1*> \brief \b DSGT01 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 DSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D, 12* WORK, RESULT ) 13* 14* .. Scalar Arguments .. 15* CHARACTER UPLO 16* INTEGER ITYPE, LDA, LDB, LDZ, M, N 17* .. 18* .. Array Arguments .. 19* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ), 20* $ WORK( * ), Z( LDZ, * ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> DDGT01 checks a decomposition of the form 30*> 31*> A Z = B Z D or 32*> A B Z = Z D or 33*> B A Z = Z D 34*> 35*> where A is a symmetric matrix, B is 36*> symmetric positive definite, Z is orthogonal, and D is diagonal. 37*> 38*> One of the following test ratios is computed: 39*> 40*> ITYPE = 1: RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp ) 41*> 42*> ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp ) 43*> 44*> ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp ) 45*> \endverbatim 46* 47* Arguments: 48* ========== 49* 50*> \param[in] ITYPE 51*> \verbatim 52*> ITYPE is INTEGER 53*> The form of the symmetric generalized eigenproblem. 54*> = 1: A*z = (lambda)*B*z 55*> = 2: A*B*z = (lambda)*z 56*> = 3: B*A*z = (lambda)*z 57*> \endverbatim 58*> 59*> \param[in] UPLO 60*> \verbatim 61*> UPLO is CHARACTER*1 62*> Specifies whether the upper or lower triangular part of the 63*> symmetric matrices A and B is stored. 64*> = 'U': Upper triangular 65*> = 'L': Lower triangular 66*> \endverbatim 67*> 68*> \param[in] N 69*> \verbatim 70*> N is INTEGER 71*> The order of the matrix A. N >= 0. 72*> \endverbatim 73*> 74*> \param[in] M 75*> \verbatim 76*> M is INTEGER 77*> The number of eigenvalues found. 0 <= M <= N. 78*> \endverbatim 79*> 80*> \param[in] A 81*> \verbatim 82*> A is DOUBLE PRECISION array, dimension (LDA, N) 83*> The original symmetric matrix A. 84*> \endverbatim 85*> 86*> \param[in] LDA 87*> \verbatim 88*> LDA is INTEGER 89*> The leading dimension of the array A. LDA >= max(1,N). 90*> \endverbatim 91*> 92*> \param[in] B 93*> \verbatim 94*> B is DOUBLE PRECISION array, dimension (LDB, N) 95*> The original symmetric positive definite matrix B. 96*> \endverbatim 97*> 98*> \param[in] LDB 99*> \verbatim 100*> LDB is INTEGER 101*> The leading dimension of the array B. LDB >= max(1,N). 102*> \endverbatim 103*> 104*> \param[in] Z 105*> \verbatim 106*> Z is DOUBLE PRECISION array, dimension (LDZ, M) 107*> The computed eigenvectors of the generalized eigenproblem. 108*> \endverbatim 109*> 110*> \param[in] LDZ 111*> \verbatim 112*> LDZ is INTEGER 113*> The leading dimension of the array Z. LDZ >= max(1,N). 114*> \endverbatim 115*> 116*> \param[in] D 117*> \verbatim 118*> D is DOUBLE PRECISION array, dimension (M) 119*> The computed eigenvalues of the generalized eigenproblem. 120*> \endverbatim 121*> 122*> \param[out] WORK 123*> \verbatim 124*> WORK is DOUBLE PRECISION array, dimension (N*N) 125*> \endverbatim 126*> 127*> \param[out] RESULT 128*> \verbatim 129*> RESULT is DOUBLE PRECISION array, dimension (1) 130*> The test ratio as described above. 131*> \endverbatim 132* 133* Authors: 134* ======== 135* 136*> \author Univ. of Tennessee 137*> \author Univ. of California Berkeley 138*> \author Univ. of Colorado Denver 139*> \author NAG Ltd. 140* 141*> \date November 2011 142* 143*> \ingroup double_eig 144* 145* ===================================================================== 146 SUBROUTINE DSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D, 147 $ WORK, RESULT ) 148* 149* -- LAPACK test routine (version 3.4.0) -- 150* -- LAPACK is a software package provided by Univ. of Tennessee, -- 151* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 152* November 2011 153* 154* .. Scalar Arguments .. 155 CHARACTER UPLO 156 INTEGER ITYPE, LDA, LDB, LDZ, M, N 157* .. 158* .. Array Arguments .. 159 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ), 160 $ WORK( * ), Z( LDZ, * ) 161* .. 162* 163* ===================================================================== 164* 165* .. Parameters .. 166 DOUBLE PRECISION ZERO, ONE 167 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) 168* .. 169* .. Local Scalars .. 170 INTEGER I 171 DOUBLE PRECISION ANORM, ULP 172* .. 173* .. External Functions .. 174 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY 175 EXTERNAL DLAMCH, DLANGE, DLANSY 176* .. 177* .. External Subroutines .. 178 EXTERNAL DSCAL, DSYMM 179* .. 180* .. Executable Statements .. 181* 182 RESULT( 1 ) = ZERO 183 IF( N.LE.0 ) 184 $ RETURN 185* 186 ULP = DLAMCH( 'Epsilon' ) 187* 188* Compute product of 1-norms of A and Z. 189* 190 ANORM = DLANSY( '1', UPLO, N, A, LDA, WORK )* 191 $ DLANGE( '1', N, M, Z, LDZ, WORK ) 192 IF( ANORM.EQ.ZERO ) 193 $ ANORM = ONE 194* 195 IF( ITYPE.EQ.1 ) THEN 196* 197* Norm of AZ - BZD 198* 199 CALL DSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO, 200 $ WORK, N ) 201 DO 10 I = 1, M 202 CALL DSCAL( N, D( I ), Z( 1, I ), 1 ) 203 10 CONTINUE 204 CALL DSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, -ONE, 205 $ WORK, N ) 206* 207 RESULT( 1 ) = ( DLANGE( '1', N, M, WORK, N, WORK ) / ANORM ) / 208 $ ( N*ULP ) 209* 210 ELSE IF( ITYPE.EQ.2 ) THEN 211* 212* Norm of ABZ - ZD 213* 214 CALL DSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, ZERO, 215 $ WORK, N ) 216 DO 20 I = 1, M 217 CALL DSCAL( N, D( I ), Z( 1, I ), 1 ) 218 20 CONTINUE 219 CALL DSYMM( 'Left', UPLO, N, M, ONE, A, LDA, WORK, N, -ONE, Z, 220 $ LDZ ) 221* 222 RESULT( 1 ) = ( DLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) / 223 $ ( N*ULP ) 224* 225 ELSE IF( ITYPE.EQ.3 ) THEN 226* 227* Norm of BAZ - ZD 228* 229 CALL DSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO, 230 $ WORK, N ) 231 DO 30 I = 1, M 232 CALL DSCAL( N, D( I ), Z( 1, I ), 1 ) 233 30 CONTINUE 234 CALL DSYMM( 'Left', UPLO, N, M, ONE, B, LDB, WORK, N, -ONE, Z, 235 $ LDZ ) 236* 237 RESULT( 1 ) = ( DLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) / 238 $ ( N*ULP ) 239 END IF 240* 241 RETURN 242* 243* End of DDGT01 244* 245 END 246