SRC/dlatrs3.f(3)

NAME
SRC/dlatrs3.f

SYNOPSIS

  Functions/Subroutines
subroutine dlatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info)
DLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

Function/Subroutine Documentation

  subroutine dlatrs3 (character uplo, character trans, character diag, character normin, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) scale, double precision, dimension( * ) cnorm, double precision, dimension( * ) work, integer lwork, integer info)

DLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

Purpose:

     DLATRS3 solves one of the triangular systems
        A * X = B * diag(scale)  or  A**T * X = B * diag(scale)
     with scaling to prevent overflow.  Here A is an upper or lower
     triangular matrix, A**T denotes the transpose of A. X and B are
     n by nrhs matrices and scale is an nrhs element vector of scaling
     factors. A scaling factor scale(j) is usually less than or equal
     to 1, chosen such that X(:,j) is less than the overflow threshold.
     If the matrix A is singular (A(j,j) = 0 for some j), then
     a non-trivial solution to A*X = 0 is returned. If the system is
     so badly scaled that the solution cannot be represented as
     (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.
     This is a BLAS-3 version of LATRS for solving several right
     hand sides simultaneously.

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the matrix A is upper or lower triangular.
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    TRANS

              TRANS is CHARACTER*1
              Specifies the operation applied to A.
              = 'N':  Solve A * x = s*b  (No transpose)
              = 'T':  Solve A**T* x = s*b  (Transpose)
              = 'C':  Solve A**T* x = s*b  (Conjugate transpose = Transpose)

    DIAG

              DIAG is CHARACTER*1
              Specifies whether or not the matrix A is unit triangular.
              = 'N':  Non-unit triangular
              = 'U':  Unit triangular

    NORMIN

              NORMIN is CHARACTER*1
              Specifies whether CNORM has been set or not.
              = 'Y':  CNORM contains the column norms on entry
              = 'N':  CNORM is not set on entry.  On exit, the norms will
                      be computed and stored in CNORM.

    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    NRHS

              NRHS is INTEGER
              The number of columns of X.  NRHS >= 0.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              The triangular matrix A.  If UPLO = 'U', the leading n by n
              upper triangular part of the array A contains the upper
              triangular matrix, and the strictly lower triangular part of
              A is not referenced.  If UPLO = 'L', the leading n by n lower
              triangular part of the array A contains the lower triangular
              matrix, and the strictly upper triangular part of A is not
              referenced.  If DIAG = 'U', the diagonal elements of A are
              also not referenced and are assumed to be 1.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max (1,N).

    X

              X is DOUBLE PRECISION array, dimension (LDX,NRHS)
              On entry, the right hand side B of the triangular system.
              On exit, X is overwritten by the solution matrix X.

    LDX

              LDX is INTEGER
              The leading dimension of the array X.  LDX >= max (1,N).

    SCALE

              SCALE is DOUBLE PRECISION array, dimension (NRHS)
              The scaling factor s(k) is for the triangular system
              A * x(:,k) = s(k)*b(:,k)  or  A**T* x(:,k) = s(k)*b(:,k).
              If SCALE = 0, the matrix A is singular or badly scaled.
              If A(j,j) = 0 is encountered, a non-trivial vector x(:,k)
              that is an exact or approximate solution to A*x(:,k) = 0
              is returned. If the system so badly scaled that solution
              cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0
              is returned.

    CNORM

              CNORM is DOUBLE PRECISION array, dimension (N)
              If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
              contains the norm of the off-diagonal part of the j-th column
              of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
              to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
              must be greater than or equal to the 1-norm.
              If NORMIN = 'N', CNORM is an output argument and CNORM(j)
              returns the 1-norm of the offdiagonal part of the j-th column
              of A.

    WORK

              WORK is DOUBLE PRECISION array, dimension (LWORK).
              On exit, if INFO = 0, WORK(1) returns the optimal size of
              WORK.

    LWORK LWORK is INTEGER LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where NBA = (N + NB - 1)/NB and NB is the optimal block size.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal dimensions of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

Parameters
    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -k, the k-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

Definition at line 227 of file dlatrs3.f.

Author

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