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Diffstat (limited to 'blas/fortran/dtbmv.f')
| -rw-r--r-- | blas/fortran/dtbmv.f | 335 |
1 files changed, 335 insertions, 0 deletions
diff --git a/blas/fortran/dtbmv.f b/blas/fortran/dtbmv.f new file mode 100644 index 000000000..a87ffdeae --- /dev/null +++ b/blas/fortran/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 |