tpmv(3)

NAME
tpmv - tpmv: triangular matrix-vector multiply

SYNOPSIS

  Functions

subroutine ctpmv (uplo, trans, diag, n, ap, x, incx)
CTPMV
subroutine dtpmv (uplo, trans, diag, n, ap, x, incx)
DTPMV
subroutine stpmv (uplo, trans, diag, n, ap, x, incx)
STPMV
subroutine ztpmv (uplo, trans, diag, n, ap, x, incx)
ZTPMV

Detailed Description

Function Documentation

  subroutine ctpmv (character uplo, character trans, character diag, integer n, complex, dimension(*) ap, complex, dimension(*) x, integer incx)

CTPMV

Purpose:

    !>
    !> CTPMV  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, supplied in packed form.
    !>

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.
    !>

    AP

    !>          AP is COMPLEX array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with  UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular matrix packed sequentially,
    !>           column by column, so that AP( 1 ) contains a( 1, 1 ),
    !>           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
    !>           respectively, and so on.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular matrix packed sequentially,
    !>           column by column, so that AP( 1 ) contains a( 1, 1 ),
    !>           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
    !>           respectively, and so on.
    !>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    !>           A are not referenced, but are assumed to be unity.
    !>

    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 dtpmv (character uplo, character trans, character diag, integer n, double precision, dimension(*) ap, double precision, dimension(*) x, integer incx)

DTPMV

Purpose:

    !>
    !> DTPMV  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, supplied in packed form.
    !>

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.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with  UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular matrix packed sequentially,
    !>           column by column, so that AP( 1 ) contains a( 1, 1 ),
    !>           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
    !>           respectively, and so on.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular matrix packed sequentially,
    !>           column by column, so that AP( 1 ) contains a( 1, 1 ),
    !>           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
    !>           respectively, and so on.
    !>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    !>           A are not referenced, but are assumed to be unity.
    !>

    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 stpmv (character uplo, character trans, character diag, integer n, real, dimension(*) ap, real, dimension(*) x, integer incx)

STPMV

Purpose:

    !>
    !> STPMV  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, supplied in packed form.
    !>

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.
    !>

    AP

    !>          AP is REAL array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with  UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular matrix packed sequentially,
    !>           column by column, so that AP( 1 ) contains a( 1, 1 ),
    !>           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
    !>           respectively, and so on.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular matrix packed sequentially,
    !>           column by column, so that AP( 1 ) contains a( 1, 1 ),
    !>           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
    !>           respectively, and so on.
    !>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    !>           A are not referenced, but are assumed to be unity.
    !>

    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 ztpmv (character uplo, character trans, character diag, integer n, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx)

ZTPMV

Purpose:

    !>
    !> ZTPMV  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, supplied in packed form.
    !>

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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension at least
    !>           ( ( n*( n + 1 ) )/2 ).
    !>           Before entry with  UPLO = 'U' or 'u', the array AP must
    !>           contain the upper triangular matrix packed sequentially,
    !>           column by column, so that AP( 1 ) contains a( 1, 1 ),
    !>           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
    !>           respectively, and so on.
    !>           Before entry with UPLO = 'L' or 'l', the array AP must
    !>           contain the lower triangular matrix packed sequentially,
    !>           column by column, so that AP( 1 ) contains a( 1, 1 ),
    !>           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
    !>           respectively, and so on.
    !>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    !>           A are not referenced, but are assumed to be unity.
    !>

    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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