1*> \brief \b ZSYT01 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE ZSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, 12* RWORK, RESID ) 13* 14* .. Scalar Arguments .. 15* CHARACTER UPLO 16* INTEGER LDA, LDAFAC, LDC, N 17* DOUBLE PRECISION RESID 18* .. 19* .. Array Arguments .. 20* INTEGER IPIV( * ) 21* DOUBLE PRECISION RWORK( * ) 22* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) 23* .. 24* 25* 26*> \par Purpose: 27* ============= 28*> 29*> \verbatim 30*> 31*> ZSYT01 reconstructs a complex symmetric indefinite matrix A from its 32*> block L*D*L' or U*D*U' factorization and computes the residual 33*> norm( C - A ) / ( N * norm(A) * EPS ), 34*> where C is the reconstructed matrix, EPS is the machine epsilon, 35*> L' is the transpose of L, and U' is the transpose of U. 36*> \endverbatim 37* 38* Arguments: 39* ========== 40* 41*> \param[in] UPLO 42*> \verbatim 43*> UPLO is CHARACTER*1 44*> Specifies whether the upper or lower triangular part of the 45*> complex symmetric matrix A is stored: 46*> = 'U': Upper triangular 47*> = 'L': Lower triangular 48*> \endverbatim 49*> 50*> \param[in] N 51*> \verbatim 52*> N is INTEGER 53*> The number of rows and columns of the matrix A. N >= 0. 54*> \endverbatim 55*> 56*> \param[in] A 57*> \verbatim 58*> A is COMPLEX*16 array, dimension (LDA,N) 59*> The original complex symmetric matrix A. 60*> \endverbatim 61*> 62*> \param[in] LDA 63*> \verbatim 64*> LDA is INTEGER 65*> The leading dimension of the array A. LDA >= max(1,N) 66*> \endverbatim 67*> 68*> \param[in] AFAC 69*> \verbatim 70*> AFAC is COMPLEX*16 array, dimension (LDAFAC,N) 71*> The factored form of the matrix A. AFAC contains the block 72*> diagonal matrix D and the multipliers used to obtain the 73*> factor L or U from the block L*D*L' or U*D*U' factorization 74*> as computed by ZSYTRF. 75*> \endverbatim 76*> 77*> \param[in] LDAFAC 78*> \verbatim 79*> LDAFAC is INTEGER 80*> The leading dimension of the array AFAC. LDAFAC >= max(1,N). 81*> \endverbatim 82*> 83*> \param[in] IPIV 84*> \verbatim 85*> IPIV is INTEGER array, dimension (N) 86*> The pivot indices from ZSYTRF. 87*> \endverbatim 88*> 89*> \param[out] C 90*> \verbatim 91*> C is COMPLEX*16 array, dimension (LDC,N) 92*> \endverbatim 93*> 94*> \param[in] LDC 95*> \verbatim 96*> LDC is INTEGER 97*> The leading dimension of the array C. LDC >= max(1,N). 98*> \endverbatim 99*> 100*> \param[out] RWORK 101*> \verbatim 102*> RWORK is DOUBLE PRECISION array, dimension (N) 103*> \endverbatim 104*> 105*> \param[out] RESID 106*> \verbatim 107*> RESID is DOUBLE PRECISION 108*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) 109*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) 110*> \endverbatim 111* 112* Authors: 113* ======== 114* 115*> \author Univ. of Tennessee 116*> \author Univ. of California Berkeley 117*> \author Univ. of Colorado Denver 118*> \author NAG Ltd. 119* 120*> \date November 2013 121* 122*> \ingroup complex16_lin 123* 124* ===================================================================== 125 SUBROUTINE ZSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, 126 $ RWORK, RESID ) 127* 128* -- LAPACK test routine (version 3.5.0) -- 129* -- LAPACK is a software package provided by Univ. of Tennessee, -- 130* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 131* November 2013 132* 133* .. Scalar Arguments .. 134 CHARACTER UPLO 135 INTEGER LDA, LDAFAC, LDC, N 136 DOUBLE PRECISION RESID 137* .. 138* .. Array Arguments .. 139 INTEGER IPIV( * ) 140 DOUBLE PRECISION RWORK( * ) 141 COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) 142* .. 143* 144* ===================================================================== 145* 146* .. Parameters .. 147 DOUBLE PRECISION ZERO, ONE 148 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 149 COMPLEX*16 CZERO, CONE 150 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), 151 $ CONE = ( 1.0D+0, 0.0D+0 ) ) 152* .. 153* .. Local Scalars .. 154 INTEGER I, INFO, J 155 DOUBLE PRECISION ANORM, EPS 156* .. 157* .. External Functions .. 158 LOGICAL LSAME 159 DOUBLE PRECISION DLAMCH, ZLANSY 160 EXTERNAL LSAME, DLAMCH, ZLANSY 161* .. 162* .. External Subroutines .. 163 EXTERNAL ZLASET, ZLAVSY 164* .. 165* .. Intrinsic Functions .. 166 INTRINSIC DBLE 167* .. 168* .. Executable Statements .. 169* 170* Quick exit if N = 0. 171* 172 IF( N.LE.0 ) THEN 173 RESID = ZERO 174 RETURN 175 END IF 176* 177* Determine EPS and the norm of A. 178* 179 EPS = DLAMCH( 'Epsilon' ) 180 ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK ) 181* 182* Initialize C to the identity matrix. 183* 184 CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC ) 185* 186* Call ZLAVSY to form the product D * U' (or D * L' ). 187* 188 CALL ZLAVSY( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, LDAFAC, 189 $ IPIV, C, LDC, INFO ) 190* 191* Call ZLAVSY again to multiply by U (or L ). 192* 193 CALL ZLAVSY( UPLO, 'No transpose', 'Unit', N, N, AFAC, LDAFAC, 194 $ IPIV, C, LDC, INFO ) 195* 196* Compute the difference C - A . 197* 198 IF( LSAME( UPLO, 'U' ) ) THEN 199 DO 20 J = 1, N 200 DO 10 I = 1, J 201 C( I, J ) = C( I, J ) - A( I, J ) 202 10 CONTINUE 203 20 CONTINUE 204 ELSE 205 DO 40 J = 1, N 206 DO 30 I = J, N 207 C( I, J ) = C( I, J ) - A( I, J ) 208 30 CONTINUE 209 40 CONTINUE 210 END IF 211* 212* Compute norm( C - A ) / ( N * norm(A) * EPS ) 213* 214 RESID = ZLANSY( '1', UPLO, N, C, LDC, RWORK ) 215* 216 IF( ANORM.LE.ZERO ) THEN 217 IF( RESID.NE.ZERO ) 218 $ RESID = ONE / EPS 219 ELSE 220 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS 221 END IF 222* 223 RETURN 224* 225* End of ZSYT01 226* 227 END 228