From 7aaae9d6dfbb57390a4ab9370a3553e7e1501fdd Mon Sep 17 00:00:00 2001 From: Gael Guennebaud Date: Thu, 1 Dec 2011 18:10:12 +0100 Subject: remove useless blas reference code --- blas/ctbsv.f | 370 ----------------------------------------------------------- blas/dtbsv.f | 339 ------------------------------------------------------ blas/stbsv.f | 339 ------------------------------------------------------ blas/ztbsv.f | 370 ----------------------------------------------------------- 4 files changed, 1418 deletions(-) delete mode 100644 blas/ctbsv.f delete mode 100644 blas/dtbsv.f delete mode 100644 blas/stbsv.f delete mode 100644 blas/ztbsv.f (limited to 'blas') diff --git a/blas/ctbsv.f b/blas/ctbsv.f deleted file mode 100644 index 853b9d75e..000000000 --- a/blas/ctbsv.f +++ /dev/null @@ -1,370 +0,0 @@ - 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/dtbsv.f b/blas/dtbsv.f deleted file mode 100644 index cfeb0b82b..000000000 --- a/blas/dtbsv.f +++ /dev/null @@ -1,339 +0,0 @@ - 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/stbsv.f b/blas/stbsv.f deleted file mode 100644 index b846be85c..000000000 --- a/blas/stbsv.f +++ /dev/null @@ -1,339 +0,0 @@ - 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/ztbsv.f b/blas/ztbsv.f deleted file mode 100644 index 42b234a77..000000000 --- a/blas/ztbsv.f +++ /dev/null @@ -1,370 +0,0 @@ - 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 -- cgit v1.2.3