1*> \brief \b ZHET01_AA 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 ZHET01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, 12* C, LDC, 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*> ZHET01_AA 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 ZHETRF. 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 ZHETRF. 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*> \ingroup complex16_lin 120* 121* ===================================================================== 122 SUBROUTINE ZHET01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, 123 $ LDC, RWORK, RESID ) 124* 125* -- LAPACK test routine -- 126* -- LAPACK is a software package provided by Univ. of Tennessee, -- 127* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 128* 129* .. Scalar Arguments .. 130 CHARACTER UPLO 131 INTEGER LDA, LDAFAC, LDC, N 132 DOUBLE PRECISION RESID 133* .. 134* .. Array Arguments .. 135 INTEGER IPIV( * ) 136 DOUBLE PRECISION RWORK( * ) 137 COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) 138* .. 139* 140* ===================================================================== 141* 142* .. Parameters .. 143 COMPLEX*16 CZERO, CONE 144 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), 145 $ CONE = ( 1.0D+0, 0.0D+0 ) ) 146 DOUBLE PRECISION ZERO, ONE 147 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 148* .. 149* .. Local Scalars .. 150 INTEGER I, J 151 DOUBLE PRECISION ANORM, EPS 152* .. 153* .. External Functions .. 154 LOGICAL LSAME 155 DOUBLE PRECISION DLAMCH, ZLANHE 156 EXTERNAL LSAME, DLAMCH, ZLANHE 157* .. 158* .. External Subroutines .. 159 EXTERNAL ZLASET, ZLAVHE 160* .. 161* .. Intrinsic Functions .. 162 INTRINSIC DBLE 163* .. 164* .. Executable Statements .. 165* 166* Quick exit if N = 0. 167* 168 IF( N.LE.0 ) THEN 169 RESID = ZERO 170 RETURN 171 END IF 172* 173* Determine EPS and the norm of A. 174* 175 EPS = DLAMCH( 'Epsilon' ) 176 ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK ) 177* 178* Initialize C to the tridiagonal matrix T. 179* 180 CALL ZLASET( 'Full', N, N, CZERO, CZERO, C, LDC ) 181 CALL ZLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 ) 182 IF( N.GT.1 ) THEN 183 IF( LSAME( UPLO, 'U' ) ) THEN 184 CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ), 185 $ LDC+1 ) 186 CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ), 187 $ LDC+1 ) 188 CALL ZLACGV( N-1, C( 2, 1 ), LDC+1 ) 189 ELSE 190 CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ), 191 $ LDC+1 ) 192 CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ), 193 $ LDC+1 ) 194 CALL ZLACGV( N-1, C( 1, 2 ), LDC+1 ) 195 ENDIF 196* 197* Call ZTRMM to form the product U' * D (or L * D ). 198* 199 IF( LSAME( UPLO, 'U' ) ) THEN 200 CALL ZTRMM( 'Left', UPLO, 'Conjugate transpose', 'Unit', 201 $ N-1, N, CONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), 202 $ LDC ) 203 ELSE 204 CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N, 205 $ CONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC ) 206 END IF 207* 208* Call ZTRMM again to multiply by U (or L ). 209* 210 IF( LSAME( UPLO, 'U' ) ) THEN 211 CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1, 212 $ CONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC ) 213 ELSE 214 CALL ZTRMM( 'Right', UPLO, 'Conjugate transpose', 'Unit', N, 215 $ N-1, CONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), 216 $ LDC ) 217 END IF 218* 219* Apply hermitian pivots 220* 221 DO J = N, 1, -1 222 I = IPIV( J ) 223 IF( I.NE.J ) 224 $ CALL ZSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC ) 225 END DO 226 DO J = N, 1, -1 227 I = IPIV( J ) 228 IF( I.NE.J ) 229 $ CALL ZSWAP( N, C( 1, J ), 1, C( 1, I ), 1 ) 230 END DO 231 ENDIF 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 = ZLANHE( '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 ZHET01_AA 264* 265 END 266