--- rpl/lapack/blas/zhbmv.f 2011/07/22 07:38:03 1.7 +++ rpl/lapack/blas/zhbmv.f 2023/08/07 08:38:45 1.16 @@ -1,147 +1,213 @@ +*> \brief \b ZHBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER INCX,INCY,K,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> 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. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is 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. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of super-diagonals of the +*> matrix A. K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array, 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. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array, dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX*16 array, 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. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup complex16_blas_level2 +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- 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. +*> \endverbatim +*> +* ===================================================================== SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* -- Reference BLAS level2 routine -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* * .. Scalar Arguments .. - DOUBLE COMPLEX ALPHA,BETA + COMPLEX*16 ALPHA,BETA INTEGER INCX,INCY,K,LDA,N CHARACTER UPLO * .. * .. Array Arguments .. - DOUBLE COMPLEX A(LDA,*),X(*),Y(*) + COMPLEX*16 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. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 -* -* -- 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 + COMPLEX*16 ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) - DOUBLE COMPLEX ZERO + COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. - DOUBLE COMPLEX TEMP1,TEMP2 + COMPLEX*16 TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L * .. * .. External Functions .. @@ -306,6 +372,6 @@ * RETURN * -* End of ZHBMV . +* End of ZHBMV * END