gbmv(3)

NAME
gbmv - gbmv: general matrix-vector multiply

SYNOPSIS

  Functions

subroutine cgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
CGBMV
subroutine dgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
DGBMV
subroutine sgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
SGBMV
subroutine zgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
ZGBMV

Detailed Description

Function Documentation

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

CGBMV

Purpose:

    !>
    !> CGBMV  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 band matrix, with kl sub-diagonals and ku super-diagonals.
    !>

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.
    !>

    KL

    !>          KL is INTEGER
    !>           On entry, KL specifies the number of sub-diagonals of the
    !>           matrix A. KL must satisfy  0 .le. KL.
    !>

    KU

    !>          KU is INTEGER
    !>           On entry, KU specifies the number of super-diagonals of the
    !>           matrix A. KU must satisfy  0 .le. KU.
    !>

    ALPHA

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

    A

    !>          A is COMPLEX array, 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
    !>

    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
    !>           ( kl + ku + 1 ).
    !>

    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, 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 dgbmv (character trans, integer m, integer n, integer kl, integer ku, 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)

DGBMV

Purpose:

    !>
    !> DGBMV  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 band matrix, with kl sub-diagonals and ku super-diagonals.
    !>

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.
    !>

    KL

    !>          KL is INTEGER
    !>           On entry, KL specifies the number of sub-diagonals of the
    !>           matrix A. KL must satisfy  0 .le. KL.
    !>

    KU

    !>          KU is INTEGER
    !>           On entry, KU specifies the number of super-diagonals of the
    !>           matrix A. KU must satisfy  0 .le. KU.
    !>

    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 ( 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
    !>

    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
    !>           ( kl + ku + 1 ).
    !>

    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, 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 sgbmv (character trans, integer m, integer n, integer kl, integer ku, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx, real beta, real, dimension(*) y, integer incy)

SGBMV

Purpose:

    !>
    !> SGBMV  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 band matrix, with kl sub-diagonals and ku super-diagonals.
    !>

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.
    !>

    KL

    !>          KL is INTEGER
    !>           On entry, KL specifies the number of sub-diagonals of the
    !>           matrix A. KL must satisfy  0 .le. KL.
    !>

    KU

    !>          KU is INTEGER
    !>           On entry, KU specifies the number of super-diagonals of the
    !>           matrix A. KU must satisfy  0 .le. KU.
    !>

    ALPHA

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

    A

    !>          A is REAL array, 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
    !>

    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
    !>           ( kl + ku + 1 ).
    !>

    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, 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 zgbmv (character trans, integer m, integer n, integer kl, integer ku, 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)

ZGBMV

Purpose:

    !>
    !> ZGBMV  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 band matrix, with kl sub-diagonals and ku super-diagonals.
    !>

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.
    !>

    KL

    !>          KL is INTEGER
    !>           On entry, KL specifies the number of sub-diagonals of the
    !>           matrix A. KL must satisfy  0 .le. KL.
    !>

    KU

    !>          KU is INTEGER
    !>           On entry, KU specifies the number of super-diagonals of the
    !>           matrix A. KU must satisfy  0 .le. KU.
    !>

    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 ( 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
    !>

    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
    !>           ( kl + ku + 1 ).
    !>

    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, 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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