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    1:       SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
    2:      $                   INFO )
    3: *
    4: *  -- LAPACK routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          DIAG, TRANS, UPLO
   11:       INTEGER            INFO, LDA, LDB, N, NRHS
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  DTRTRS solves a triangular system of the form
   21: *
   22: *     A * X = B  or  A**T * X = B,
   23: *
   24: *  where A is a triangular matrix of order N, and B is an N-by-NRHS
   25: *  matrix.  A check is made to verify that A is nonsingular.
   26: *
   27: *  Arguments
   28: *  =========
   29: *
   30: *  UPLO    (input) CHARACTER*1
   31: *          = 'U':  A is upper triangular;
   32: *          = 'L':  A is lower triangular.
   33: *
   34: *  TRANS   (input) CHARACTER*1
   35: *          Specifies the form of the system of equations:
   36: *          = 'N':  A * X = B  (No transpose)
   37: *          = 'T':  A**T * X = B  (Transpose)
   38: *          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
   39: *
   40: *  DIAG    (input) CHARACTER*1
   41: *          = 'N':  A is non-unit triangular;
   42: *          = 'U':  A is unit triangular.
   43: *
   44: *  N       (input) INTEGER
   45: *          The order of the matrix A.  N >= 0.
   46: *
   47: *  NRHS    (input) INTEGER
   48: *          The number of right hand sides, i.e., the number of columns
   49: *          of the matrix B.  NRHS >= 0.
   50: *
   51: *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
   52: *          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
   53: *          upper triangular part of the array A contains the upper
   54: *          triangular matrix, and the strictly lower triangular part of
   55: *          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
   56: *          triangular part of the array A contains the lower triangular
   57: *          matrix, and the strictly upper triangular part of A is not
   58: *          referenced.  If DIAG = 'U', the diagonal elements of A are
   59: *          also not referenced and are assumed to be 1.
   60: *
   61: *  LDA     (input) INTEGER
   62: *          The leading dimension of the array A.  LDA >= max(1,N).
   63: *
   64: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
   65: *          On entry, the right hand side matrix B.
   66: *          On exit, if INFO = 0, the solution matrix X.
   67: *
   68: *  LDB     (input) INTEGER
   69: *          The leading dimension of the array B.  LDB >= max(1,N).
   70: *
   71: *  INFO    (output) INTEGER
   72: *          = 0:  successful exit
   73: *          < 0: if INFO = -i, the i-th argument had an illegal value
   74: *          > 0: if INFO = i, the i-th diagonal element of A is zero,
   75: *               indicating that the matrix is singular and the solutions
   76: *               X have not been computed.
   77: *
   78: *  =====================================================================
   79: *
   80: *     .. Parameters ..
   81:       DOUBLE PRECISION   ZERO, ONE
   82:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
   83: *     ..
   84: *     .. Local Scalars ..
   85:       LOGICAL            NOUNIT
   86: *     ..
   87: *     .. External Functions ..
   88:       LOGICAL            LSAME
   89:       EXTERNAL           LSAME
   90: *     ..
   91: *     .. External Subroutines ..
   92:       EXTERNAL           DTRSM, XERBLA
   93: *     ..
   94: *     .. Intrinsic Functions ..
   95:       INTRINSIC          MAX
   96: *     ..
   97: *     .. Executable Statements ..
   98: *
   99: *     Test the input parameters.
  100: *
  101:       INFO = 0
  102:       NOUNIT = LSAME( DIAG, 'N' )
  103:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  104:          INFO = -1
  105:       ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
  106:      $         LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
  107:          INFO = -2
  108:       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
  109:          INFO = -3
  110:       ELSE IF( N.LT.0 ) THEN
  111:          INFO = -4
  112:       ELSE IF( NRHS.LT.0 ) THEN
  113:          INFO = -5
  114:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  115:          INFO = -7
  116:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  117:          INFO = -9
  118:       END IF
  119:       IF( INFO.NE.0 ) THEN
  120:          CALL XERBLA( 'DTRTRS', -INFO )
  121:          RETURN
  122:       END IF
  123: *
  124: *     Quick return if possible
  125: *
  126:       IF( N.EQ.0 )
  127:      $   RETURN
  128: *
  129: *     Check for singularity.
  130: *
  131:       IF( NOUNIT ) THEN
  132:          DO 10 INFO = 1, N
  133:             IF( A( INFO, INFO ).EQ.ZERO )
  134:      $         RETURN
  135:    10    CONTINUE
  136:       END IF
  137:       INFO = 0
  138: *
  139: *     Solve A * x = b  or  A' * x = b.
  140: *
  141:       CALL DTRSM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
  142:      $            LDB )
  143: *
  144:       RETURN
  145: *
  146: *     End of DTRTRS
  147: *
  148:       END