trsv(3)

NAME
trsv - trsv: triangular matrix-vector solve

SYNOPSIS

  Functions

subroutine ctrsv (uplo, trans, diag, n, a, lda, x, incx)
CTRSV
subroutine dtrsv (uplo, trans, diag, n, a, lda, x, incx)
DTRSV
subroutine strsv (uplo, trans, diag, n, a, lda, x, incx)
STRSV
subroutine ztrsv (uplo, trans, diag, n, a, lda, x, incx)
ZTRSV

Detailed Description

Function Documentation

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

CTRSV

Purpose:

    !>
    !> CTRSV  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.
    !>
    !> 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.
    !>

    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 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 dtrsv (character uplo, character trans, character diag, integer n, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx)

DTRSV

Purpose:

    !>
    !> DTRSV  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.
    !>
    !> 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.
    !>

    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 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.
    !>
    !>  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
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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

STRSV

Purpose:

    !>
    !> STRSV  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.
    !>
    !> 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.
    !>

    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 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 ztrsv (character uplo, character trans, character diag, integer n, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTRSV

Purpose:

    !>
    !> ZTRSV  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.
    !>
    !> 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.
    !>

    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 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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