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_AA( 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 hermitian 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 and EPS is the machine epsilon. 35*> \endverbatim 36* 37* Arguments: 38* ========== 39* 40*> \param[in] UPLO 41*> \verbatim 42*> UPLO is CHARACTER*1 43*> Specifies whether the upper or lower triangular part of the 44*> hermitian matrix A is stored: 45*> = 'U': Upper triangular 46*> = 'L': Lower triangular 47*> \endverbatim 48*> 49*> \param[in] N 50*> \verbatim 51*> N is INTEGER 52*> The number of rows and columns of the matrix A. N >= 0. 53*> \endverbatim 54*> 55*> \param[in] A 56*> \verbatim 57*> A is COMPLEX*16 array, dimension (LDA,N) 58*> The original hermitian matrix A. 59*> \endverbatim 60*> 61*> \param[in] LDA 62*> \verbatim 63*> LDA is INTEGER 64*> The leading dimension of the array A. LDA >= max(1,N) 65*> \endverbatim 66*> 67*> \param[in] AFAC 68*> \verbatim 69*> AFAC is COMPLEX*16 array, dimension (LDAFAC,N) 70*> The factored form of the matrix A. AFAC contains the block 71*> diagonal matrix D and the multipliers used to obtain the 72*> factor L or U from the block L*D*L' or U*D*U' factorization 73*> as computed by ZSYTRF. 74*> \endverbatim 75*> 76*> \param[in] LDAFAC 77*> \verbatim 78*> LDAFAC is INTEGER 79*> The leading dimension of the array AFAC. LDAFAC >= max(1,N). 80*> \endverbatim 81*> 82*> \param[in] IPIV 83*> \verbatim 84*> IPIV is INTEGER array, dimension (N) 85*> The pivot indices from ZSYTRF. 86*> \endverbatim 87*> 88*> \param[out] C 89*> \verbatim 90*> C is COMPLEX*16 array, dimension (LDC,N) 91*> \endverbatim 92*> 93*> \param[in] LDC 94*> \verbatim 95*> LDC is INTEGER 96*> The leading dimension of the array C. LDC >= max(1,N). 97*> \endverbatim 98*> 99*> \param[out] RWORK 100*> \verbatim 101*> RWORK is COMPLEX*16 array, dimension (N) 102*> \endverbatim 103*> 104*> \param[out] RESID 105*> \verbatim 106*> RESID is COMPLEX*16 107*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) 108*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) 109*> \endverbatim 110* 111* Authors: 112* ======== 113* 114*> \author Univ. of Tennessee 115*> \author Univ. of California Berkeley 116*> \author Univ. of Colorado Denver 117*> \author NAG Ltd. 118* 119*> \date December 2016 120* 121* @generated from LIN/dsyt01_aa.f, fortran d -> z, Thu Nov 17 13:01:50 2016 122* 123*> \ingroup complex16_lin 124* 125* ===================================================================== 126 SUBROUTINE ZSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, 127 $ LDC, RWORK, RESID ) 128* 129* -- LAPACK test routine (version 3.7.0) -- 130* -- LAPACK is a software package provided by Univ. of Tennessee, -- 131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 132* December 2016 133* 134* .. Scalar Arguments .. 135 CHARACTER UPLO 136 INTEGER LDA, LDAFAC, LDC, N 137 DOUBLE PRECISION RESID 138* .. 139* .. Array Arguments .. 140 INTEGER IPIV( * ) 141 COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) 142 DOUBLE PRECISION RWORK( * ) 143* .. 144* 145* ===================================================================== 146* 147* .. Parameters .. 148 DOUBLE PRECISION ZERO, ONE 149 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 150 COMPLEX*16 CZERO, CONE 151 PARAMETER ( CZERO = 0.0E+0, CONE = 1.0E+0 ) 152* .. 153* .. Local Scalars .. 154 INTEGER I, 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 tridiagonal matrix T. 183* 184 CALL ZLASET( 'Full', N, N, CZERO, CZERO, C, LDC ) 185 CALL ZLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 ) 186 IF( N.GT.1 ) THEN 187 IF( LSAME( UPLO, 'U' ) ) THEN 188 CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ), 189 $ LDC+1 ) 190 CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ), 191 $ LDC+1 ) 192 ELSE 193 CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ), 194 $ LDC+1 ) 195 CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ), 196 $ LDC+1 ) 197 ENDIF 198* 199* Call ZTRMM to form the product U' * D (or L * D ). 200* 201 IF( LSAME( UPLO, 'U' ) ) THEN 202 CALL ZTRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N, 203 $ CONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC ) 204 ELSE 205 CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N, 206 $ CONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC ) 207 END IF 208* 209* Call ZTRMM again to multiply by U (or L ). 210* 211 IF( LSAME( UPLO, 'U' ) ) THEN 212 CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1, 213 $ CONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC ) 214 ELSE 215 CALL ZTRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1, 216 $ CONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC ) 217 END IF 218 ENDIF 219* 220* Apply symmetric pivots 221* 222 DO J = N, 1, -1 223 I = IPIV( J ) 224 IF( I.NE.J ) 225 $ CALL ZSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC ) 226 END DO 227 DO J = N, 1, -1 228 I = IPIV( J ) 229 IF( I.NE.J ) 230 $ CALL ZSWAP( N, C( 1, J ), 1, C( 1, I ), 1 ) 231 END DO 232* 233* 234* Compute the difference C - A . 235* 236 IF( LSAME( UPLO, 'U' ) ) THEN 237 DO J = 1, N 238 DO I = 1, J 239 C( I, J ) = C( I, J ) - A( I, J ) 240 END DO 241 END DO 242 ELSE 243 DO J = 1, N 244 DO I = J, N 245 C( I, J ) = C( I, J ) - A( I, J ) 246 END DO 247 END DO 248 END IF 249* 250* Compute norm( C - A ) / ( N * norm(A) * EPS ) 251* 252 RESID = ZLANSY( '1', UPLO, N, C, LDC, RWORK ) 253* 254 IF( ANORM.LE.ZERO ) THEN 255 IF( RESID.NE.ZERO ) 256 $ RESID = ONE / EPS 257 ELSE 258 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS 259 END IF 260* 261 RETURN 262* 263* End of ZSYT01 264* 265 END 266