LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zposv.f
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00001 *> \brief <b> ZPOSV computes the solution to system of linear equations A * X = B for PO matrices</b>
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZPOSV + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zposv.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, LDA, LDB, N, NRHS
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX*16         A( LDA, * ), B( LDB, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> ZPOSV computes the solution to a complex system of linear equations
00038 *>    A * X = B,
00039 *> where A is an N-by-N Hermitian positive definite matrix and X and B
00040 *> are N-by-NRHS matrices.
00041 *>
00042 *> The Cholesky decomposition is used to factor A as
00043 *>    A = U**H* U,  if UPLO = 'U', or
00044 *>    A = L * L**H,  if UPLO = 'L',
00045 *> where U is an upper triangular matrix and  L is a lower triangular
00046 *> matrix.  The factored form of A is then used to solve the system of
00047 *> equations A * X = B.
00048 *> \endverbatim
00049 *
00050 *  Arguments:
00051 *  ==========
00052 *
00053 *> \param[in] UPLO
00054 *> \verbatim
00055 *>          UPLO is CHARACTER*1
00056 *>          = 'U':  Upper triangle of A is stored;
00057 *>          = 'L':  Lower triangle of A is stored.
00058 *> \endverbatim
00059 *>
00060 *> \param[in] N
00061 *> \verbatim
00062 *>          N is INTEGER
00063 *>          The number of linear equations, i.e., the order of the
00064 *>          matrix A.  N >= 0.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] NRHS
00068 *> \verbatim
00069 *>          NRHS is INTEGER
00070 *>          The number of right hand sides, i.e., the number of columns
00071 *>          of the matrix B.  NRHS >= 0.
00072 *> \endverbatim
00073 *>
00074 *> \param[in,out] A
00075 *> \verbatim
00076 *>          A is COMPLEX*16 array, dimension (LDA,N)
00077 *>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
00078 *>          N-by-N upper triangular part of A contains the upper
00079 *>          triangular part of the matrix A, and the strictly lower
00080 *>          triangular part of A is not referenced.  If UPLO = 'L', the
00081 *>          leading N-by-N lower triangular part of A contains the lower
00082 *>          triangular part of the matrix A, and the strictly upper
00083 *>          triangular part of A is not referenced.
00084 *>
00085 *>          On exit, if INFO = 0, the factor U or L from the Cholesky
00086 *>          factorization A = U**H *U or A = L*L**H.
00087 *> \endverbatim
00088 *>
00089 *> \param[in] LDA
00090 *> \verbatim
00091 *>          LDA is INTEGER
00092 *>          The leading dimension of the array A.  LDA >= max(1,N).
00093 *> \endverbatim
00094 *>
00095 *> \param[in,out] B
00096 *> \verbatim
00097 *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
00098 *>          On entry, the N-by-NRHS right hand side matrix B.
00099 *>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
00100 *> \endverbatim
00101 *>
00102 *> \param[in] LDB
00103 *> \verbatim
00104 *>          LDB is INTEGER
00105 *>          The leading dimension of the array B.  LDB >= max(1,N).
00106 *> \endverbatim
00107 *>
00108 *> \param[out] INFO
00109 *> \verbatim
00110 *>          INFO is INTEGER
00111 *>          = 0:  successful exit
00112 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00113 *>          > 0:  if INFO = i, the leading minor of order i of A is not
00114 *>                positive definite, so the factorization could not be
00115 *>                completed, and the solution has not been computed.
00116 *> \endverbatim
00117 *
00118 *  Authors:
00119 *  ========
00120 *
00121 *> \author Univ. of Tennessee 
00122 *> \author Univ. of California Berkeley 
00123 *> \author Univ. of Colorado Denver 
00124 *> \author NAG Ltd. 
00125 *
00126 *> \date November 2011
00127 *
00128 *> \ingroup complex16POsolve
00129 *
00130 *  =====================================================================
00131       SUBROUTINE ZPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
00132 *
00133 *  -- LAPACK driver routine (version 3.4.0) --
00134 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00135 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00136 *     November 2011
00137 *
00138 *     .. Scalar Arguments ..
00139       CHARACTER          UPLO
00140       INTEGER            INFO, LDA, LDB, N, NRHS
00141 *     ..
00142 *     .. Array Arguments ..
00143       COMPLEX*16         A( LDA, * ), B( LDB, * )
00144 *     ..
00145 *
00146 *  =====================================================================
00147 *
00148 *     .. External Functions ..
00149       LOGICAL            LSAME
00150       EXTERNAL           LSAME
00151 *     ..
00152 *     .. External Subroutines ..
00153       EXTERNAL           XERBLA, ZPOTRF, ZPOTRS
00154 *     ..
00155 *     .. Intrinsic Functions ..
00156       INTRINSIC          MAX
00157 *     ..
00158 *     .. Executable Statements ..
00159 *
00160 *     Test the input parameters.
00161 *
00162       INFO = 0
00163       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00164          INFO = -1
00165       ELSE IF( N.LT.0 ) THEN
00166          INFO = -2
00167       ELSE IF( NRHS.LT.0 ) THEN
00168          INFO = -3
00169       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00170          INFO = -5
00171       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00172          INFO = -7
00173       END IF
00174       IF( INFO.NE.0 ) THEN
00175          CALL XERBLA( 'ZPOSV ', -INFO )
00176          RETURN
00177       END IF
00178 *
00179 *     Compute the Cholesky factorization A = U**H *U or A = L*L**H.
00180 *
00181       CALL ZPOTRF( UPLO, N, A, LDA, INFO )
00182       IF( INFO.EQ.0 ) THEN
00183 *
00184 *        Solve the system A*X = B, overwriting B with X.
00185 *
00186          CALL ZPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
00187 *
00188       END IF
00189       RETURN
00190 *
00191 *     End of ZPOSV
00192 *
00193       END
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