Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       gemv - gemv: general matrix-vector multiply

SYNOPSIS

   Functions
       subroutine cgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
           CGEMV
       subroutine dgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
           DGEMV
       subroutine sgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
           SGEMV
       subroutine zgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
           ZGEMV

Detailed Description

Function Documentation

   subroutine cgemv (character trans, integer m, integer n, complex alpha, complex,
       dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx, complex beta,
       complex, dimension(*) y, integer incy)
       CGEMV

       Purpose:

            CGEMV performs one of the matrix-vector operations

               y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or

               y := alpha*A**H*x + beta*y,

            where alpha and beta are scalars, x and y are vectors and A is an
            m by n matrix.

       Parameters
           TRANS

                     TRANS is 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**T*x + beta*y.

                         TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.

           M

                     M is INTEGER
                      On entry, M specifies the number of rows of the matrix A.
                      M must be at least zero.

           N

                     N is INTEGER
                      On entry, N specifies the number of columns of the matrix A.
                      N must be at least zero.

           ALPHA

                     ALPHA is COMPLEX
                      On entry, ALPHA specifies the scalar alpha.

           A

                     A is COMPLEX array, dimension ( LDA, N )
                      Before entry, the leading m by n part of the array A must
                      contain the matrix of coefficients.

           LDA

                     LDA is INTEGER
                      On entry, LDA specifies the first dimension of A as declared
                      in the calling (sub) program. LDA must be at least
                      max( 1, m ).

           X

                     X is COMPLEX array, 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.

           INCX

                     INCX is INTEGER
                      On entry, INCX specifies the increment for the elements of
                      X. INCX must not be zero.

           BETA

                     BETA is COMPLEX
                      On entry, BETA specifies the scalar beta. When BETA is
                      supplied as zero then Y need not be set on input.

           Y

                     Y is COMPLEX array, dimension at least
                      ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
                      and at least
                      ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
                      Before entry with BETA non-zero, the incremented array Y
                      must contain the vector y. On exit, Y is overwritten by the
                      updated vector y.
                      If either m or n is zero, then Y not referenced and the function
                      performs a quick return.

           INCY

                     INCY is INTEGER
                      On entry, INCY specifies the increment for the elements of
                      Y. INCY must not be zero.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

   subroutine dgemv (character trans, integer m, integer n, double precision alpha, double
       precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer
       incx, double precision beta, double precision, dimension(*) y, integer incy)
       DGEMV

       Purpose:

            DGEMV  performs one of the matrix-vector operations

               y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,

            where alpha and beta are scalars, x and y are vectors and A is an
            m by n matrix.

       Parameters
           TRANS

                     TRANS is 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**T*x + beta*y.

                         TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.

           M

                     M is INTEGER
                      On entry, M specifies the number of rows of the matrix A.
                      M must be at least zero.

           N

                     N is INTEGER
                      On entry, N specifies the number of columns of the matrix A.
                      N must be at least zero.

           ALPHA

                     ALPHA is DOUBLE PRECISION.
                      On entry, ALPHA specifies the scalar alpha.

           A

                     A is DOUBLE PRECISION array, dimension ( LDA, N )
                      Before entry, the leading m by n part of the array A must
                      contain the matrix of coefficients.

           LDA

                     LDA is INTEGER
                      On entry, LDA specifies the first dimension of A as declared
                      in the calling (sub) program. LDA must be at least
                      max( 1, m ).

           X

                     X is DOUBLE PRECISION array, 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.

           INCX

                     INCX is INTEGER
                      On entry, INCX specifies the increment for the elements of
                      X. INCX must not be zero.

           BETA

                     BETA is DOUBLE PRECISION.
                      On entry, BETA specifies the scalar beta. When BETA is
                      supplied as zero then Y need not be set on input.

           Y

                     Y is DOUBLE PRECISION array, dimension at least
                      ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
                      and at least
                      ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
                      Before entry with BETA non-zero, the incremented array Y
                      must contain the vector y. On exit, Y is overwritten by the
                      updated vector y.
                      If either m or n is zero, then Y not referenced and the function
                      performs a quick return.

           INCY

                     INCY is INTEGER
                      On entry, INCY specifies the increment for the elements of
                      Y. INCY must not be zero.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

   subroutine sgemv (character trans, integer m, integer n, real alpha, real, dimension(lda,*) a,
       integer lda, real, dimension(*) x, integer incx, real beta, real, dimension(*) y, integer
       incy)
       SGEMV

       Purpose:

            SGEMV  performs one of the matrix-vector operations

               y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,

            where alpha and beta are scalars, x and y are vectors and A is an
            m by n matrix.

       Parameters
           TRANS

                     TRANS is 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**T*x + beta*y.

                         TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.

           M

                     M is INTEGER
                      On entry, M specifies the number of rows of the matrix A.
                      M must be at least zero.

           N

                     N is INTEGER
                      On entry, N specifies the number of columns of the matrix A.
                      N must be at least zero.

           ALPHA

                     ALPHA is REAL
                      On entry, ALPHA specifies the scalar alpha.

           A

                     A is REAL array, dimension ( LDA, N )
                      Before entry, the leading m by n part of the array A must
                      contain the matrix of coefficients.

           LDA

                     LDA is INTEGER
                      On entry, LDA specifies the first dimension of A as declared
                      in the calling (sub) program. LDA must be at least
                      max( 1, m ).

           X

                     X is REAL array, 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.

           INCX

                     INCX is INTEGER
                      On entry, INCX specifies the increment for the elements of
                      X. INCX must not be zero.

           BETA

                     BETA is REAL
                      On entry, BETA specifies the scalar beta. When BETA is
                      supplied as zero then Y need not be set on input.

           Y

                     Y is REAL array, dimension at least
                      ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
                      and at least
                      ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
                      Before entry with BETA non-zero, the incremented array Y
                      must contain the vector y. On exit, Y is overwritten by the
                      updated vector y.
                      If either m or n is zero, then Y not referenced and the function
                      performs a quick return.

           INCY

                     INCY is INTEGER
                      On entry, INCY specifies the increment for the elements of
                      Y. INCY must not be zero.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

   subroutine zgemv (character trans, integer m, integer n, complex*16 alpha, complex*16,
       dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16
       beta, complex*16, dimension(*) y, integer incy)
       ZGEMV

       Purpose:

            ZGEMV  performs one of the matrix-vector operations

               y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or

               y := alpha*A**H*x + beta*y,

            where alpha and beta are scalars, x and y are vectors and A is an
            m by n matrix.

       Parameters
           TRANS

                     TRANS is 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**T*x + beta*y.

                         TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.

           M

                     M is INTEGER
                      On entry, M specifies the number of rows of the matrix A.
                      M must be at least zero.

           N

                     N is INTEGER
                      On entry, N specifies the number of columns of the matrix A.
                      N must be at least zero.

           ALPHA

                     ALPHA is COMPLEX*16
                      On entry, ALPHA specifies the scalar alpha.

           A

                     A is COMPLEX*16 array, dimension ( LDA, N )
                      Before entry, the leading m by n part of the array A must
                      contain the matrix of coefficients.

           LDA

                     LDA is INTEGER
                      On entry, LDA specifies the first dimension of A as declared
                      in the calling (sub) program. LDA must be at least
                      max( 1, m ).

           X

                     X is COMPLEX*16 array, 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.

           INCX

                     INCX is INTEGER
                      On entry, INCX specifies the increment for the elements of
                      X. INCX must not be zero.

           BETA

                     BETA is COMPLEX*16
                      On entry, BETA specifies the scalar beta. When BETA is
                      supplied as zero then Y need not be set on input.

           Y

                     Y is COMPLEX*16 array, dimension at least
                      ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
                      and at least
                      ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
                      Before entry with BETA non-zero, the incremented array Y
                      must contain the vector y. On exit, Y is overwritten by the
                      updated vector y.
                      If either m or n is zero, then Y not referenced and the function
                      performs a quick return.

           INCY

                     INCY is INTEGER
                      On entry, INCY specifies the increment for the elements of
                      Y. INCY must not be zero.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

Author

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