DTRTRS  - 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 A * X = B or
       A**T * X = B, 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 lead­
               ing  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 refer­
               enced.  If UPLO = 'L', the  leading  N-by-N  lower
               triangular  part of the array A contains the lower
               triangular matrix, and the strictly upper triangu­
               lar  part  of A is not referenced.  If DIAG = 'U',
               the diagonal elements of A are also not referenced


       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  ille­
               gal 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.


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