130 CONTINUE + X(J) = TEMP + KK = KK + (N-J+1) + 140 CONTINUE + ELSE + JX = KX + DO 160 J = 1,N + TEMP = X(JX) + IX = JX + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 150 K = KK + 1,KK + N - J + IX = IX + INCX + TEMP = TEMP + AP(K)*X(IX) + 150 CONTINUE + X(JX) = TEMP + JX = JX + INCX + KK = KK + (N-J+1) + 160 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of STPMV . +* + END diff --git a/blas/stpsv.f b/blas/stpsv.f new file mode 100644 index 000000000..7d95efbde --- /dev/null +++ b/blas/stpsv.f @@ -0,0 +1,296 @@ + SUBROUTINE STPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* STPSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular matrix, supplied in packed form. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' A'*x = b. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* AP - REAL array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +* respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +* respectively, and so on. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced, but are assumed to be unity. +* Unchanged on exit. +* +* X - REAL array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER (ZERO=0.0E+0) +* .. +* .. Local Scalars .. + REAL TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX + LOGICAL NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (INCX.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('STPSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of AP are +* accessed sequentially with one pass through AP. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/AP(KK) + TEMP = X(J) + K = KK - 1 + DO 10 I = J - 1,1,-1 + X(I) = X(I) - TEMP*AP(K) + K = K - 1 + 10 CONTINUE + END IF + KK = KK - J + 20 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 40 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/AP(KK) + TEMP = X(JX) + IX = JX + DO 30 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + X(IX) = X(IX) - TEMP*AP(K) + 30 CONTINUE + END IF + JX = JX - INCX + KK = KK - J + 40 CONTINUE + END IF + ELSE + KK = 1 + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/AP(KK) + TEMP = X(J) + K = KK + 1 + DO 50 I = J + 1,N + X(I) = X(I) - TEMP*AP(K) + K = K + 1 + 50 CONTINUE + END IF + KK = KK + (N-J+1) + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/AP(KK) + TEMP = X(JX) + IX = JX + DO 70 K = KK + 1,KK + N - J + IX = IX + INCX + X(IX) = X(IX) - TEMP*AP(K) + 70 CONTINUE + END IF + JX = JX + INCX + KK = KK + (N-J+1) + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A' )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = 1 + IF (INCX.EQ.1) THEN + DO 100 J = 1,N + TEMP = X(J) + K = KK + DO 90 I = 1,J - 1 + TEMP = TEMP - AP(K)*X(I) + K = K + 1 + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) + X(J) = TEMP + KK = KK + J + 100 CONTINUE + ELSE + JX = KX + DO 120 J = 1,N + TEMP = X(JX) + IX = KX + DO 110 K = KK,KK + J - 2 + TEMP = TEMP - AP(K)*X(IX) + IX = IX + INCX + 110 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) + X(JX) = TEMP + JX = JX + INCX + KK = KK + J + 120 CONTINUE + END IF + ELSE + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 140 J = N,1,-1 + TEMP = X(J) + K = KK + DO 130 I = N,J + 1,-1 + TEMP = TEMP - AP(K)*X(I) + K = K - 1 + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) + X(J) = TEMP + KK = KK - (N-J+1) + 140 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 160 J = N,1,-1 + TEMP = X(JX) + IX = KX + DO 150 K = KK,KK - (N- (J+1)),-1 + TEMP = TEMP - AP(K)*X(IX) + IX = IX - INCX + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) + X(JX) = TEMP + JX = JX - INCX + KK = KK - (N-J+1) + 160 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of STPSV . +* + END diff --git a/blas/zgbmv.f b/blas/zgbmv.f new file mode 100644 index 000000000..5a2228d04 --- /dev/null +++ b/blas/zgbmv.f @@ -0,0 +1,322 @@ + SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + DOUBLE COMPLEX ALPHA,BETA + INTEGER INCX,INCY,KL,KU,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + DOUBLE COMPLEX A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* ZGBMV performs one of the matrix-vector operations +* +* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or +* +* y := alpha*conjg( A' )*x + beta*y, +* +* where alpha and beta are scalars, x and y are vectors and A is an +* m by n band matrix, with kl sub-diagonals and ku super-diagonals. +* +* Arguments +* ========== +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +* +* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. +* +* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. +* +* Unchanged on exit. +* +* M - INTEGER. +* On entry, M specifies the number of rows of the matrix A. +* M must be at least zero. +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the number of columns of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* KL - INTEGER. +* On entry, KL specifies the number of sub-diagonals of the +* matrix A. KL must satisfy 0 .le. KL. +* Unchanged on exit. +* +* KU - INTEGER. +* On entry, KU specifies the number of super-diagonals of the +* matrix A. KU must satisfy 0 .le. KU. +* Unchanged on exit. +* +* ALPHA - COMPLEX*16 . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - COMPLEX*16 array of DIMENSION ( LDA, n ). +* Before entry, the leading ( kl + ku + 1 ) by n part of the +* array A must contain the matrix of coefficients, supplied +* column by column, with the leading diagonal of the matrix in +* row ( ku + 1 ) of the array, the first super-diagonal +* starting at position 2 in row ku, the first sub-diagonal +* starting at position 1 in row ( ku + 2 ), and so on. +* Elements in the array A that do not correspond to elements +* in the band matrix (such as the top left ku by ku triangle) +* are not referenced. +* The following program segment will transfer a band matrix +* from conventional full matrix storage to band storage: +* +* DO 20, J = 1, N +* K = KU + 1 - J +* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) +* A( K + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( kl + ku + 1 ). +* Unchanged on exit. +* +* X - COMPLEX*16 array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +* and at least +* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +* Before entry, the incremented array X must contain the +* vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - COMPLEX*16 . +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then Y need not be set on input. +* Unchanged on exit. +* +* Y - COMPLEX*16 array of DIMENSION at least +* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +* and at least +* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +* Before entry, the incremented array Y must contain the +* vector y. On exit, Y is overwritten by the updated vector y. +* +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ONE + PARAMETER (ONE= (1.0D+0,0.0D+0)) + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP + INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY + LOGICAL NOCONJ +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG,MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 1 + ELSE IF (M.LT.0) THEN + INFO = 2 + ELSE IF (N.LT.0) THEN + INFO = 3 + ELSE IF (KL.LT.0) THEN + INFO = 4 + ELSE IF (KU.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (KL+KU+1)) THEN + INFO = 8 + ELSE IF (INCX.EQ.0) THEN + INFO = 10 + ELSE IF (INCY.EQ.0) THEN + INFO = 13 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZGBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* + NOCONJ = LSAME(TRANS,'T') +* +* Set LENX and LENY, the lengths of the vectors x and y, and set +* up the start points in X and Y. +* + IF (LSAME(TRANS,'N')) THEN + LENX = N + LENY = M + ELSE + LENX = M + LENY = N + END IF + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (LENX-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (LENY-1)*INCY + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through the band part of A. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,LENY + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,LENY + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,LENY + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,LENY + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + KUP1 = KU + 1 + IF (LSAME(TRANS,'N')) THEN +* +* Form y := alpha*A*x + y. +* + JX = KX + IF (INCY.EQ.1) THEN + DO 60 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + K = KUP1 - J + DO 50 I = MAX(1,J-KU),MIN(M,J+KL) + Y(I) = Y(I) + TEMP*A(K+I,J) + 50 CONTINUE + END IF + JX = JX + INCX + 60 CONTINUE + ELSE + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*X(JX) + IY = KY + K = KUP1 - J + DO 70 I = MAX(1,J-KU),MIN(M,J+KL) + Y(IY) = Y(IY) + TEMP*A(K+I,J) + IY = IY + INCY + 70 CONTINUE + END IF + JX = JX + INCX + IF (J.GT.KU) KY = KY + INCY + 80 CONTINUE + END IF + ELSE +* +* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. +* + JY = KY + IF (INCX.EQ.1) THEN + DO 110 J = 1,N + TEMP = ZERO + K = KUP1 - J + IF (NOCONJ) THEN + DO 90 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + A(K+I,J)*X(I) + 90 CONTINUE + ELSE + DO 100 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + DCONJG(A(K+I,J))*X(I) + 100 CONTINUE + END IF + Y(JY) = Y(JY) + ALPHA*TEMP + JY = JY + INCY + 110 CONTINUE + ELSE + DO 140 J = 1,N + TEMP = ZERO + IX = KX + K = KUP1 - J + IF (NOCONJ) THEN + DO 120 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + A(K+I,J)*X(IX) + IX = IX + INCX + 120 CONTINUE + ELSE + DO 130 I = MAX(1,J-KU),MIN(M,J+KL) + TEMP = TEMP + DCONJG(A(K+I,J))*X(IX) + IX = IX + INCX + 130 CONTINUE + END IF + Y(JY) = Y(JY) + ALPHA*TEMP + JY = JY + INCY + IF (J.GT.KU) KX = KX + INCX + 140 CONTINUE + END IF + END IF +* + RETURN +* +* End of ZGBMV . +* + END diff --git a/blas/zhbmv.f b/blas/zhbmv.f new file mode 100644 index 000000000..bca0da5fc --- /dev/null +++ b/blas/zhbmv.f @@ -0,0 +1,310 @@ + SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + DOUBLE COMPLEX ALPHA,BETA + INTEGER INCX,INCY,K,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE COMPLEX A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* ZHBMV performs the matrix-vector operation +* +* y := alpha*A*x + beta*y, +* +* where alpha and beta are scalars, x and y are n element vectors and +* A is an n by n hermitian band matrix, with k super-diagonals. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the band matrix A is being supplied as +* follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* being supplied. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* being supplied. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry, K specifies the number of super-diagonals of the +* matrix A. K must satisfy 0 .le. K. +* Unchanged on exit. +* +* ALPHA - COMPLEX*16 . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - COMPLEX*16 array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the hermitian matrix, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer the upper +* triangular part of a hermitian band matrix from conventional +* full matrix storage to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the hermitian matrix, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer the lower +* triangular part of a hermitian band matrix from conventional +* full matrix storage to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that the imaginary parts of the diagonal elements need +* not be set and are assumed to be zero. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - COMPLEX*16 array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the +* vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - COMPLEX*16 . +* On entry, BETA specifies the scalar beta. +* Unchanged on exit. +* +* Y - COMPLEX*16 array of DIMENSION at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the +* vector y. On exit, Y is overwritten by the updated vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ONE + PARAMETER (ONE= (1.0D+0,0.0D+0)) + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE,DCONJG,MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (K.LT.0) THEN + INFO = 3 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 6 + ELSE IF (INCX.EQ.0) THEN + INFO = 8 + ELSE IF (INCY.EQ.0) THEN + INFO = 11 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZHBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set up the start points in X and Y. +* + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF +* +* Start the operations. In this version the elements of the array A +* are accessed sequentially with one pass through A. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,N + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,N + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,N + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,N + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + IF (LSAME(UPLO,'U')) THEN +* +* Form y when upper triangle of A is stored. +* + KPLUS1 = K + 1 + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + L = KPLUS1 - J + DO 50 I = MAX(1,J-K),J - 1 + Y(I) = Y(I) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I) + 50 CONTINUE + Y(J) = Y(J) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2 + 60 CONTINUE + ELSE + JX = KX + JY = KY + DO 80 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + IX = KX + IY = KY + L = KPLUS1 - J + DO 70 I = MAX(1,J-K),J - 1 + Y(IY) = Y(IY) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX) + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + Y(JY) = Y(JY) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + IF (J.GT.K) THEN + KX = KX + INCX + KY = KY + INCY + END IF + 80 CONTINUE + END IF + ELSE +* +* Form y when lower triangle of A is stored. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 100 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + Y(J) = Y(J) + TEMP1*DBLE(A(1,J)) + L = 1 - J + DO 90 I = J + 1,MIN(N,J+K) + Y(I) = Y(I) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I) + 90 CONTINUE + Y(J) = Y(J) + ALPHA*TEMP2 + 100 CONTINUE + ELSE + JX = KX + JY = KY + DO 120 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + Y(JY) = Y(JY) + TEMP1*DBLE(A(1,J)) + L = 1 - J + IX = JX + IY = JY + DO 110 I = J + 1,MIN(N,J+K) + IX = IX + INCX + IY = IY + INCY + Y(IY) = Y(IY) + TEMP1*A(L+I,J) + TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX) + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of ZHBMV . +* + END diff --git a/blas/zhpmv.f b/blas/zhpmv.f new file mode 100644 index 000000000..b686108b3 --- /dev/null +++ b/blas/zhpmv.f @@ -0,0 +1,272 @@ + SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) +* .. Scalar Arguments .. + DOUBLE COMPLEX ALPHA,BETA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE COMPLEX AP(*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* ZHPMV performs the matrix-vector operation +* +* y := alpha*A*x + beta*y, +* +* where alpha and beta are scalars, x and y are n element vectors and +* A is an n by n hermitian matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - COMPLEX*16 . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* AP - COMPLEX*16 array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. +* Note that the imaginary parts of the diagonal elements need +* not be set and are assumed to be zero. +* Unchanged on exit. +* +* X - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* BETA - COMPLEX*16 . +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then Y need not be set on input. +* Unchanged on exit. +* +* Y - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. On exit, Y is overwritten by the updated +* vector y. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ONE + PARAMETER (ONE= (1.0D+0,0.0D+0)) + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE,DCONJG +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 6 + ELSE IF (INCY.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZHPMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN +* +* Set up the start points in X and Y. +* + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* +* First form y := beta*y. +* + IF (BETA.NE.ONE) THEN + IF (INCY.EQ.1) THEN + IF (BETA.EQ.ZERO) THEN + DO 10 I = 1,N + Y(I) = ZERO + 10 CONTINUE + ELSE + DO 20 I = 1,N + Y(I) = BETA*Y(I) + 20 CONTINUE + END IF + ELSE + IY = KY + IF (BETA.EQ.ZERO) THEN + DO 30 I = 1,N + Y(IY) = ZERO + IY = IY + INCY + 30 CONTINUE + ELSE + DO 40 I = 1,N + Y(IY) = BETA*Y(IY) + IY = IY + INCY + 40 CONTINUE + END IF + END IF + END IF + IF (ALPHA.EQ.ZERO) RETURN + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form y when AP contains the upper triangle. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + K = KK + DO 50 I = 1,J - 1 + Y(I) = Y(I) + TEMP1*AP(K) + TEMP2 = TEMP2 + DCONJG(AP(K))*X(I) + K = K + 1 + 50 CONTINUE + Y(J) = Y(J) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2 + KK = KK + J + 60 CONTINUE + ELSE + JX = KX + JY = KY + DO 80 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + IX = KX + IY = KY + DO 70 K = KK,KK + J - 2 + Y(IY) = Y(IY) + TEMP1*AP(K) + TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX) + IX = IX + INCX + IY = IY + INCY + 70 CONTINUE + Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + KK = KK + J + 80 CONTINUE + END IF + ELSE +* +* Form y when AP contains the lower triangle. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 100 J = 1,N + TEMP1 = ALPHA*X(J) + TEMP2 = ZERO + Y(J) = Y(J) + TEMP1*DBLE(AP(KK)) + K = KK + 1 + DO 90 I = J + 1,N + Y(I) = Y(I) + TEMP1*AP(K) + TEMP2 = TEMP2 + DCONJG(AP(K))*X(I) + K = K + 1 + 90 CONTINUE + Y(J) = Y(J) + ALPHA*TEMP2 + KK = KK + (N-J+1) + 100 CONTINUE + ELSE + JX = KX + JY = KY + DO 120 J = 1,N + TEMP1 = ALPHA*X(JX) + TEMP2 = ZERO + Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK)) + IX = JX + IY = JY + DO 110 K = KK + 1,KK + N - J + IX = IX + INCX + IY = IY + INCY + Y(IY) = Y(IY) + TEMP1*AP(K) + TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX) + 110 CONTINUE + Y(JY) = Y(JY) + ALPHA*TEMP2 + JX = JX + INCX + JY = JY + INCY + KK = KK + (N-J+1) + 120 CONTINUE + END IF + END IF +* + RETURN +* +* End of ZHPMV . +* + END diff --git a/blas/zhpr.f b/blas/zhpr.f new file mode 100644 index 000000000..40efbc7d5 --- /dev/null +++ b/blas/zhpr.f @@ -0,0 +1,220 @@ + SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE COMPLEX AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* ZHPR performs the hermitian rank 1 operation +* +* A := alpha*x*conjg( x' ) + A, +* +* where alpha is a real scalar, x is an n element vector and A is an +* n by n hermitian matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* AP - COMPLEX*16 array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. On exit, the array +* AP is overwritten by the upper triangular part of the +* updated matrix. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. On exit, the array +* AP is overwritten by the lower triangular part of the +* updated matrix. +* Note that the imaginary parts of the diagonal elements need +* not be set, they are assumed to be zero, and on exit they +* are set to zero. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE,DCONJG +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZHPR ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN +* +* Set the start point in X if the increment is not unity. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form A when upper triangle is stored in AP. +* + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = ALPHA*DCONJG(X(J)) + K = KK + DO 10 I = 1,J - 1 + AP(K) = AP(K) + X(I)*TEMP + K = K + 1 + 10 CONTINUE + AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP) + ELSE + AP(KK+J-1) = DBLE(AP(KK+J-1)) + END IF + KK = KK + J + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*DCONJG(X(JX)) + IX = KX + DO 30 K = KK,KK + J - 2 + AP(K) = AP(K) + X(IX)*TEMP + IX = IX + INCX + 30 CONTINUE + AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP) + ELSE + AP(KK+J-1) = DBLE(AP(KK+J-1)) + END IF + JX = JX + INCX + KK = KK + J + 40 CONTINUE + END IF + ELSE +* +* Form A when lower triangle is stored in AP. +* + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = ALPHA*DCONJG(X(J)) + AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J)) + K = KK + 1 + DO 50 I = J + 1,N + AP(K) = AP(K) + X(I)*TEMP + K = K + 1 + 50 CONTINUE + ELSE + AP(KK) = DBLE(AP(KK)) + END IF + KK = KK + N - J + 1 + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = ALPHA*DCONJG(X(JX)) + AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX)) + IX = JX + DO 70 K = KK + 1,KK + N - J + IX = IX + INCX + AP(K) = AP(K) + X(IX)*TEMP + 70 CONTINUE + ELSE + AP(KK) = DBLE(AP(KK)) + END IF + JX = JX + INCX + KK = KK + N - J + 1 + 80 CONTINUE + END IF + END IF +* + RETURN +* +* End of ZHPR . +* + END diff --git a/blas/zhpr2.f b/blas/zhpr2.f new file mode 100644 index 000000000..99977462e --- /dev/null +++ b/blas/zhpr2.f @@ -0,0 +1,255 @@ + SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) +* .. Scalar Arguments .. + DOUBLE COMPLEX ALPHA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE COMPLEX AP(*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* ZHPR2 performs the hermitian rank 2 operation +* +* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, +* +* where alpha is a scalar, x and y are n element vectors and A is an +* n by n hermitian matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the upper or lower +* triangular part of the matrix A is supplied in the packed +* array AP as follows: +* +* UPLO = 'U' or 'u' The upper triangular part of A is +* supplied in AP. +* +* UPLO = 'L' or 'l' The lower triangular part of A is +* supplied in AP. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - COMPLEX*16 . +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Y - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. +* Unchanged on exit. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* AP - COMPLEX*16 array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +* and a( 2, 2 ) respectively, and so on. On exit, the array +* AP is overwritten by the upper triangular part of the +* updated matrix. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular part of the hermitian matrix +* packed sequentially, column by column, so that AP( 1 ) +* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +* and a( 3, 1 ) respectively, and so on. On exit, the array +* AP is overwritten by the lower triangular part of the +* updated matrix. +* Note that the imaginary parts of the diagonal elements need +* not be set, they are assumed to be zero, and on exit they +* are set to zero. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP1,TEMP2 + INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE,DCONJG +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + ELSE IF (INCY.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZHPR2 ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN +* +* Set up the start points in X and Y if the increments are not both +* unity. +* + IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (N-1)*INCX + END IF + IF (INCY.GT.0) THEN + KY = 1 + ELSE + KY = 1 - (N-1)*INCY + END IF + JX = KX + JY = KY + END IF +* +* Start the operations. In this version the elements of the array AP +* are accessed sequentially with one pass through AP. +* + KK = 1 + IF (LSAME(UPLO,'U')) THEN +* +* Form A when upper triangle is stored in AP. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 20 J = 1,N + IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN + TEMP1 = ALPHA*DCONJG(Y(J)) + TEMP2 = DCONJG(ALPHA*X(J)) + K = KK + DO 10 I = 1,J - 1 + AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 + K = K + 1 + 10 CONTINUE + AP(KK+J-1) = DBLE(AP(KK+J-1)) + + + DBLE(X(J)*TEMP1+Y(J)*TEMP2) + ELSE + AP(KK+J-1) = DBLE(AP(KK+J-1)) + END IF + KK = KK + J + 20 CONTINUE + ELSE + DO 40 J = 1,N + IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN + TEMP1 = ALPHA*DCONJG(Y(JY)) + TEMP2 = DCONJG(ALPHA*X(JX)) + IX = KX + IY = KY + DO 30 K = KK,KK + J - 2 + AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 + IX = IX + INCX + IY = IY + INCY + 30 CONTINUE + AP(KK+J-1) = DBLE(AP(KK+J-1)) + + + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) + ELSE + AP(KK+J-1) = DBLE(AP(KK+J-1)) + END IF + JX = JX + INCX + JY = JY + INCY + KK = KK + J + 40 CONTINUE + END IF + ELSE +* +* Form A when lower triangle is stored in AP. +* + IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN + DO 60 J = 1,N + IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN + TEMP1 = ALPHA*DCONJG(Y(J)) + TEMP2 = DCONJG(ALPHA*X(J)) + AP(KK) = DBLE(AP(KK)) + + + DBLE(X(J)*TEMP1+Y(J)*TEMP2) + K = KK + 1 + DO 50 I = J + 1,N + AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 + K = K + 1 + 50 CONTINUE + ELSE + AP(KK) = DBLE(AP(KK)) + END IF + KK = KK + N - J + 1 + 60 CONTINUE + ELSE + DO 80 J = 1,N + IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN + TEMP1 = ALPHA*DCONJG(Y(JY)) + TEMP2 = DCONJG(ALPHA*X(JX)) + AP(KK) = DBLE(AP(KK)) + + + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) + IX = JX + IY = JY + DO 70 K = KK + 1,KK + N - J + IX = IX + INCX + IY = IY + INCY + AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 + 70 CONTINUE + ELSE + AP(KK) = DBLE(AP(KK)) + END IF + JX = JX + INCX + JY = JY + INCY + KK = KK + N - J + 1 + 80 CONTINUE + END IF + END IF +* + RETURN +* +* End of ZHPR2 . +* + END diff --git a/blas/ztbmv.f b/blas/ztbmv.f new file mode 100644 index 000000000..7c85c1b55 --- /dev/null +++ b/blas/ztbmv.f @@ -0,0 +1,366 @@ + SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE COMPLEX A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* ZTBMV performs one of the matrix-vector operations +* +* x := A*x, or x := A'*x, or x := conjg( A' )*x, +* +* where x is an n element vector and A is an n by n unit, or non-unit, +* upper or lower triangular band matrix, with ( k + 1 ) diagonals. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' x := A*x. +* +* TRANS = 'T' or 't' x := A'*x. +* +* TRANS = 'C' or 'c' x := conjg( A' )*x. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry with UPLO = 'U' or 'u', K specifies the number of +* super-diagonals of the matrix A. +* On entry with UPLO = 'L' or 'l', K specifies the number of +* sub-diagonals of the matrix A. +* K must satisfy 0 .le. K. +* Unchanged on exit. +* +* A - COMPLEX*16 array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer an upper +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer a lower +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that when DIAG = 'U' or 'u' the elements of the array A +* corresponding to the diagonal elements of the matrix are not +* referenced, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. On exit, X is overwritten with the +* tranformed vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG,MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 7 + ELSE IF (INCX.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZTBMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := A*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + L = KPLUS1 - J + DO 10 I = MAX(1,J-K),J - 1 + X(I) = X(I) + TEMP*A(L+I,J) + 10 CONTINUE + IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) + END IF + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + L = KPLUS1 - J + DO 30 I = MAX(1,J-K),J - 1 + X(IX) = X(IX) + TEMP*A(L+I,J) + IX = IX + INCX + 30 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) + END IF + JX = JX + INCX + IF (J.GT.K) KX = KX + INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + L = 1 - J + DO 50 I = MIN(N,J+K),J + 1,-1 + X(I) = X(I) + TEMP*A(L+I,J) + 50 CONTINUE + IF (NOUNIT) X(J) = X(J)*A(1,J) + END IF + 60 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 80 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + L = 1 - J + DO 70 I = MIN(N,J+K),J + 1,-1 + X(IX) = X(IX) + TEMP*A(L+I,J) + IX = IX - INCX + 70 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*A(1,J) + END IF + JX = JX - INCX + IF ((N-J).GE.K) KX = KX - INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := A'*x or x := conjg( A' )*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 110 J = N,1,-1 + TEMP = X(J) + L = KPLUS1 - J + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) + DO 90 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + A(L+I,J)*X(I) + 90 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) + DO 100 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + DCONJG(A(L+I,J))*X(I) + 100 CONTINUE + END IF + X(J) = TEMP + 110 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 140 J = N,1,-1 + TEMP = X(JX) + KX = KX - INCX + IX = KX + L = KPLUS1 - J + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) + DO 120 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + A(L+I,J)*X(IX) + IX = IX - INCX + 120 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) + DO 130 I = J - 1,MAX(1,J-K),-1 + TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) + IX = IX - INCX + 130 CONTINUE + END IF + X(JX) = TEMP + JX = JX - INCX + 140 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 170 J = 1,N + TEMP = X(J) + L = 1 - J + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*A(1,J) + DO 150 I = J + 1,MIN(N,J+K) + TEMP = TEMP + A(L+I,J)*X(I) + 150 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) + DO 160 I = J + 1,MIN(N,J+K) + TEMP = TEMP + DCONJG(A(L+I,J))*X(I) + 160 CONTINUE + END IF + X(J) = TEMP + 170 CONTINUE + ELSE + JX = KX + DO 200 J = 1,N + TEMP = X(JX) + KX = KX + INCX + IX = KX + L = 1 - J + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*A(1,J) + DO 180 I = J + 1,MIN(N,J+K) + TEMP = TEMP + A(L+I,J)*X(IX) + IX = IX + INCX + 180 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) + DO 190 I = J + 1,MIN(N,J+K) + TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) + IX = IX + INCX + 190 CONTINUE + END IF + X(JX) = TEMP + JX = JX + INCX + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of ZTBMV . +* + END diff --git a/blas/ztbsv.f b/blas/ztbsv.f new file mode 100644 index 000000000..42b234a77 --- /dev/null +++ b/blas/ztbsv.f @@ -0,0 +1,370 @@ + SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE COMPLEX A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* ZTBSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, or conjg( A' )*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular band matrix, with ( k + 1 ) +* diagonals. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' conjg( A' )*x = b. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry with UPLO = 'U' or 'u', K specifies the number of +* super-diagonals of the matrix A. +* On entry with UPLO = 'L' or 'l', K specifies the number of +* sub-diagonals of the matrix A. +* K must satisfy 0 .le. K. +* Unchanged on exit. +* +* A - COMPLEX*16 array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +* by n part of the array A must contain the upper triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row +* ( k + 1 ) of the array, the first super-diagonal starting at +* position 2 in row k, and so on. The top left k by k triangle +* of the array A is not referenced. +* The following program segment will transfer an upper +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = K + 1 - J +* DO 10, I = MAX( 1, J - K ), J +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +* by n part of the array A must contain the lower triangular +* band part of the matrix of coefficients, supplied column by +* column, with the leading diagonal of the matrix in row 1 of +* the array, the first sub-diagonal starting at position 1 in +* row 2, and so on. The bottom right k by k triangle of the +* array A is not referenced. +* The following program segment will transfer a lower +* triangular band matrix from conventional full matrix storage +* to band storage: +* +* DO 20, J = 1, N +* M = 1 - J +* DO 10, I = J, MIN( N, J + K ) +* A( M + I, J ) = matrix( I, J ) +* 10 CONTINUE +* 20 CONTINUE +* +* Note that when DIAG = 'U' or 'u' the elements of the array A +* corresponding to the diagonal elements of the matrix are not +* referenced, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* ( k + 1 ). +* Unchanged on exit. +* +* X - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG,MAX,MIN +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT. (K+1)) THEN + INFO = 7 + ELSE IF (INCX.EQ.0) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZTBSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed by sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + L = KPLUS1 - J + IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J) + TEMP = X(J) + DO 10 I = J - 1,MAX(1,J-K),-1 + X(I) = X(I) - TEMP*A(L+I,J) + 10 CONTINUE + END IF + 20 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 40 J = N,1,-1 + KX = KX - INCX + IF (X(JX).NE.ZERO) THEN + IX = KX + L = KPLUS1 - J + IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J) + TEMP = X(JX) + DO 30 I = J - 1,MAX(1,J-K),-1 + X(IX) = X(IX) - TEMP*A(L+I,J) + IX = IX - INCX + 30 CONTINUE + END IF + JX = JX - INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + L = 1 - J + IF (NOUNIT) X(J) = X(J)/A(1,J) + TEMP = X(J) + DO 50 I = J + 1,MIN(N,J+K) + X(I) = X(I) - TEMP*A(L+I,J) + 50 CONTINUE + END IF + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + KX = KX + INCX + IF (X(JX).NE.ZERO) THEN + IX = KX + L = 1 - J + IF (NOUNIT) X(JX) = X(JX)/A(1,J) + TEMP = X(JX) + DO 70 I = J + 1,MIN(N,J+K) + X(IX) = X(IX) - TEMP*A(L+I,J) + IX = IX + INCX + 70 CONTINUE + END IF + JX = JX + INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A' )*x or x := inv( conjg( A') )*x. +* + IF (LSAME(UPLO,'U')) THEN + KPLUS1 = K + 1 + IF (INCX.EQ.1) THEN + DO 110 J = 1,N + TEMP = X(J) + L = KPLUS1 - J + IF (NOCONJ) THEN + DO 90 I = MAX(1,J-K),J - 1 + TEMP = TEMP - A(L+I,J)*X(I) + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) + ELSE + DO 100 I = MAX(1,J-K),J - 1 + TEMP = TEMP - DCONJG(A(L+I,J))*X(I) + 100 CONTINUE + IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J)) + END IF + X(J) = TEMP + 110 CONTINUE + ELSE + JX = KX + DO 140 J = 1,N + TEMP = X(JX) + IX = KX + L = KPLUS1 - J + IF (NOCONJ) THEN + DO 120 I = MAX(1,J-K),J - 1 + TEMP = TEMP - A(L+I,J)*X(IX) + IX = IX + INCX + 120 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) + ELSE + DO 130 I = MAX(1,J-K),J - 1 + TEMP = TEMP - DCONJG(A(L+I,J))*X(IX) + IX = IX + INCX + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J)) + END IF + X(JX) = TEMP + JX = JX + INCX + IF (J.GT.K) KX = KX + INCX + 140 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 170 J = N,1,-1 + TEMP = X(J) + L = 1 - J + IF (NOCONJ) THEN + DO 150 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - A(L+I,J)*X(I) + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(1,J) + ELSE + DO 160 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - DCONJG(A(L+I,J))*X(I) + 160 CONTINUE + IF (NOUNIT) TEMP = TEMP/DCONJG(A(1,J)) + END IF + X(J) = TEMP + 170 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 200 J = N,1,-1 + TEMP = X(JX) + IX = KX + L = 1 - J + IF (NOCONJ) THEN + DO 180 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - A(L+I,J)*X(IX) + IX = IX - INCX + 180 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(1,J) + ELSE + DO 190 I = MIN(N,J+K),J + 1,-1 + TEMP = TEMP - DCONJG(A(L+I,J))*X(IX) + IX = IX - INCX + 190 CONTINUE + IF (NOUNIT) TEMP = TEMP/DCONJG(A(1,J)) + END IF + X(JX) = TEMP + JX = JX - INCX + IF ((N-J).GE.K) KX = KX - INCX + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of ZTBSV . +* + END diff --git a/blas/ztpmv.f b/blas/ztpmv.f new file mode 100644 index 000000000..5a7b3b8b7 --- /dev/null +++ b/blas/ztpmv.f @@ -0,0 +1,329 @@ + SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE COMPLEX AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* ZTPMV performs one of the matrix-vector operations +* +* x := A*x, or x := A'*x, or x := conjg( A' )*x, +* +* where x is an n element vector and A is an n by n unit, or non-unit, +* upper or lower triangular matrix, supplied in packed form. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the operation to be performed as +* follows: +* +* TRANS = 'N' or 'n' x := A*x. +* +* TRANS = 'T' or 't' x := A'*x. +* +* TRANS = 'C' or 'c' x := conjg( A' )*x. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* AP - COMPLEX*16 array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +* respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +* respectively, and so on. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced, but are assumed to be unity. +* Unchanged on exit. +* +* X - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element vector x. On exit, X is overwritten with the +* tranformed vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (INCX.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZTPMV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of AP are +* accessed sequentially with one pass through AP. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x:= A*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = 1 + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + K = KK + DO 10 I = 1,J - 1 + X(I) = X(I) + TEMP*AP(K) + K = K + 1 + 10 CONTINUE + IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) + END IF + KK = KK + J + 20 CONTINUE + ELSE + JX = KX + DO 40 J = 1,N + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + DO 30 K = KK,KK + J - 2 + X(IX) = X(IX) + TEMP*AP(K) + IX = IX + INCX + 30 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) + END IF + JX = JX + INCX + KK = KK + J + 40 CONTINUE + END IF + ELSE + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 60 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + TEMP = X(J) + K = KK + DO 50 I = N,J + 1,-1 + X(I) = X(I) + TEMP*AP(K) + K = K - 1 + 50 CONTINUE + IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) + END IF + KK = KK - (N-J+1) + 60 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 80 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + TEMP = X(JX) + IX = KX + DO 70 K = KK,KK - (N- (J+1)),-1 + X(IX) = X(IX) + TEMP*AP(K) + IX = IX - INCX + 70 CONTINUE + IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) + END IF + JX = JX - INCX + KK = KK - (N-J+1) + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := A'*x or x := conjg( A' )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 110 J = N,1,-1 + TEMP = X(J) + K = KK - 1 + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 90 I = J - 1,1,-1 + TEMP = TEMP + AP(K)*X(I) + K = K - 1 + 90 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) + DO 100 I = J - 1,1,-1 + TEMP = TEMP + DCONJG(AP(K))*X(I) + K = K - 1 + 100 CONTINUE + END IF + X(J) = TEMP + KK = KK - J + 110 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 140 J = N,1,-1 + TEMP = X(JX) + IX = JX + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 120 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + TEMP = TEMP + AP(K)*X(IX) + 120 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) + DO 130 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + TEMP = TEMP + DCONJG(AP(K))*X(IX) + 130 CONTINUE + END IF + X(JX) = TEMP + JX = JX - INCX + KK = KK - J + 140 CONTINUE + END IF + ELSE + KK = 1 + IF (INCX.EQ.1) THEN + DO 170 J = 1,N + TEMP = X(J) + K = KK + 1 + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 150 I = J + 1,N + TEMP = TEMP + AP(K)*X(I) + K = K + 1 + 150 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) + DO 160 I = J + 1,N + TEMP = TEMP + DCONJG(AP(K))*X(I) + K = K + 1 + 160 CONTINUE + END IF + X(J) = TEMP + KK = KK + (N-J+1) + 170 CONTINUE + ELSE + JX = KX + DO 200 J = 1,N + TEMP = X(JX) + IX = JX + IF (NOCONJ) THEN + IF (NOUNIT) TEMP = TEMP*AP(KK) + DO 180 K = KK + 1,KK + N - J + IX = IX + INCX + TEMP = TEMP + AP(K)*X(IX) + 180 CONTINUE + ELSE + IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) + DO 190 K = KK + 1,KK + N - J + IX = IX + INCX + TEMP = TEMP + DCONJG(AP(K))*X(IX) + 190 CONTINUE + END IF + X(JX) = TEMP + JX = JX + INCX + KK = KK + (N-J+1) + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of ZTPMV . +* + END diff --git a/blas/ztpsv.f b/blas/ztpsv.f new file mode 100644 index 000000000..b56e1d8c4 --- /dev/null +++ b/blas/ztpsv.f @@ -0,0 +1,332 @@ + SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE COMPLEX AP(*),X(*) +* .. +* +* Purpose +* ======= +* +* ZTPSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, or conjg( A' )*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular matrix, supplied in packed form. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' conjg( A' )*x = b. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit +* triangular as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* AP - COMPLEX*16 array of DIMENSION at least +* ( ( n*( n + 1 ) )/2 ). +* Before entry with UPLO = 'U' or 'u', the array AP must +* contain the upper triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +* respectively, and so on. +* Before entry with UPLO = 'L' or 'l', the array AP must +* contain the lower triangular matrix packed sequentially, +* column by column, so that AP( 1 ) contains a( 1, 1 ), +* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +* respectively, and so on. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced, but are assumed to be unity. +* Unchanged on exit. +* +* X - COMPLEX*16 array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ZERO + PARAMETER (ZERO= (0.0D+0,0.0D+0)) +* .. +* .. Local Scalars .. + DOUBLE COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,K,KK,KX + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN + INFO = 1 + ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + + .NOT.LSAME(TRANS,'C')) THEN + INFO = 2 + ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (INCX.EQ.0) THEN + INFO = 7 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('ZTPSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of AP are +* accessed sequentially with one pass through AP. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/AP(KK) + TEMP = X(J) + K = KK - 1 + DO 10 I = J - 1,1,-1 + X(I) = X(I) - TEMP*AP(K) + K = K - 1 + 10 CONTINUE + END IF + KK = KK - J + 20 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 40 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/AP(KK) + TEMP = X(JX) + IX = JX + DO 30 K = KK - 1,KK - J + 1,-1 + IX = IX - INCX + X(IX) = X(IX) - TEMP*AP(K) + 30 CONTINUE + END IF + JX = JX - INCX + KK = KK - J + 40 CONTINUE + END IF + ELSE + KK = 1 + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/AP(KK) + TEMP = X(J) + K = KK + 1 + DO 50 I = J + 1,N + X(I) = X(I) - TEMP*AP(K) + K = K + 1 + 50 CONTINUE + END IF + KK = KK + (N-J+1) + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/AP(KK) + TEMP = X(JX) + IX = JX + DO 70 K = KK + 1,KK + N - J + IX = IX + INCX + X(IX) = X(IX) - TEMP*AP(K) + 70 CONTINUE + END IF + JX = JX + INCX + KK = KK + (N-J+1) + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. +* + IF (LSAME(UPLO,'U')) THEN + KK = 1 + IF (INCX.EQ.1) THEN + DO 110 J = 1,N + TEMP = X(J) + K = KK + IF (NOCONJ) THEN + DO 90 I = 1,J - 1 + TEMP = TEMP - AP(K)*X(I) + K = K + 1 + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) + ELSE + DO 100 I = 1,J - 1 + TEMP = TEMP - DCONJG(AP(K))*X(I) + K = K + 1 + 100 CONTINUE + IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1)) + END IF + X(J) = TEMP + KK = KK + J + 110 CONTINUE + ELSE + JX = KX + DO 140 J = 1,N + TEMP = X(JX) + IX = KX + IF (NOCONJ) THEN + DO 120 K = KK,KK + J - 2 + TEMP = TEMP - AP(K)*X(IX) + IX = IX + INCX + 120 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) + ELSE + DO 130 K = KK,KK + J - 2 + TEMP = TEMP - DCONJG(AP(K))*X(IX) + IX = IX + INCX + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1)) + END IF + X(JX) = TEMP + JX = JX + INCX + KK = KK + J + 140 CONTINUE + END IF + ELSE + KK = (N* (N+1))/2 + IF (INCX.EQ.1) THEN + DO 170 J = N,1,-1 + TEMP = X(J) + K = KK + IF (NOCONJ) THEN + DO 150 I = N,J + 1,-1 + TEMP = TEMP - AP(K)*X(I) + K = K - 1 + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) + ELSE + DO 160 I = N,J + 1,-1 + TEMP = TEMP - DCONJG(AP(K))*X(I) + K = K - 1 + 160 CONTINUE + IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J)) + END IF + X(J) = TEMP + KK = KK - (N-J+1) + 170 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 200 J = N,1,-1 + TEMP = X(JX) + IX = KX + IF (NOCONJ) THEN + DO 180 K = KK,KK - (N- (J+1)),-1 + TEMP = TEMP - AP(K)*X(IX) + IX = IX - INCX + 180 CONTINUE + IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) + ELSE + DO 190 K = KK,KK - (N- (J+1)),-1 + TEMP = TEMP - DCONJG(AP(K))*X(IX) + IX = IX - INCX + 190 CONTINUE + IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J)) + END IF + X(JX) = TEMP + JX = JX - INCX + KK = KK - (N-J+1) + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of ZTPSV . +* + END |