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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CPOT01 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 CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID ) 00012 * 00013 * .. Scalar Arguments .. 00014 * CHARACTER UPLO 00015 * INTEGER LDA, LDAFAC, N 00016 * REAL RESID 00017 * .. 00018 * .. Array Arguments .. 00019 * REAL RWORK( * ) 00020 * COMPLEX A( LDA, * ), AFAC( LDAFAC, * ) 00021 * .. 00022 * 00023 * 00024 *> \par Purpose: 00025 * ============= 00026 *> 00027 *> \verbatim 00028 *> 00029 *> CPOT01 reconstructs a Hermitian positive definite matrix A from 00030 *> its L*L' or U'*U factorization and computes the residual 00031 *> norm( L*L' - A ) / ( N * norm(A) * EPS ) or 00032 *> norm( U'*U - A ) / ( N * norm(A) * EPS ), 00033 *> where EPS is the machine epsilon, L' is the conjugate transpose of L, 00034 *> and U' is the conjugate transpose of U. 00035 *> \endverbatim 00036 * 00037 * Arguments: 00038 * ========== 00039 * 00040 *> \param[in] UPLO 00041 *> \verbatim 00042 *> UPLO is CHARACTER*1 00043 *> Specifies whether the upper or lower triangular part of the 00044 *> Hermitian matrix A is stored: 00045 *> = 'U': Upper triangular 00046 *> = 'L': Lower triangular 00047 *> \endverbatim 00048 *> 00049 *> \param[in] N 00050 *> \verbatim 00051 *> N is INTEGER 00052 *> The number of rows and columns of the matrix A. N >= 0. 00053 *> \endverbatim 00054 *> 00055 *> \param[in] A 00056 *> \verbatim 00057 *> A is COMPLEX array, dimension (LDA,N) 00058 *> The original Hermitian matrix A. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] LDA 00062 *> \verbatim 00063 *> LDA is INTEGER 00064 *> The leading dimension of the array A. LDA >= max(1,N) 00065 *> \endverbatim 00066 *> 00067 *> \param[in,out] AFAC 00068 *> \verbatim 00069 *> AFAC is COMPLEX array, dimension (LDAFAC,N) 00070 *> On entry, the factor L or U from the L*L' or U'*U 00071 *> factorization of A. 00072 *> Overwritten with the reconstructed matrix, and then with the 00073 *> difference L*L' - A (or U'*U - A). 00074 *> \endverbatim 00075 *> 00076 *> \param[in] LDAFAC 00077 *> \verbatim 00078 *> LDAFAC is INTEGER 00079 *> The leading dimension of the array AFAC. LDAFAC >= max(1,N). 00080 *> \endverbatim 00081 *> 00082 *> \param[out] RWORK 00083 *> \verbatim 00084 *> RWORK is REAL array, dimension (N) 00085 *> \endverbatim 00086 *> 00087 *> \param[out] RESID 00088 *> \verbatim 00089 *> RESID is REAL 00090 *> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) 00091 *> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) 00092 *> \endverbatim 00093 * 00094 * Authors: 00095 * ======== 00096 * 00097 *> \author Univ. of Tennessee 00098 *> \author Univ. of California Berkeley 00099 *> \author Univ. of Colorado Denver 00100 *> \author NAG Ltd. 00101 * 00102 *> \date November 2011 00103 * 00104 *> \ingroup complex_lin 00105 * 00106 * ===================================================================== 00107 SUBROUTINE CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID ) 00108 * 00109 * -- LAPACK test routine (version 3.4.0) -- 00110 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00111 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00112 * November 2011 00113 * 00114 * .. Scalar Arguments .. 00115 CHARACTER UPLO 00116 INTEGER LDA, LDAFAC, N 00117 REAL RESID 00118 * .. 00119 * .. Array Arguments .. 00120 REAL RWORK( * ) 00121 COMPLEX A( LDA, * ), AFAC( LDAFAC, * ) 00122 * .. 00123 * 00124 * ===================================================================== 00125 * 00126 * .. Parameters .. 00127 REAL ZERO, ONE 00128 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00129 * .. 00130 * .. Local Scalars .. 00131 INTEGER I, J, K 00132 REAL ANORM, EPS, TR 00133 COMPLEX TC 00134 * .. 00135 * .. External Functions .. 00136 LOGICAL LSAME 00137 REAL CLANHE, SLAMCH 00138 COMPLEX CDOTC 00139 EXTERNAL LSAME, CLANHE, SLAMCH, CDOTC 00140 * .. 00141 * .. External Subroutines .. 00142 EXTERNAL CHER, CSCAL, CTRMV 00143 * .. 00144 * .. Intrinsic Functions .. 00145 INTRINSIC AIMAG, REAL 00146 * .. 00147 * .. Executable Statements .. 00148 * 00149 * Quick exit if N = 0. 00150 * 00151 IF( N.LE.0 ) THEN 00152 RESID = ZERO 00153 RETURN 00154 END IF 00155 * 00156 * Exit with RESID = 1/EPS if ANORM = 0. 00157 * 00158 EPS = SLAMCH( 'Epsilon' ) 00159 ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK ) 00160 IF( ANORM.LE.ZERO ) THEN 00161 RESID = ONE / EPS 00162 RETURN 00163 END IF 00164 * 00165 * Check the imaginary parts of the diagonal elements and return with 00166 * an error code if any are nonzero. 00167 * 00168 DO 10 J = 1, N 00169 IF( AIMAG( AFAC( J, J ) ).NE.ZERO ) THEN 00170 RESID = ONE / EPS 00171 RETURN 00172 END IF 00173 10 CONTINUE 00174 * 00175 * Compute the product U'*U, overwriting U. 00176 * 00177 IF( LSAME( UPLO, 'U' ) ) THEN 00178 DO 20 K = N, 1, -1 00179 * 00180 * Compute the (K,K) element of the result. 00181 * 00182 TR = CDOTC( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 ) 00183 AFAC( K, K ) = TR 00184 * 00185 * Compute the rest of column K. 00186 * 00187 CALL CTRMV( 'Upper', 'Conjugate', 'Non-unit', K-1, AFAC, 00188 $ LDAFAC, AFAC( 1, K ), 1 ) 00189 * 00190 20 CONTINUE 00191 * 00192 * Compute the product L*L', overwriting L. 00193 * 00194 ELSE 00195 DO 30 K = N, 1, -1 00196 * 00197 * Add a multiple of column K of the factor L to each of 00198 * columns K+1 through N. 00199 * 00200 IF( K+1.LE.N ) 00201 $ CALL CHER( 'Lower', N-K, ONE, AFAC( K+1, K ), 1, 00202 $ AFAC( K+1, K+1 ), LDAFAC ) 00203 * 00204 * Scale column K by the diagonal element. 00205 * 00206 TC = AFAC( K, K ) 00207 CALL CSCAL( N-K+1, TC, AFAC( K, K ), 1 ) 00208 * 00209 30 CONTINUE 00210 END IF 00211 * 00212 * Compute the difference L*L' - A (or U'*U - A). 00213 * 00214 IF( LSAME( UPLO, 'U' ) ) THEN 00215 DO 50 J = 1, N 00216 DO 40 I = 1, J - 1 00217 AFAC( I, J ) = AFAC( I, J ) - A( I, J ) 00218 40 CONTINUE 00219 AFAC( J, J ) = AFAC( J, J ) - REAL( A( J, J ) ) 00220 50 CONTINUE 00221 ELSE 00222 DO 70 J = 1, N 00223 AFAC( J, J ) = AFAC( J, J ) - REAL( A( J, J ) ) 00224 DO 60 I = J + 1, N 00225 AFAC( I, J ) = AFAC( I, J ) - A( I, J ) 00226 60 CONTINUE 00227 70 CONTINUE 00228 END IF 00229 * 00230 * Compute norm( L*U - A ) / ( N * norm(A) * EPS ) 00231 * 00232 RESID = CLANHE( '1', UPLO, N, AFAC, LDAFAC, RWORK ) 00233 * 00234 RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS 00235 * 00236 RETURN 00237 * 00238 * End of CPOT01 00239 * 00240 END