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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CSYT01 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 CSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, 00012 * RWORK, RESID ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER UPLO 00016 * INTEGER LDA, LDAFAC, LDC, N 00017 * REAL RESID 00018 * .. 00019 * .. Array Arguments .. 00020 * INTEGER IPIV( * ) 00021 * REAL RWORK( * ) 00022 * COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) 00023 * .. 00024 * 00025 * 00026 *> \par Purpose: 00027 * ============= 00028 *> 00029 *> \verbatim 00030 *> 00031 *> CSYT01 reconstructs a complex symmetric indefinite matrix A from its 00032 *> block L*D*L' or U*D*U' factorization and computes the residual 00033 *> norm( C - A ) / ( N * norm(A) * EPS ), 00034 *> where C is the reconstructed matrix, EPS is the machine epsilon, 00035 *> L' is the transpose of L, and U' is the transpose of U. 00036 *> \endverbatim 00037 * 00038 * Arguments: 00039 * ========== 00040 * 00041 *> \param[in] UPLO 00042 *> \verbatim 00043 *> UPLO is CHARACTER*1 00044 *> Specifies whether the upper or lower triangular part of the 00045 *> complex symmetric matrix A is stored: 00046 *> = 'U': Upper triangular 00047 *> = 'L': Lower triangular 00048 *> \endverbatim 00049 *> 00050 *> \param[in] N 00051 *> \verbatim 00052 *> N is INTEGER 00053 *> The number of rows and columns of the matrix A. N >= 0. 00054 *> \endverbatim 00055 *> 00056 *> \param[in] A 00057 *> \verbatim 00058 *> A is COMPLEX array, dimension (LDA,N) 00059 *> The original complex symmetric matrix A. 00060 *> \endverbatim 00061 *> 00062 *> \param[in] LDA 00063 *> \verbatim 00064 *> LDA is INTEGER 00065 *> The leading dimension of the array A. LDA >= max(1,N) 00066 *> \endverbatim 00067 *> 00068 *> \param[in] AFAC 00069 *> \verbatim 00070 *> AFAC is COMPLEX array, dimension (LDAFAC,N) 00071 *> The factored form of the matrix A. AFAC contains the block 00072 *> diagonal matrix D and the multipliers used to obtain the 00073 *> factor L or U from the block L*D*L' or U*D*U' factorization 00074 *> as computed by CSYTRF. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] LDAFAC 00078 *> \verbatim 00079 *> LDAFAC is INTEGER 00080 *> The leading dimension of the array AFAC. LDAFAC >= max(1,N). 00081 *> \endverbatim 00082 *> 00083 *> \param[in] IPIV 00084 *> \verbatim 00085 *> IPIV is INTEGER array, dimension (N) 00086 *> The pivot indices from CSYTRF. 00087 *> \endverbatim 00088 *> 00089 *> \param[out] C 00090 *> \verbatim 00091 *> C is COMPLEX array, dimension (LDC,N) 00092 *> \endverbatim 00093 *> 00094 *> \param[in] LDC 00095 *> \verbatim 00096 *> LDC is INTEGER 00097 *> The leading dimension of the array C. LDC >= max(1,N). 00098 *> \endverbatim 00099 *> 00100 *> \param[out] RWORK 00101 *> \verbatim 00102 *> RWORK is REAL array, dimension (N) 00103 *> \endverbatim 00104 *> 00105 *> \param[out] RESID 00106 *> \verbatim 00107 *> RESID is REAL 00108 *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) 00109 *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) 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 April 2012 00121 * 00122 *> \ingroup complex_lin 00123 * 00124 * ===================================================================== 00125 SUBROUTINE CSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, 00126 $ RWORK, RESID ) 00127 * 00128 * -- LAPACK test routine (version 3.4.1) -- 00129 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00131 * April 2012 00132 * 00133 * .. Scalar Arguments .. 00134 CHARACTER UPLO 00135 INTEGER LDA, LDAFAC, LDC, N 00136 REAL RESID 00137 * .. 00138 * .. Array Arguments .. 00139 INTEGER IPIV( * ) 00140 REAL RWORK( * ) 00141 COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) 00142 * .. 00143 * 00144 * ===================================================================== 00145 * 00146 * .. Parameters .. 00147 REAL ZERO, ONE 00148 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00149 COMPLEX CZERO, CONE 00150 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), 00151 $ CONE = ( 1.0E+0, 0.0E+0 ) ) 00152 * .. 00153 * .. Local Scalars .. 00154 INTEGER I, INFO, J 00155 REAL ANORM, EPS 00156 * .. 00157 * .. External Functions .. 00158 LOGICAL LSAME 00159 REAL CLANSY, SLAMCH 00160 EXTERNAL LSAME, CLANSY, SLAMCH 00161 * .. 00162 * .. External Subroutines .. 00163 EXTERNAL CLASET, CLAVSY 00164 * .. 00165 * .. Intrinsic Functions .. 00166 INTRINSIC REAL 00167 * .. 00168 * .. Executable Statements .. 00169 * 00170 * Quick exit if N = 0. 00171 * 00172 IF( N.LE.0 ) THEN 00173 RESID = ZERO 00174 RETURN 00175 END IF 00176 * 00177 * Determine EPS and the norm of A. 00178 * 00179 EPS = SLAMCH( 'Epsilon' ) 00180 ANORM = CLANSY( '1', UPLO, N, A, LDA, RWORK ) 00181 * 00182 * Initialize C to the identity matrix. 00183 * 00184 CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC ) 00185 * 00186 * Call CLAVSY to form the product D * U' (or D * L' ). 00187 * 00188 CALL CLAVSY( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, LDAFAC, 00189 $ IPIV, C, LDC, INFO ) 00190 * 00191 * Call CLAVSY again to multiply by U (or L ). 00192 * 00193 CALL CLAVSY( UPLO, 'No transpose', 'Unit', N, N, AFAC, LDAFAC, 00194 $ IPIV, C, LDC, INFO ) 00195 * 00196 * Compute the difference C - A . 00197 * 00198 IF( LSAME( UPLO, 'U' ) ) THEN 00199 DO 20 J = 1, N 00200 DO 10 I = 1, J 00201 C( I, J ) = C( I, J ) - A( I, J ) 00202 10 CONTINUE 00203 20 CONTINUE 00204 ELSE 00205 DO 40 J = 1, N 00206 DO 30 I = J, N 00207 C( I, J ) = C( I, J ) - A( I, J ) 00208 30 CONTINUE 00209 40 CONTINUE 00210 END IF 00211 * 00212 * Compute norm( C - A ) / ( N * norm(A) * EPS ) 00213 * 00214 RESID = CLANSY( '1', UPLO, N, C, LDC, RWORK ) 00215 * 00216 IF( ANORM.LE.ZERO ) THEN 00217 IF( RESID.NE.ZERO ) 00218 $ RESID = ONE / EPS 00219 ELSE 00220 RESID = ( ( RESID/REAL( N ) )/ANORM ) / EPS 00221 END IF 00222 * 00223 RETURN 00224 * 00225 * End of CSYT01 00226 * 00227 END