LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztrtrs.f
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00001 *> \brief \b ZTRTRS
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00009 *> Download ZTRTRS + dependencies 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
00022 *                          INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          DIAG, TRANS, UPLO
00026 *       INTEGER            INFO, LDA, LDB, N, NRHS
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       COMPLEX*16         A( LDA, * ), B( LDB, * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> ZTRTRS solves a triangular system of the form
00039 *>
00040 *>    A * X = B,  A**T * X = B,  or  A**H * X = B,
00041 *>
00042 *> where A is a triangular matrix of order N, and B is an N-by-NRHS
00043 *> matrix.  A check is made to verify that A is nonsingular.
00044 *> \endverbatim
00045 *
00046 *  Arguments:
00047 *  ==========
00048 *
00049 *> \param[in] UPLO
00050 *> \verbatim
00051 *>          UPLO is CHARACTER*1
00052 *>          = 'U':  A is upper triangular;
00053 *>          = 'L':  A is lower triangular.
00054 *> \endverbatim
00055 *>
00056 *> \param[in] TRANS
00057 *> \verbatim
00058 *>          TRANS is CHARACTER*1
00059 *>          Specifies the form of the system of equations:
00060 *>          = 'N':  A * X = B     (No transpose)
00061 *>          = 'T':  A**T * X = B  (Transpose)
00062 *>          = 'C':  A**H * X = B  (Conjugate transpose)
00063 *> \endverbatim
00064 *>
00065 *> \param[in] DIAG
00066 *> \verbatim
00067 *>          DIAG is CHARACTER*1
00068 *>          = 'N':  A is non-unit triangular;
00069 *>          = 'U':  A is unit triangular.
00070 *> \endverbatim
00071 *>
00072 *> \param[in] N
00073 *> \verbatim
00074 *>          N is INTEGER
00075 *>          The order of the matrix A.  N >= 0.
00076 *> \endverbatim
00077 *>
00078 *> \param[in] NRHS
00079 *> \verbatim
00080 *>          NRHS is INTEGER
00081 *>          The number of right hand sides, i.e., the number of columns
00082 *>          of the matrix B.  NRHS >= 0.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] A
00086 *> \verbatim
00087 *>          A is COMPLEX*16 array, dimension (LDA,N)
00088 *>          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
00089 *>          upper triangular part of the array A contains the upper
00090 *>          triangular matrix, and the strictly lower triangular part of
00091 *>          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
00092 *>          triangular part of the array A contains the lower triangular
00093 *>          matrix, and the strictly upper triangular part of A is not
00094 *>          referenced.  If DIAG = 'U', the diagonal elements of A are
00095 *>          also not referenced and are assumed to be 1.
00096 *> \endverbatim
00097 *>
00098 *> \param[in] LDA
00099 *> \verbatim
00100 *>          LDA is INTEGER
00101 *>          The leading dimension of the array A.  LDA >= max(1,N).
00102 *> \endverbatim
00103 *>
00104 *> \param[in,out] B
00105 *> \verbatim
00106 *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
00107 *>          On entry, the right hand side matrix B.
00108 *>          On exit, if INFO = 0, the solution matrix X.
00109 *> \endverbatim
00110 *>
00111 *> \param[in] LDB
00112 *> \verbatim
00113 *>          LDB is INTEGER
00114 *>          The leading dimension of the array B.  LDB >= max(1,N).
00115 *> \endverbatim
00116 *>
00117 *> \param[out] INFO
00118 *> \verbatim
00119 *>          INFO is INTEGER
00120 *>          = 0:  successful exit
00121 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00122 *>          > 0: if INFO = i, the i-th diagonal element of A is zero,
00123 *>               indicating that the matrix is singular and the solutions
00124 *>               X have not been computed.
00125 *> \endverbatim
00126 *
00127 *  Authors:
00128 *  ========
00129 *
00130 *> \author Univ. of Tennessee 
00131 *> \author Univ. of California Berkeley 
00132 *> \author Univ. of Colorado Denver 
00133 *> \author NAG Ltd. 
00134 *
00135 *> \date November 2011
00136 *
00137 *> \ingroup complex16OTHERcomputational
00138 *
00139 *  =====================================================================
00140       SUBROUTINE ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
00141      $                   INFO )
00142 *
00143 *  -- LAPACK computational routine (version 3.4.0) --
00144 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00145 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00146 *     November 2011
00147 *
00148 *     .. Scalar Arguments ..
00149       CHARACTER          DIAG, TRANS, UPLO
00150       INTEGER            INFO, LDA, LDB, N, NRHS
00151 *     ..
00152 *     .. Array Arguments ..
00153       COMPLEX*16         A( LDA, * ), B( LDB, * )
00154 *     ..
00155 *
00156 *  =====================================================================
00157 *
00158 *     .. Parameters ..
00159       COMPLEX*16         ZERO, ONE
00160       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
00161      $                   ONE = ( 1.0D+0, 0.0D+0 ) )
00162 *     ..
00163 *     .. Local Scalars ..
00164       LOGICAL            NOUNIT
00165 *     ..
00166 *     .. External Functions ..
00167       LOGICAL            LSAME
00168       EXTERNAL           LSAME
00169 *     ..
00170 *     .. External Subroutines ..
00171       EXTERNAL           XERBLA, ZTRSM
00172 *     ..
00173 *     .. Intrinsic Functions ..
00174       INTRINSIC          MAX
00175 *     ..
00176 *     .. Executable Statements ..
00177 *
00178 *     Test the input parameters.
00179 *
00180       INFO = 0
00181       NOUNIT = LSAME( DIAG, 'N' )
00182       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00183          INFO = -1
00184       ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
00185      $         LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
00186          INFO = -2
00187       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
00188          INFO = -3
00189       ELSE IF( N.LT.0 ) THEN
00190          INFO = -4
00191       ELSE IF( NRHS.LT.0 ) THEN
00192          INFO = -5
00193       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00194          INFO = -7
00195       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00196          INFO = -9
00197       END IF
00198       IF( INFO.NE.0 ) THEN
00199          CALL XERBLA( 'ZTRTRS', -INFO )
00200          RETURN
00201       END IF
00202 *
00203 *     Quick return if possible
00204 *
00205       IF( N.EQ.0 )
00206      $   RETURN
00207 *
00208 *     Check for singularity.
00209 *
00210       IF( NOUNIT ) THEN
00211          DO 10 INFO = 1, N
00212             IF( A( INFO, INFO ).EQ.ZERO )
00213      $         RETURN
00214    10    CONTINUE
00215       END IF
00216       INFO = 0
00217 *
00218 *     Solve A * x = b,  A**T * x = b,  or  A**H * x = b.
00219 *
00220       CALL ZTRSM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
00221      $            LDB )
00222 *
00223       RETURN
00224 *
00225 *     End of ZTRTRS
00226 *
00227       END
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