![]() |
LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
|
00001 *> \brief \b CSPT02 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE CSPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, 00012 * RESID ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER UPLO 00016 * INTEGER LDB, LDX, N, NRHS 00017 * REAL RESID 00018 * .. 00019 * .. Array Arguments .. 00020 * REAL RWORK( * ) 00021 * COMPLEX A( * ), B( LDB, * ), X( LDX, * ) 00022 * .. 00023 * 00024 * 00025 *> \par Purpose: 00026 * ============= 00027 *> 00028 *> \verbatim 00029 *> 00030 *> CSPT02 computes the residual in the solution of a complex symmetric 00031 *> system of linear equations A*x = b when packed storage is used for 00032 *> the coefficient matrix. The ratio computed is 00033 *> 00034 *> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS). 00035 *> 00036 *> where EPS is the machine precision. 00037 *> \endverbatim 00038 * 00039 * Arguments: 00040 * ========== 00041 * 00042 *> \param[in] UPLO 00043 *> \verbatim 00044 *> UPLO is CHARACTER*1 00045 *> Specifies whether the upper or lower triangular part of the 00046 *> complex symmetric matrix A is stored: 00047 *> = 'U': Upper triangular 00048 *> = 'L': Lower triangular 00049 *> \endverbatim 00050 *> 00051 *> \param[in] N 00052 *> \verbatim 00053 *> N is INTEGER 00054 *> The number of rows and columns of the matrix A. N >= 0. 00055 *> \endverbatim 00056 *> 00057 *> \param[in] NRHS 00058 *> \verbatim 00059 *> NRHS is INTEGER 00060 *> The number of columns of B, the matrix of right hand sides. 00061 *> NRHS >= 0. 00062 *> \endverbatim 00063 *> 00064 *> \param[in] A 00065 *> \verbatim 00066 *> A is COMPLEX array, dimension (N*(N+1)/2) 00067 *> The original complex symmetric matrix A, stored as a packed 00068 *> triangular matrix. 00069 *> \endverbatim 00070 *> 00071 *> \param[in] X 00072 *> \verbatim 00073 *> X is COMPLEX array, dimension (LDX,NRHS) 00074 *> The computed solution vectors for the system of linear 00075 *> equations. 00076 *> \endverbatim 00077 *> 00078 *> \param[in] LDX 00079 *> \verbatim 00080 *> LDX is INTEGER 00081 *> The leading dimension of the array X. LDX >= max(1,N). 00082 *> \endverbatim 00083 *> 00084 *> \param[in,out] B 00085 *> \verbatim 00086 *> B is COMPLEX array, dimension (LDB,NRHS) 00087 *> On entry, the right hand side vectors for the system of 00088 *> linear equations. 00089 *> On exit, B is overwritten with the difference B - A*X. 00090 *> \endverbatim 00091 *> 00092 *> \param[in] LDB 00093 *> \verbatim 00094 *> LDB is INTEGER 00095 *> The leading dimension of the array B. LDB >= max(1,N). 00096 *> \endverbatim 00097 *> 00098 *> \param[out] RWORK 00099 *> \verbatim 00100 *> RWORK is REAL array, dimension (N) 00101 *> \endverbatim 00102 *> 00103 *> \param[out] RESID 00104 *> \verbatim 00105 *> RESID is REAL 00106 *> The maximum over the number of right hand sides of 00107 *> norm(B - A*X) / ( norm(A) * norm(X) * EPS ). 00108 *> \endverbatim 00109 * 00110 * Authors: 00111 * ======== 00112 * 00113 *> \author Univ. of Tennessee 00114 *> \author Univ. of California Berkeley 00115 *> \author Univ. of Colorado Denver 00116 *> \author NAG Ltd. 00117 * 00118 *> \date November 2011 00119 * 00120 *> \ingroup complex_lin 00121 * 00122 * ===================================================================== 00123 SUBROUTINE CSPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, 00124 $ RESID ) 00125 * 00126 * -- LAPACK test routine (version 3.4.0) -- 00127 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00129 * November 2011 00130 * 00131 * .. Scalar Arguments .. 00132 CHARACTER UPLO 00133 INTEGER LDB, LDX, N, NRHS 00134 REAL RESID 00135 * .. 00136 * .. Array Arguments .. 00137 REAL RWORK( * ) 00138 COMPLEX A( * ), B( LDB, * ), X( LDX, * ) 00139 * .. 00140 * 00141 * ===================================================================== 00142 * 00143 * .. Parameters .. 00144 REAL ZERO, ONE 00145 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00146 COMPLEX CONE 00147 PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) 00148 * .. 00149 * .. Local Scalars .. 00150 INTEGER J 00151 REAL ANORM, BNORM, EPS, XNORM 00152 * .. 00153 * .. External Functions .. 00154 REAL CLANSP, SCASUM, SLAMCH 00155 EXTERNAL CLANSP, SCASUM, SLAMCH 00156 * .. 00157 * .. External Subroutines .. 00158 EXTERNAL CSPMV 00159 * .. 00160 * .. Intrinsic Functions .. 00161 INTRINSIC MAX 00162 * .. 00163 * .. Executable Statements .. 00164 * 00165 * Quick exit if N = 0 or NRHS = 0 00166 * 00167 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 00168 RESID = ZERO 00169 RETURN 00170 END IF 00171 * 00172 * Exit with RESID = 1/EPS if ANORM = 0. 00173 * 00174 EPS = SLAMCH( 'Epsilon' ) 00175 ANORM = CLANSP( '1', UPLO, N, A, RWORK ) 00176 IF( ANORM.LE.ZERO ) THEN 00177 RESID = ONE / EPS 00178 RETURN 00179 END IF 00180 * 00181 * Compute B - A*X for the matrix of right hand sides B. 00182 * 00183 DO 10 J = 1, NRHS 00184 CALL CSPMV( UPLO, N, -CONE, A, X( 1, J ), 1, CONE, B( 1, J ), 00185 $ 1 ) 00186 10 CONTINUE 00187 * 00188 * Compute the maximum over the number of right hand sides of 00189 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) . 00190 * 00191 RESID = ZERO 00192 DO 20 J = 1, NRHS 00193 BNORM = SCASUM( N, B( 1, J ), 1 ) 00194 XNORM = SCASUM( N, X( 1, J ), 1 ) 00195 IF( XNORM.LE.ZERO ) THEN 00196 RESID = ONE / EPS 00197 ELSE 00198 RESID = MAX( RESID, ( ( BNORM/ANORM )/XNORM )/EPS ) 00199 END IF 00200 20 CONTINUE 00201 * 00202 RETURN 00203 * 00204 * End of CSPT02 00205 * 00206 END