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


SYNOPSIS

       SUBROUTINE DTPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB,
                          INFO )

           CHARACTER      DIAG, TRANS, UPLO

           INTEGER        INFO, LDB, N, NRHS

           DOUBLE         PRECISION AP( * ), B( LDB, * )


PURPOSE

       DTPTRS solves a triangular system of the form A * X = B or
       A**T * X = B, where A is a triangular matrix  of  order  N
       stored  in packed format, 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.

       AP      (input) DOUBLE PRECISION array, dimension
               (N*(N+1)/2)
               The  upper  or  lower  triangular matrix A, packed
               columnwise in a linear array.  The j-th column  of
               A  is stored in the array AP as follows: if UPLO =
               'U', AP(i + (j-1)*j/2) = A(i,j)  for  1<=i<=j;  if
               UPLO  =  'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for
               j<=i<=n.

               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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