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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief <b> CPPSV computes the solution to system of linear equations A * X = B for OTHER 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 CPPSV + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cppsv.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cppsv.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cppsv.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDB, N, NRHS 00026 * .. 00027 * .. Array Arguments .. 00028 * COMPLEX AP( * ), B( LDB, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> CPPSV 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 stored in 00040 *> packed format and X and B 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] AP 00075 *> \verbatim 00076 *> AP is COMPLEX array, dimension (N*(N+1)/2) 00077 *> On entry, the upper or lower triangle of the Hermitian matrix 00078 *> A, packed columnwise in a linear array. The j-th column of A 00079 *> is stored in the array AP as follows: 00080 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00081 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00082 *> See below for further details. 00083 *> 00084 *> On exit, if INFO = 0, the factor U or L from the Cholesky 00085 *> factorization A = U**H*U or A = L*L**H, in the same storage 00086 *> format as A. 00087 *> \endverbatim 00088 *> 00089 *> \param[in,out] B 00090 *> \verbatim 00091 *> B is COMPLEX array, dimension (LDB,NRHS) 00092 *> On entry, the N-by-NRHS right hand side matrix B. 00093 *> On exit, if INFO = 0, the N-by-NRHS solution matrix X. 00094 *> \endverbatim 00095 *> 00096 *> \param[in] LDB 00097 *> \verbatim 00098 *> LDB is INTEGER 00099 *> The leading dimension of the array B. LDB >= max(1,N). 00100 *> \endverbatim 00101 *> 00102 *> \param[out] INFO 00103 *> \verbatim 00104 *> INFO is INTEGER 00105 *> = 0: successful exit 00106 *> < 0: if INFO = -i, the i-th argument had an illegal value 00107 *> > 0: if INFO = i, the leading minor of order i of A is not 00108 *> positive definite, so the factorization could not be 00109 *> completed, and the solution has not been computed. 00110 *> \endverbatim 00111 * 00112 * Authors: 00113 * ======== 00114 * 00115 *> \author Univ. of Tennessee 00116 *> \author Univ. of California Berkeley 00117 *> \author Univ. of Colorado Denver 00118 *> \author NAG Ltd. 00119 * 00120 *> \date November 2011 00121 * 00122 *> \ingroup complexOTHERsolve 00123 * 00124 *> \par Further Details: 00125 * ===================== 00126 *> 00127 *> \verbatim 00128 *> 00129 *> The packed storage scheme is illustrated by the following example 00130 *> when N = 4, UPLO = 'U': 00131 *> 00132 *> Two-dimensional storage of the Hermitian matrix A: 00133 *> 00134 *> a11 a12 a13 a14 00135 *> a22 a23 a24 00136 *> a33 a34 (aij = conjg(aji)) 00137 *> a44 00138 *> 00139 *> Packed storage of the upper triangle of A: 00140 *> 00141 *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] 00142 *> \endverbatim 00143 *> 00144 * ===================================================================== 00145 SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO ) 00146 * 00147 * -- LAPACK driver routine (version 3.4.0) -- 00148 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00150 * November 2011 00151 * 00152 * .. Scalar Arguments .. 00153 CHARACTER UPLO 00154 INTEGER INFO, LDB, N, NRHS 00155 * .. 00156 * .. Array Arguments .. 00157 COMPLEX AP( * ), B( LDB, * ) 00158 * .. 00159 * 00160 * ===================================================================== 00161 * 00162 * .. External Functions .. 00163 LOGICAL LSAME 00164 EXTERNAL LSAME 00165 * .. 00166 * .. External Subroutines .. 00167 EXTERNAL CPPTRF, CPPTRS, XERBLA 00168 * .. 00169 * .. Intrinsic Functions .. 00170 INTRINSIC MAX 00171 * .. 00172 * .. Executable Statements .. 00173 * 00174 * Test the input parameters. 00175 * 00176 INFO = 0 00177 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00178 INFO = -1 00179 ELSE IF( N.LT.0 ) THEN 00180 INFO = -2 00181 ELSE IF( NRHS.LT.0 ) THEN 00182 INFO = -3 00183 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00184 INFO = -6 00185 END IF 00186 IF( INFO.NE.0 ) THEN 00187 CALL XERBLA( 'CPPSV ', -INFO ) 00188 RETURN 00189 END IF 00190 * 00191 * Compute the Cholesky factorization A = U**H *U or A = L*L**H. 00192 * 00193 CALL CPPTRF( UPLO, N, AP, INFO ) 00194 IF( INFO.EQ.0 ) THEN 00195 * 00196 * Solve the system A*X = B, overwriting B with X. 00197 * 00198 CALL CPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO ) 00199 * 00200 END IF 00201 RETURN 00202 * 00203 * End of CPPSV 00204 * 00205 END