1*> \brief \b SSYT01_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 SSYT01_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* REAL RESID 18* .. 19* .. Array Arguments .. 20* INTEGER IPIV( * ) 21* REAL A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ), 22* $ RWORK( * ) 23* .. 24* 25* 26*> \par Purpose: 27* ============= 28*> 29*> \verbatim 30*> 31*> SSYT01_AA reconstructs a 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 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*> symmetric 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 REAL array, dimension (LDA,N) 58*> The original symmetric 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 REAL 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 SSYTRF. 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 SSYTRF. 86*> \endverbatim 87*> 88*> \param[out] C 89*> \verbatim 90*> C is REAL 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 REAL array, dimension (N) 102*> \endverbatim 103*> 104*> \param[out] RESID 105*> \verbatim 106*> RESID is REAL 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 November 2017 120* 121* 122*> \ingroup real_lin 123* 124* ===================================================================== 125 SUBROUTINE SSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, 126 $ LDC, RWORK, RESID ) 127* 128* -- LAPACK test routine (version 3.8.0) -- 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 2017 132* 133* .. Scalar Arguments .. 134 CHARACTER UPLO 135 INTEGER LDA, LDAFAC, LDC, N 136 REAL RESID 137* .. 138* .. Array Arguments .. 139 INTEGER IPIV( * ) 140 REAL A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ), 141 $ RWORK( * ) 142* .. 143* 144* ===================================================================== 145* 146* .. Parameters .. 147 REAL ZERO, ONE 148 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 149* .. 150* .. Local Scalars .. 151 INTEGER I, J 152 REAL ANORM, EPS 153* .. 154* .. External Functions .. 155 LOGICAL LSAME 156 REAL SLAMCH, SLANSY 157 EXTERNAL LSAME, SLAMCH, SLANSY 158* .. 159* .. External Subroutines .. 160 EXTERNAL SLASET, SLAVSY, SSWAP, STRMM, SLACPY 161* .. 162* .. Intrinsic Functions .. 163 INTRINSIC DBLE 164* .. 165* .. Executable Statements .. 166* 167* Quick exit if N = 0. 168* 169 IF( N.LE.0 ) THEN 170 RESID = ZERO 171 RETURN 172 END IF 173* 174* Determine EPS and the norm of A. 175* 176 EPS = SLAMCH( 'Epsilon' ) 177 ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK ) 178* 179* Initialize C to the tridiagonal matrix T. 180* 181 CALL SLASET( 'Full', N, N, ZERO, ZERO, C, LDC ) 182 CALL SLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 ) 183 IF( N.GT.1 ) THEN 184 IF( LSAME( UPLO, 'U' ) ) THEN 185 CALL SLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ), 186 $ LDC+1 ) 187 CALL SLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ), 188 $ LDC+1 ) 189 ELSE 190 CALL SLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ), 191 $ LDC+1 ) 192 CALL SLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ), 193 $ LDC+1 ) 194 ENDIF 195* 196* Call STRMM to form the product U' * D (or L * D ). 197* 198 IF( LSAME( UPLO, 'U' ) ) THEN 199 CALL STRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N, 200 $ ONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC ) 201 ELSE 202 CALL STRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N, 203 $ ONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC ) 204 END IF 205* 206* Call STRMM again to multiply by U (or L ). 207* 208 IF( LSAME( UPLO, 'U' ) ) THEN 209 CALL STRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1, 210 $ ONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC ) 211 ELSE 212 CALL STRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1, 213 $ ONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC ) 214 END IF 215 ENDIF 216* 217* Apply symmetric pivots 218* 219 DO J = N, 1, -1 220 I = IPIV( J ) 221 IF( I.NE.J ) 222 $ CALL SSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC ) 223 END DO 224 DO J = N, 1, -1 225 I = IPIV( J ) 226 IF( I.NE.J ) 227 $ CALL SSWAP( N, C( 1, J ), 1, C( 1, I ), 1 ) 228 END DO 229* 230* 231* Compute the difference C - A . 232* 233 IF( LSAME( UPLO, 'U' ) ) THEN 234 DO J = 1, N 235 DO I = 1, J 236 C( I, J ) = C( I, J ) - A( I, J ) 237 END DO 238 END DO 239 ELSE 240 DO J = 1, N 241 DO I = J, N 242 C( I, J ) = C( I, J ) - A( I, J ) 243 END DO 244 END DO 245 END IF 246* 247* Compute norm( C - A ) / ( N * norm(A) * EPS ) 248* 249 RESID = SLANSY( '1', UPLO, N, C, LDC, RWORK ) 250* 251 IF( ANORM.LE.ZERO ) THEN 252 IF( RESID.NE.ZERO ) 253 $ RESID = ONE / EPS 254 ELSE 255 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS 256 END IF 257* 258 RETURN 259* 260* End of SSYT01_AA 261* 262 END 263