tpsv(3)

NAME
tpsv - tpsv: triangular matrix-vector solve

SYNOPSIS

  Functions

subroutine ctpsv (uplo, trans, diag, n, ap, x, incx)
CTPSV
subroutine dtpsv (uplo, trans, diag, n, ap, x, incx)
DTPSV
subroutine stpsv (uplo, trans, diag, n, ap, x, incx)
STPSV
subroutine ztpsv (uplo, trans, diag, n, ap, x, incx)
ZTPSV

Detailed Description

Function Documentation

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

CTPSV

Purpose:

    !>
    !> CTPSV  solves one of the systems of equations
    !>
    !>    A*x = b,   or   A**T*x = b,   or   A**H*x = b,
    !>
    !> where b and x are n element vectors and A is an n by n unit, or
    !> non-unit, upper or lower triangular matrix, supplied in packed form.
    !>
    !> No test for singularity or near-singularity is included in this
    !> routine. Such tests must be performed before calling this routine.
    !>

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 equations to be solved as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   A*x = b.
    !>
    !>              TRANS = 'T' or 't'   A**T*x = b.
    !>
    !>              TRANS = 'C' or 'c'   A**H*x = b.
    !>

    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 right-hand side vector b. On exit, X is overwritten
    !>           with the solution 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.
    !>
    !>  -- 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 dtpsv (character uplo, character trans, character diag, integer n, double precision, dimension(*) ap, double precision, dimension(*) x, integer incx)

DTPSV

Purpose:

    !>
    !> DTPSV  solves one of the systems of equations
    !>
    !>    A*x = b,   or   A**T*x = b,
    !>
    !> where b and x are n element vectors and A is an n by n unit, or
    !> non-unit, upper or lower triangular matrix, supplied in packed form.
    !>
    !> No test for singularity or near-singularity is included in this
    !> routine. Such tests must be performed before calling this routine.
    !>

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 equations to be solved as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   A*x = b.
    !>
    !>              TRANS = 'T' or 't'   A**T*x = b.
    !>
    !>              TRANS = 'C' or 'c'   A**T*x = b.
    !>

    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 right-hand side vector b. On exit, X is overwritten
    !>           with the solution 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.
    !>
    !>  -- 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 stpsv (character uplo, character trans, character diag, integer n, real, dimension(*) ap, real, dimension(*) x, integer incx)

STPSV

Purpose:

    !>
    !> STPSV  solves one of the systems of equations
    !>
    !>    A*x = b,   or   A**T*x = b,
    !>
    !> where b and x are n element vectors and A is an n by n unit, or
    !> non-unit, upper or lower triangular matrix, supplied in packed form.
    !>
    !> No test for singularity or near-singularity is included in this
    !> routine. Such tests must be performed before calling this routine.
    !>

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 equations to be solved as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   A*x = b.
    !>
    !>              TRANS = 'T' or 't'   A**T*x = b.
    !>
    !>              TRANS = 'C' or 'c'   A**T*x = b.
    !>

    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 right-hand side vector b. On exit, X is overwritten
    !>           with the solution 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.
    !>
    !>  -- 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 ztpsv (character uplo, character trans, character diag, integer n, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx)

ZTPSV

Purpose:

    !>
    !> ZTPSV  solves one of the systems of equations
    !>
    !>    A*x = b,   or   A**T*x = b,   or   A**H*x = b,
    !>
    !> where b and x are n element vectors and A is an n by n unit, or
    !> non-unit, upper or lower triangular matrix, supplied in packed form.
    !>
    !> No test for singularity or near-singularity is included in this
    !> routine. Such tests must be performed before calling this routine.
    !>

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 equations to be solved as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   A*x = b.
    !>
    !>              TRANS = 'T' or 't'   A**T*x = b.
    !>
    !>              TRANS = 'C' or 'c'   A**H*x = b.
    !>

    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 right-hand side vector b. On exit, X is overwritten
    !>           with the solution 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.
    !>
    !>  -- 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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