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Annotation of rpl/lapack/lapack/dtrtrs.f, revision 1.8

1.1       bertrand    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: *
1.8     ! bertrand  139: *     Solve A * x = b  or  A**T * x = b.
1.1       bertrand  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