trmv(3)

NAME
trmv - trmv: triangular matrix-vector multiply

SYNOPSIS

  Functions

subroutine ctrmv (uplo, trans, diag, n, a, lda, x, incx)
CTRMV
subroutine dtrmv (uplo, trans, diag, n, a, lda, x, incx)
DTRMV
subroutine strmv (uplo, trans, diag, n, a, lda, x, incx)
STRMV
subroutine ztrmv (uplo, trans, diag, n, a, lda, x, incx)
ZTRMV

Detailed Description

Function Documentation

  subroutine ctrmv (character uplo, character trans, character diag, integer n, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx)

CTRMV

Purpose:

    !>
    !> CTRMV  performs one of the matrix-vector operations
    !>
    !>    x := A*x,   or   x := A**T*x,   or   x := A**H*x,
    !>
    !> where x is an n element vector and  A is an n by n unit, or non-unit,
    !> upper or lower triangular matrix.
    !>

Parameters
    UPLO

    !>          UPLO is 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.
    !>

    TRANS

    !>          TRANS is 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**T*x.
    !>
    !>              TRANS = 'C' or 'c'   x := A**H*x.
    !>

    DIAG

    !>          DIAG is 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.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the order of the matrix A.
    !>           N must be at least zero.
    !>

    A

    !>          A is COMPLEX array, dimension ( LDA, N ).
    !>           Before entry with  UPLO = 'U' or 'u', the leading n by n
    !>           upper triangular part of the array A must contain the upper
    !>           triangular matrix and the strictly lower triangular part of
    !>           A is not referenced.
    !>           Before entry with UPLO = 'L' or 'l', the leading n by n
    !>           lower triangular part of the array A must contain the lower
    !>           triangular matrix and the strictly upper triangular part of
    !>           A is not referenced.
    !>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    !>           A are not referenced either, but are assumed to be unity.
    !>

    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, n ).
    !>

    X

    !>          X is COMPLEX array, 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
    !>           transformed vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX 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 dtrmv (character uplo, character trans, character diag, integer n, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx)

DTRMV

Purpose:

    !>
    !> DTRMV  performs one of the matrix-vector operations
    !>
    !>    x := A*x,   or   x := A**T*x,
    !>
    !> where x is an n element vector and  A is an n by n unit, or non-unit,
    !> upper or lower triangular matrix.
    !>

Parameters
    UPLO

    !>          UPLO is 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.
    !>

    TRANS

    !>          TRANS is 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**T*x.
    !>
    !>              TRANS = 'C' or 'c'   x := A**T*x.
    !>

    DIAG

    !>          DIAG is 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.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the order of the matrix A.
    !>           N must be at least zero.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension ( LDA, N )
    !>           Before entry with  UPLO = 'U' or 'u', the leading n by n
    !>           upper triangular part of the array A must contain the upper
    !>           triangular matrix and the strictly lower triangular part of
    !>           A is not referenced.
    !>           Before entry with UPLO = 'L' or 'l', the leading n by n
    !>           lower triangular part of the array A must contain the lower
    !>           triangular matrix and the strictly upper triangular part of
    !>           A is not referenced.
    !>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    !>           A are not referenced either, but are assumed to be unity.
    !>

    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, n ).
    !>

    X

    !>          X is DOUBLE PRECISION array, 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
    !>           transformed vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX 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 strmv (character uplo, character trans, character diag, integer n, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx)

STRMV

Purpose:

    !>
    !> STRMV  performs one of the matrix-vector operations
    !>
    !>    x := A*x,   or   x := A**T*x,
    !>
    !> where x is an n element vector and  A is an n by n unit, or non-unit,
    !> upper or lower triangular matrix.
    !>

Parameters
    UPLO

    !>          UPLO is 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.
    !>

    TRANS

    !>          TRANS is 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**T*x.
    !>
    !>              TRANS = 'C' or 'c'   x := A**T*x.
    !>

    DIAG

    !>          DIAG is 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.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the order of the matrix A.
    !>           N must be at least zero.
    !>

    A

    !>          A is REAL array, dimension ( LDA, N )
    !>           Before entry with  UPLO = 'U' or 'u', the leading n by n
    !>           upper triangular part of the array A must contain the upper
    !>           triangular matrix and the strictly lower triangular part of
    !>           A is not referenced.
    !>           Before entry with UPLO = 'L' or 'l', the leading n by n
    !>           lower triangular part of the array A must contain the lower
    !>           triangular matrix and the strictly upper triangular part of
    !>           A is not referenced.
    !>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    !>           A are not referenced either, but are assumed to be unity.
    !>

    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, n ).
    !>

    X

    !>          X is REAL array, 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
    !>           transformed vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX 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 ztrmv (character uplo, character trans, character diag, integer n, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTRMV

Purpose:

    !>
    !> ZTRMV  performs one of the matrix-vector operations
    !>
    !>    x := A*x,   or   x := A**T*x,   or   x := A**H*x,
    !>
    !> where x is an n element vector and  A is an n by n unit, or non-unit,
    !> upper or lower triangular matrix.
    !>

Parameters
    UPLO

    !>          UPLO is 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.
    !>

    TRANS

    !>          TRANS is 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**T*x.
    !>
    !>              TRANS = 'C' or 'c'   x := A**H*x.
    !>

    DIAG

    !>          DIAG is 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.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the order of the matrix A.
    !>           N must be at least zero.
    !>

    A

    !>          A is COMPLEX*16 array, dimension ( LDA, N ).
    !>           Before entry with  UPLO = 'U' or 'u', the leading n by n
    !>           upper triangular part of the array A must contain the upper
    !>           triangular matrix and the strictly lower triangular part of
    !>           A is not referenced.
    !>           Before entry with UPLO = 'L' or 'l', the leading n by n
    !>           lower triangular part of the array A must contain the lower
    !>           triangular matrix and the strictly upper triangular part of
    !>           A is not referenced.
    !>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    !>           A are not referenced either, but are assumed to be unity.
    !>

    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, n ).
    !>

    X

    !>          X is COMPLEX*16 array, 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
    !>           transformed vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX 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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