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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CHPT01 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 CHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID ) 00012 * 00013 * .. Scalar Arguments .. 00014 * CHARACTER UPLO 00015 * INTEGER LDC, N 00016 * REAL RESID 00017 * .. 00018 * .. Array Arguments .. 00019 * INTEGER IPIV( * ) 00020 * REAL RWORK( * ) 00021 * COMPLEX A( * ), AFAC( * ), C( LDC, * ) 00022 * .. 00023 * 00024 * 00025 *> \par Purpose: 00026 * ============= 00027 *> 00028 *> \verbatim 00029 *> 00030 *> CHPT01 reconstructs a Hermitian indefinite packed matrix A from its 00031 *> block L*D*L' or U*D*U' factorization and computes the residual 00032 *> norm( C - A ) / ( N * norm(A) * EPS ), 00033 *> where C is the reconstructed matrix, EPS is the machine epsilon, 00034 *> L' is the conjugate transpose of L, and U' is the conjugate transpose 00035 *> 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 *> Hermitian 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 (N*(N+1)/2) 00059 *> The original Hermitian matrix A, stored as a packed 00060 *> triangular matrix. 00061 *> \endverbatim 00062 *> 00063 *> \param[in] AFAC 00064 *> \verbatim 00065 *> AFAC is COMPLEX array, dimension (N*(N+1)/2) 00066 *> The factored form of the matrix A, stored as a packed 00067 *> triangular matrix. AFAC contains the block diagonal matrix D 00068 *> and the multipliers used to obtain the factor L or U from the 00069 *> block L*D*L' or U*D*U' factorization as computed by CHPTRF. 00070 *> \endverbatim 00071 *> 00072 *> \param[in] IPIV 00073 *> \verbatim 00074 *> IPIV is INTEGER array, dimension (N) 00075 *> The pivot indices from CHPTRF. 00076 *> \endverbatim 00077 *> 00078 *> \param[out] C 00079 *> \verbatim 00080 *> C is COMPLEX array, dimension (LDC,N) 00081 *> \endverbatim 00082 *> 00083 *> \param[in] LDC 00084 *> \verbatim 00085 *> LDC is INTEGER 00086 *> The leading dimension of the array C. LDC >= max(1,N). 00087 *> \endverbatim 00088 *> 00089 *> \param[out] RWORK 00090 *> \verbatim 00091 *> RWORK is REAL array, dimension (N) 00092 *> \endverbatim 00093 *> 00094 *> \param[out] RESID 00095 *> \verbatim 00096 *> RESID is REAL 00097 *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) 00098 *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) 00099 *> \endverbatim 00100 * 00101 * Authors: 00102 * ======== 00103 * 00104 *> \author Univ. of Tennessee 00105 *> \author Univ. of California Berkeley 00106 *> \author Univ. of Colorado Denver 00107 *> \author NAG Ltd. 00108 * 00109 *> \date November 2011 00110 * 00111 *> \ingroup complex_lin 00112 * 00113 * ===================================================================== 00114 SUBROUTINE CHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID ) 00115 * 00116 * -- LAPACK test routine (version 3.4.0) -- 00117 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00119 * November 2011 00120 * 00121 * .. Scalar Arguments .. 00122 CHARACTER UPLO 00123 INTEGER LDC, N 00124 REAL RESID 00125 * .. 00126 * .. Array Arguments .. 00127 INTEGER IPIV( * ) 00128 REAL RWORK( * ) 00129 COMPLEX A( * ), AFAC( * ), C( LDC, * ) 00130 * .. 00131 * 00132 * ===================================================================== 00133 * 00134 * .. Parameters .. 00135 REAL ZERO, ONE 00136 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00137 COMPLEX CZERO, CONE 00138 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), 00139 $ CONE = ( 1.0E+0, 0.0E+0 ) ) 00140 * .. 00141 * .. Local Scalars .. 00142 INTEGER I, INFO, J, JC 00143 REAL ANORM, EPS 00144 * .. 00145 * .. External Functions .. 00146 LOGICAL LSAME 00147 REAL CLANHE, CLANHP, SLAMCH 00148 EXTERNAL LSAME, CLANHE, CLANHP, SLAMCH 00149 * .. 00150 * .. External Subroutines .. 00151 EXTERNAL CLAVHP, CLASET 00152 * .. 00153 * .. Intrinsic Functions .. 00154 INTRINSIC AIMAG, REAL 00155 * .. 00156 * .. Executable Statements .. 00157 * 00158 * Quick exit if N = 0. 00159 * 00160 IF( N.LE.0 ) THEN 00161 RESID = ZERO 00162 RETURN 00163 END IF 00164 * 00165 * Determine EPS and the norm of A. 00166 * 00167 EPS = SLAMCH( 'Epsilon' ) 00168 ANORM = CLANHP( '1', UPLO, N, A, RWORK ) 00169 * 00170 * Check the imaginary parts of the diagonal elements and return with 00171 * an error code if any are nonzero. 00172 * 00173 JC = 1 00174 IF( LSAME( UPLO, 'U' ) ) THEN 00175 DO 10 J = 1, N 00176 IF( AIMAG( AFAC( JC ) ).NE.ZERO ) THEN 00177 RESID = ONE / EPS 00178 RETURN 00179 END IF 00180 JC = JC + J + 1 00181 10 CONTINUE 00182 ELSE 00183 DO 20 J = 1, N 00184 IF( AIMAG( AFAC( JC ) ).NE.ZERO ) THEN 00185 RESID = ONE / EPS 00186 RETURN 00187 END IF 00188 JC = JC + N - J + 1 00189 20 CONTINUE 00190 END IF 00191 * 00192 * Initialize C to the identity matrix. 00193 * 00194 CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC ) 00195 * 00196 * Call CLAVHP to form the product D * U' (or D * L' ). 00197 * 00198 CALL CLAVHP( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, IPIV, C, 00199 $ LDC, INFO ) 00200 * 00201 * Call CLAVHP again to multiply by U ( or L ). 00202 * 00203 CALL CLAVHP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C, 00204 $ LDC, INFO ) 00205 * 00206 * Compute the difference C - A . 00207 * 00208 IF( LSAME( UPLO, 'U' ) ) THEN 00209 JC = 0 00210 DO 40 J = 1, N 00211 DO 30 I = 1, J - 1 00212 C( I, J ) = C( I, J ) - A( JC+I ) 00213 30 CONTINUE 00214 C( J, J ) = C( J, J ) - REAL( A( JC+J ) ) 00215 JC = JC + J 00216 40 CONTINUE 00217 ELSE 00218 JC = 1 00219 DO 60 J = 1, N 00220 C( J, J ) = C( J, J ) - REAL( A( JC ) ) 00221 DO 50 I = J + 1, N 00222 C( I, J ) = C( I, J ) - A( JC+I-J ) 00223 50 CONTINUE 00224 JC = JC + N - J + 1 00225 60 CONTINUE 00226 END IF 00227 * 00228 * Compute norm( C - A ) / ( N * norm(A) * EPS ) 00229 * 00230 RESID = CLANHE( '1', UPLO, N, C, LDC, RWORK ) 00231 * 00232 IF( ANORM.LE.ZERO ) THEN 00233 IF( RESID.NE.ZERO ) 00234 $ RESID = ONE / EPS 00235 ELSE 00236 RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS 00237 END IF 00238 * 00239 RETURN 00240 * 00241 * End of CHPT01 00242 * 00243 END