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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZSPT01 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 ZSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID ) 00012 * 00013 * .. Scalar Arguments .. 00014 * CHARACTER UPLO 00015 * INTEGER LDC, N 00016 * DOUBLE PRECISION RESID 00017 * .. 00018 * .. Array Arguments .. 00019 * INTEGER IPIV( * ) 00020 * DOUBLE PRECISION RWORK( * ) 00021 * COMPLEX*16 A( * ), AFAC( * ), C( LDC, * ) 00022 * .. 00023 * 00024 * 00025 *> \par Purpose: 00026 * ============= 00027 *> 00028 *> \verbatim 00029 *> 00030 *> ZSPT01 reconstructs a symmetric indefinite packed matrix A from its 00031 *> diagonal pivoting factorization A = U*D*U' or A = L*D*L' and computes 00032 *> the residual 00033 *> norm( C - A ) / ( N * norm(A) * EPS ), 00034 *> where C is the reconstructed matrix and EPS is the machine epsilon. 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 order of the matrix A. N >= 0. 00053 *> \endverbatim 00054 *> 00055 *> \param[in] A 00056 *> \verbatim 00057 *> A is COMPLEX*16 array, dimension (N*(N+1)/2) 00058 *> The original symmetric matrix A, stored as a packed 00059 *> triangular matrix. 00060 *> \endverbatim 00061 *> 00062 *> \param[in] AFAC 00063 *> \verbatim 00064 *> AFAC is COMPLEX*16 array, dimension (N*(N+1)/2) 00065 *> The factored form of the matrix A, stored as a packed 00066 *> triangular matrix. AFAC contains the block diagonal matrix D 00067 *> and the multipliers used to obtain the factor L or U from the 00068 *> L*D*L' or U*D*U' factorization as computed by ZSPTRF. 00069 *> \endverbatim 00070 *> 00071 *> \param[in] IPIV 00072 *> \verbatim 00073 *> IPIV is INTEGER array, dimension (N) 00074 *> The pivot indices from ZSPTRF. 00075 *> \endverbatim 00076 *> 00077 *> \param[out] C 00078 *> \verbatim 00079 *> C is COMPLEX*16 array, dimension (LDC,N) 00080 *> \endverbatim 00081 *> 00082 *> \param[in] LDC 00083 *> \verbatim 00084 *> LDC is INTEGER 00085 *> The leading dimension of the array C. LDC >= max(1,N). 00086 *> \endverbatim 00087 *> 00088 *> \param[out] RWORK 00089 *> \verbatim 00090 *> RWORK is DOUBLE PRECISION array, dimension (N) 00091 *> \endverbatim 00092 *> 00093 *> \param[out] RESID 00094 *> \verbatim 00095 *> RESID is DOUBLE PRECISION 00096 *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) 00097 *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) 00098 *> \endverbatim 00099 * 00100 * Authors: 00101 * ======== 00102 * 00103 *> \author Univ. of Tennessee 00104 *> \author Univ. of California Berkeley 00105 *> \author Univ. of Colorado Denver 00106 *> \author NAG Ltd. 00107 * 00108 *> \date November 2011 00109 * 00110 *> \ingroup complex16_lin 00111 * 00112 * ===================================================================== 00113 SUBROUTINE ZSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID ) 00114 * 00115 * -- LAPACK test routine (version 3.4.0) -- 00116 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00118 * November 2011 00119 * 00120 * .. Scalar Arguments .. 00121 CHARACTER UPLO 00122 INTEGER LDC, N 00123 DOUBLE PRECISION RESID 00124 * .. 00125 * .. Array Arguments .. 00126 INTEGER IPIV( * ) 00127 DOUBLE PRECISION RWORK( * ) 00128 COMPLEX*16 A( * ), AFAC( * ), C( LDC, * ) 00129 * .. 00130 * 00131 * ===================================================================== 00132 * 00133 * .. Parameters .. 00134 DOUBLE PRECISION ZERO, ONE 00135 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00136 COMPLEX*16 CZERO, CONE 00137 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), 00138 $ CONE = ( 1.0D+0, 0.0D+0 ) ) 00139 * .. 00140 * .. Local Scalars .. 00141 INTEGER I, INFO, J, JC 00142 DOUBLE PRECISION ANORM, EPS 00143 * .. 00144 * .. External Functions .. 00145 LOGICAL LSAME 00146 DOUBLE PRECISION DLAMCH, ZLANSP, ZLANSY 00147 EXTERNAL LSAME, DLAMCH, ZLANSP, ZLANSY 00148 * .. 00149 * .. External Subroutines .. 00150 EXTERNAL ZLASET, ZLAVSP 00151 * .. 00152 * .. Intrinsic Functions .. 00153 INTRINSIC DBLE 00154 * .. 00155 * .. Executable Statements .. 00156 * 00157 * Quick exit if N = 0. 00158 * 00159 IF( N.LE.0 ) THEN 00160 RESID = ZERO 00161 RETURN 00162 END IF 00163 * 00164 * Determine EPS and the norm of A. 00165 * 00166 EPS = DLAMCH( 'Epsilon' ) 00167 ANORM = ZLANSP( '1', UPLO, N, A, RWORK ) 00168 * 00169 * Initialize C to the identity matrix. 00170 * 00171 CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC ) 00172 * 00173 * Call ZLAVSP to form the product D * U' (or D * L' ). 00174 * 00175 CALL ZLAVSP( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, IPIV, C, 00176 $ LDC, INFO ) 00177 * 00178 * Call ZLAVSP again to multiply by U ( or L ). 00179 * 00180 CALL ZLAVSP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C, 00181 $ LDC, INFO ) 00182 * 00183 * Compute the difference C - A . 00184 * 00185 IF( LSAME( UPLO, 'U' ) ) THEN 00186 JC = 0 00187 DO 20 J = 1, N 00188 DO 10 I = 1, J 00189 C( I, J ) = C( I, J ) - A( JC+I ) 00190 10 CONTINUE 00191 JC = JC + J 00192 20 CONTINUE 00193 ELSE 00194 JC = 1 00195 DO 40 J = 1, N 00196 DO 30 I = J, N 00197 C( I, J ) = C( I, J ) - A( JC+I-J ) 00198 30 CONTINUE 00199 JC = JC + N - J + 1 00200 40 CONTINUE 00201 END IF 00202 * 00203 * Compute norm( C - A ) / ( N * norm(A) * EPS ) 00204 * 00205 RESID = ZLANSY( '1', UPLO, N, C, LDC, RWORK ) 00206 * 00207 IF( ANORM.LE.ZERO ) THEN 00208 IF( RESID.NE.ZERO ) 00209 $ RESID = ONE / EPS 00210 ELSE 00211 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS 00212 END IF 00213 * 00214 RETURN 00215 * 00216 * End of ZSPT01 00217 * 00218 END