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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DSYGST 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DSYGST + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygst.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygst.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygst.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, ITYPE, LDA, LDB, N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DSYGST reduces a real symmetric-definite generalized eigenproblem 00038 *> to standard form. 00039 *> 00040 *> If ITYPE = 1, the problem is A*x = lambda*B*x, 00041 *> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) 00042 *> 00043 *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or 00044 *> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. 00045 *> 00046 *> B must have been previously factorized as U**T*U or L*L**T by DPOTRF. 00047 *> \endverbatim 00048 * 00049 * Arguments: 00050 * ========== 00051 * 00052 *> \param[in] ITYPE 00053 *> \verbatim 00054 *> ITYPE is INTEGER 00055 *> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); 00056 *> = 2 or 3: compute U*A*U**T or L**T*A*L. 00057 *> \endverbatim 00058 *> 00059 *> \param[in] UPLO 00060 *> \verbatim 00061 *> UPLO is CHARACTER*1 00062 *> = 'U': Upper triangle of A is stored and B is factored as 00063 *> U**T*U; 00064 *> = 'L': Lower triangle of A is stored and B is factored as 00065 *> L*L**T. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] N 00069 *> \verbatim 00070 *> N is INTEGER 00071 *> The order of the matrices A and B. N >= 0. 00072 *> \endverbatim 00073 *> 00074 *> \param[in,out] A 00075 *> \verbatim 00076 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00077 *> On entry, the symmetric matrix A. If UPLO = 'U', the leading 00078 *> N-by-N upper triangular part of A contains the upper 00079 *> triangular part of the matrix A, and the strictly lower 00080 *> triangular part of A is not referenced. If UPLO = 'L', the 00081 *> leading N-by-N lower triangular part of A contains the lower 00082 *> triangular part of the matrix A, and the strictly upper 00083 *> triangular part of A is not referenced. 00084 *> 00085 *> On exit, if INFO = 0, the transformed matrix, stored in the 00086 *> same format as A. 00087 *> \endverbatim 00088 *> 00089 *> \param[in] LDA 00090 *> \verbatim 00091 *> LDA is INTEGER 00092 *> The leading dimension of the array A. LDA >= max(1,N). 00093 *> \endverbatim 00094 *> 00095 *> \param[in] B 00096 *> \verbatim 00097 *> B is DOUBLE PRECISION array, dimension (LDB,N) 00098 *> The triangular factor from the Cholesky factorization of B, 00099 *> as returned by DPOTRF. 00100 *> \endverbatim 00101 *> 00102 *> \param[in] LDB 00103 *> \verbatim 00104 *> LDB is INTEGER 00105 *> The leading dimension of the array B. LDB >= max(1,N). 00106 *> \endverbatim 00107 *> 00108 *> \param[out] INFO 00109 *> \verbatim 00110 *> INFO is INTEGER 00111 *> = 0: successful exit 00112 *> < 0: if INFO = -i, the i-th argument had an illegal value 00113 *> \endverbatim 00114 * 00115 * Authors: 00116 * ======== 00117 * 00118 *> \author Univ. of Tennessee 00119 *> \author Univ. of California Berkeley 00120 *> \author Univ. of Colorado Denver 00121 *> \author NAG Ltd. 00122 * 00123 *> \date November 2011 00124 * 00125 *> \ingroup doubleSYcomputational 00126 * 00127 * ===================================================================== 00128 SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 00129 * 00130 * -- LAPACK computational routine (version 3.4.0) -- 00131 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00132 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00133 * November 2011 00134 * 00135 * .. Scalar Arguments .. 00136 CHARACTER UPLO 00137 INTEGER INFO, ITYPE, LDA, LDB, N 00138 * .. 00139 * .. Array Arguments .. 00140 DOUBLE PRECISION A( LDA, * ), B( LDB, * ) 00141 * .. 00142 * 00143 * ===================================================================== 00144 * 00145 * .. Parameters .. 00146 DOUBLE PRECISION ONE, HALF 00147 PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) 00148 * .. 00149 * .. Local Scalars .. 00150 LOGICAL UPPER 00151 INTEGER K, KB, NB 00152 * .. 00153 * .. External Subroutines .. 00154 EXTERNAL DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA 00155 * .. 00156 * .. Intrinsic Functions .. 00157 INTRINSIC MAX, MIN 00158 * .. 00159 * .. External Functions .. 00160 LOGICAL LSAME 00161 INTEGER ILAENV 00162 EXTERNAL LSAME, ILAENV 00163 * .. 00164 * .. Executable Statements .. 00165 * 00166 * Test the input parameters. 00167 * 00168 INFO = 0 00169 UPPER = LSAME( UPLO, 'U' ) 00170 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 00171 INFO = -1 00172 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00173 INFO = -2 00174 ELSE IF( N.LT.0 ) THEN 00175 INFO = -3 00176 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00177 INFO = -5 00178 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00179 INFO = -7 00180 END IF 00181 IF( INFO.NE.0 ) THEN 00182 CALL XERBLA( 'DSYGST', -INFO ) 00183 RETURN 00184 END IF 00185 * 00186 * Quick return if possible 00187 * 00188 IF( N.EQ.0 ) 00189 $ RETURN 00190 * 00191 * Determine the block size for this environment. 00192 * 00193 NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 ) 00194 * 00195 IF( NB.LE.1 .OR. NB.GE.N ) THEN 00196 * 00197 * Use unblocked code 00198 * 00199 CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 00200 ELSE 00201 * 00202 * Use blocked code 00203 * 00204 IF( ITYPE.EQ.1 ) THEN 00205 IF( UPPER ) THEN 00206 * 00207 * Compute inv(U**T)*A*inv(U) 00208 * 00209 DO 10 K = 1, N, NB 00210 KB = MIN( N-K+1, NB ) 00211 * 00212 * Update the upper triangle of A(k:n,k:n) 00213 * 00214 CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, 00215 $ B( K, K ), LDB, INFO ) 00216 IF( K+KB.LE.N ) THEN 00217 CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit', 00218 $ KB, N-K-KB+1, ONE, B( K, K ), LDB, 00219 $ A( K, K+KB ), LDA ) 00220 CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, 00221 $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, 00222 $ A( K, K+KB ), LDA ) 00223 CALL DSYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE, 00224 $ A( K, K+KB ), LDA, B( K, K+KB ), LDB, 00225 $ ONE, A( K+KB, K+KB ), LDA ) 00226 CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, 00227 $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, 00228 $ A( K, K+KB ), LDA ) 00229 CALL DTRSM( 'Right', UPLO, 'No transpose', 00230 $ 'Non-unit', KB, N-K-KB+1, ONE, 00231 $ B( K+KB, K+KB ), LDB, A( K, K+KB ), 00232 $ LDA ) 00233 END IF 00234 10 CONTINUE 00235 ELSE 00236 * 00237 * Compute inv(L)*A*inv(L**T) 00238 * 00239 DO 20 K = 1, N, NB 00240 KB = MIN( N-K+1, NB ) 00241 * 00242 * Update the lower triangle of A(k:n,k:n) 00243 * 00244 CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, 00245 $ B( K, K ), LDB, INFO ) 00246 IF( K+KB.LE.N ) THEN 00247 CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit', 00248 $ N-K-KB+1, KB, ONE, B( K, K ), LDB, 00249 $ A( K+KB, K ), LDA ) 00250 CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, 00251 $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, 00252 $ A( K+KB, K ), LDA ) 00253 CALL DSYR2K( UPLO, 'No transpose', N-K-KB+1, KB, 00254 $ -ONE, A( K+KB, K ), LDA, B( K+KB, K ), 00255 $ LDB, ONE, A( K+KB, K+KB ), LDA ) 00256 CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, 00257 $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, 00258 $ A( K+KB, K ), LDA ) 00259 CALL DTRSM( 'Left', UPLO, 'No transpose', 00260 $ 'Non-unit', N-K-KB+1, KB, ONE, 00261 $ B( K+KB, K+KB ), LDB, A( K+KB, K ), 00262 $ LDA ) 00263 END IF 00264 20 CONTINUE 00265 END IF 00266 ELSE 00267 IF( UPPER ) THEN 00268 * 00269 * Compute U*A*U**T 00270 * 00271 DO 30 K = 1, N, NB 00272 KB = MIN( N-K+1, NB ) 00273 * 00274 * Update the upper triangle of A(1:k+kb-1,1:k+kb-1) 00275 * 00276 CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit', 00277 $ K-1, KB, ONE, B, LDB, A( 1, K ), LDA ) 00278 CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), 00279 $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) 00280 CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE, 00281 $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, 00282 $ LDA ) 00283 CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), 00284 $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) 00285 CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit', 00286 $ K-1, KB, ONE, B( K, K ), LDB, A( 1, K ), 00287 $ LDA ) 00288 CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, 00289 $ B( K, K ), LDB, INFO ) 00290 30 CONTINUE 00291 ELSE 00292 * 00293 * Compute L**T*A*L 00294 * 00295 DO 40 K = 1, N, NB 00296 KB = MIN( N-K+1, NB ) 00297 * 00298 * Update the lower triangle of A(1:k+kb-1,1:k+kb-1) 00299 * 00300 CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit', 00301 $ KB, K-1, ONE, B, LDB, A( K, 1 ), LDA ) 00302 CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), 00303 $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) 00304 CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE, 00305 $ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A, 00306 $ LDA ) 00307 CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), 00308 $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) 00309 CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB, 00310 $ K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA ) 00311 CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, 00312 $ B( K, K ), LDB, INFO ) 00313 40 CONTINUE 00314 END IF 00315 END IF 00316 END IF 00317 RETURN 00318 * 00319 * End of DSYGST 00320 * 00321 END