DTRTRS (3lapack)

solve a triangular system of the form A * X = B or A**T * X = B,

SYNOPSIS

  SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO )

      CHARACTER      DIAG, TRANS, UPLO

      INTEGER        INFO, LDA, LDB, N, NRHS

      DOUBLE         PRECISION A( LDA, * ), B( LDB, * )

PURPOSE

  DTRTRS solves a triangular system of the form

  where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.  A
  check is made to verify that A is nonsingular.

ARGUMENTS

  UPLO    (input) CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.

  TRANS   (input) CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

  DIAG    (input) CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.

  N       (input) INTEGER
          The order of the matrix A.  N >= 0.

  NRHS    (input) INTEGER
          The number of right hand sides, i.e., the number of columns of the
          matrix B.  NRHS >= 0.

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

  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.  On exit, if INFO = 0, the
          solution matrix X.

  LDB     (input) INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

  INFO    (output) INTEGER
          = 0:  successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
          > 0: if INFO = i, the i-th diagonal element of A is zero,
          indicating that the matrix is singular and the solutions X have not
          been computed.