00001 SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, 00002 $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, 00003 $ IWORK, LIWORK, INFO ) 00004 * 00005 * -- LAPACK driver routine (version 3.2.2) -- 00006 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00007 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00008 * June 2010 00009 * 00010 * .. Scalar Arguments .. 00011 CHARACTER JOBZ, RANGE, UPLO 00012 INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N 00013 DOUBLE PRECISION ABSTOL, VL, VU 00014 * .. 00015 * .. Array Arguments .. 00016 INTEGER ISUPPZ( * ), IWORK( * ) 00017 DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) 00018 * .. 00019 * 00020 * Purpose 00021 * ======= 00022 * 00023 * DSYEVR computes selected eigenvalues and, optionally, eigenvectors 00024 * of a real symmetric matrix A. Eigenvalues and eigenvectors can be 00025 * selected by specifying either a range of values or a range of 00026 * indices for the desired eigenvalues. 00027 * 00028 * DSYEVR first reduces the matrix A to tridiagonal form T with a call 00029 * to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute 00030 * the eigenspectrum using Relatively Robust Representations. DSTEMR 00031 * computes eigenvalues by the dqds algorithm, while orthogonal 00032 * eigenvectors are computed from various "good" L D L^T representations 00033 * (also known as Relatively Robust Representations). Gram-Schmidt 00034 * orthogonalization is avoided as far as possible. More specifically, 00035 * the various steps of the algorithm are as follows. 00036 * 00037 * For each unreduced block (submatrix) of T, 00038 * (a) Compute T - sigma I = L D L^T, so that L and D 00039 * define all the wanted eigenvalues to high relative accuracy. 00040 * This means that small relative changes in the entries of D and L 00041 * cause only small relative changes in the eigenvalues and 00042 * eigenvectors. The standard (unfactored) representation of the 00043 * tridiagonal matrix T does not have this property in general. 00044 * (b) Compute the eigenvalues to suitable accuracy. 00045 * If the eigenvectors are desired, the algorithm attains full 00046 * accuracy of the computed eigenvalues only right before 00047 * the corresponding vectors have to be computed, see steps c) and d). 00048 * (c) For each cluster of close eigenvalues, select a new 00049 * shift close to the cluster, find a new factorization, and refine 00050 * the shifted eigenvalues to suitable accuracy. 00051 * (d) For each eigenvalue with a large enough relative separation compute 00052 * the corresponding eigenvector by forming a rank revealing twisted 00053 * factorization. Go back to (c) for any clusters that remain. 00054 * 00055 * The desired accuracy of the output can be specified by the input 00056 * parameter ABSTOL. 00057 * 00058 * For more details, see DSTEMR's documentation and: 00059 * - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations 00060 * to compute orthogonal eigenvectors of symmetric tridiagonal matrices," 00061 * Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. 00062 * - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and 00063 * Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, 00064 * 2004. Also LAPACK Working Note 154. 00065 * - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric 00066 * tridiagonal eigenvalue/eigenvector problem", 00067 * Computer Science Division Technical Report No. UCB/CSD-97-971, 00068 * UC Berkeley, May 1997. 00069 * 00070 * 00071 * Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested 00072 * on machines which conform to the ieee-754 floating point standard. 00073 * DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and 00074 * when partial spectrum requests are made. 00075 * 00076 * Normal execution of DSTEMR may create NaNs and infinities and 00077 * hence may abort due to a floating point exception in environments 00078 * which do not handle NaNs and infinities in the ieee standard default 00079 * manner. 00080 * 00081 * Arguments 00082 * ========= 00083 * 00084 * JOBZ (input) CHARACTER*1 00085 * = 'N': Compute eigenvalues only; 00086 * = 'V': Compute eigenvalues and eigenvectors. 00087 * 00088 * RANGE (input) CHARACTER*1 00089 * = 'A': all eigenvalues will be found. 00090 * = 'V': all eigenvalues in the half-open interval (VL,VU] 00091 * will be found. 00092 * = 'I': the IL-th through IU-th eigenvalues will be found. 00093 ********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and 00094 ********** DSTEIN are called 00095 * 00096 * UPLO (input) CHARACTER*1 00097 * = 'U': Upper triangle of A is stored; 00098 * = 'L': Lower triangle of A is stored. 00099 * 00100 * N (input) INTEGER 00101 * The order of the matrix A. N >= 0. 00102 * 00103 * A (input/output) DOUBLE PRECISION array, dimension (LDA, N) 00104 * On entry, the symmetric matrix A. If UPLO = 'U', the 00105 * leading N-by-N upper triangular part of A contains the 00106 * upper triangular part of the matrix A. If UPLO = 'L', 00107 * the leading N-by-N lower triangular part of A contains 00108 * the lower triangular part of the matrix A. 00109 * On exit, the lower triangle (if UPLO='L') or the upper 00110 * triangle (if UPLO='U') of A, including the diagonal, is 00111 * destroyed. 00112 * 00113 * LDA (input) INTEGER 00114 * The leading dimension of the array A. LDA >= max(1,N). 00115 * 00116 * VL (input) DOUBLE PRECISION 00117 * VU (input) DOUBLE PRECISION 00118 * If RANGE='V', the lower and upper bounds of the interval to 00119 * be searched for eigenvalues. VL < VU. 00120 * Not referenced if RANGE = 'A' or 'I'. 00121 * 00122 * IL (input) INTEGER 00123 * IU (input) INTEGER 00124 * If RANGE='I', the indices (in ascending order) of the 00125 * smallest and largest eigenvalues to be returned. 00126 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. 00127 * Not referenced if RANGE = 'A' or 'V'. 00128 * 00129 * ABSTOL (input) DOUBLE PRECISION 00130 * The absolute error tolerance for the eigenvalues. 00131 * An approximate eigenvalue is accepted as converged 00132 * when it is determined to lie in an interval [a,b] 00133 * of width less than or equal to 00134 * 00135 * ABSTOL + EPS * max( |a|,|b| ) , 00136 * 00137 * where EPS is the machine precision. If ABSTOL is less than 00138 * or equal to zero, then EPS*|T| will be used in its place, 00139 * where |T| is the 1-norm of the tridiagonal matrix obtained 00140 * by reducing A to tridiagonal form. 00141 * 00142 * See "Computing Small Singular Values of Bidiagonal Matrices 00143 * with Guaranteed High Relative Accuracy," by Demmel and 00144 * Kahan, LAPACK Working Note #3. 00145 * 00146 * If high relative accuracy is important, set ABSTOL to 00147 * DLAMCH( 'Safe minimum' ). Doing so will guarantee that 00148 * eigenvalues are computed to high relative accuracy when 00149 * possible in future releases. The current code does not 00150 * make any guarantees about high relative accuracy, but 00151 * future releases will. See J. Barlow and J. Demmel, 00152 * "Computing Accurate Eigensystems of Scaled Diagonally 00153 * Dominant Matrices", LAPACK Working Note #7, for a discussion 00154 * of which matrices define their eigenvalues to high relative 00155 * accuracy. 00156 * 00157 * M (output) INTEGER 00158 * The total number of eigenvalues found. 0 <= M <= N. 00159 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. 00160 * 00161 * W (output) DOUBLE PRECISION array, dimension (N) 00162 * The first M elements contain the selected eigenvalues in 00163 * ascending order. 00164 * 00165 * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M)) 00166 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z 00167 * contain the orthonormal eigenvectors of the matrix A 00168 * corresponding to the selected eigenvalues, with the i-th 00169 * column of Z holding the eigenvector associated with W(i). 00170 * If JOBZ = 'N', then Z is not referenced. 00171 * Note: the user must ensure that at least max(1,M) columns are 00172 * supplied in the array Z; if RANGE = 'V', the exact value of M 00173 * is not known in advance and an upper bound must be used. 00174 * Supplying N columns is always safe. 00175 * 00176 * LDZ (input) INTEGER 00177 * The leading dimension of the array Z. LDZ >= 1, and if 00178 * JOBZ = 'V', LDZ >= max(1,N). 00179 * 00180 * ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) ) 00181 * The support of the eigenvectors in Z, i.e., the indices 00182 * indicating the nonzero elements in Z. The i-th eigenvector 00183 * is nonzero only in elements ISUPPZ( 2*i-1 ) through 00184 * ISUPPZ( 2*i ). 00185 ********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 00186 * 00187 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00188 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00189 * 00190 * LWORK (input) INTEGER 00191 * The dimension of the array WORK. LWORK >= max(1,26*N). 00192 * For optimal efficiency, LWORK >= (NB+6)*N, 00193 * where NB is the max of the blocksize for DSYTRD and DORMTR 00194 * returned by ILAENV. 00195 * 00196 * If LWORK = -1, then a workspace query is assumed; the routine 00197 * only calculates the optimal size of the WORK array, returns 00198 * this value as the first entry of the WORK array, and no error 00199 * message related to LWORK is issued by XERBLA. 00200 * 00201 * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 00202 * On exit, if INFO = 0, IWORK(1) returns the optimal LWORK. 00203 * 00204 * LIWORK (input) INTEGER 00205 * The dimension of the array IWORK. LIWORK >= max(1,10*N). 00206 * 00207 * If LIWORK = -1, then a workspace query is assumed; the 00208 * routine only calculates the optimal size of the IWORK array, 00209 * returns this value as the first entry of the IWORK array, and 00210 * no error message related to LIWORK is issued by XERBLA. 00211 * 00212 * INFO (output) INTEGER 00213 * = 0: successful exit 00214 * < 0: if INFO = -i, the i-th argument had an illegal value 00215 * > 0: Internal error 00216 * 00217 * Further Details 00218 * =============== 00219 * 00220 * Based on contributions by 00221 * Inderjit Dhillon, IBM Almaden, USA 00222 * Osni Marques, LBNL/NERSC, USA 00223 * Ken Stanley, Computer Science Division, University of 00224 * California at Berkeley, USA 00225 * Jason Riedy, Computer Science Division, University of 00226 * California at Berkeley, USA 00227 * 00228 * ===================================================================== 00229 * 00230 * .. Parameters .. 00231 DOUBLE PRECISION ZERO, ONE, TWO 00232 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) 00233 * .. 00234 * .. Local Scalars .. 00235 LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, VALEIG, WANTZ, 00236 $ TRYRAC 00237 CHARACTER ORDER 00238 INTEGER I, IEEEOK, IINFO, IMAX, INDD, INDDD, INDE, 00239 $ INDEE, INDIBL, INDIFL, INDISP, INDIWO, INDTAU, 00240 $ INDWK, INDWKN, ISCALE, J, JJ, LIWMIN, 00241 $ LLWORK, LLWRKN, LWKOPT, LWMIN, NB, NSPLIT 00242 DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, 00243 $ SIGMA, SMLNUM, TMP1, VLL, VUU 00244 * .. 00245 * .. External Functions .. 00246 LOGICAL LSAME 00247 INTEGER ILAENV 00248 DOUBLE PRECISION DLAMCH, DLANSY 00249 EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY 00250 * .. 00251 * .. External Subroutines .. 00252 EXTERNAL DCOPY, DORMTR, DSCAL, DSTEBZ, DSTEMR, DSTEIN, 00253 $ DSTERF, DSWAP, DSYTRD, XERBLA 00254 * .. 00255 * .. Intrinsic Functions .. 00256 INTRINSIC MAX, MIN, SQRT 00257 * .. 00258 * .. Executable Statements .. 00259 * 00260 * Test the input parameters. 00261 * 00262 IEEEOK = ILAENV( 10, 'DSYEVR', 'N', 1, 2, 3, 4 ) 00263 * 00264 LOWER = LSAME( UPLO, 'L' ) 00265 WANTZ = LSAME( JOBZ, 'V' ) 00266 ALLEIG = LSAME( RANGE, 'A' ) 00267 VALEIG = LSAME( RANGE, 'V' ) 00268 INDEIG = LSAME( RANGE, 'I' ) 00269 * 00270 LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LIWORK.EQ.-1 ) ) 00271 * 00272 LWMIN = MAX( 1, 26*N ) 00273 LIWMIN = MAX( 1, 10*N ) 00274 * 00275 INFO = 0 00276 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00277 INFO = -1 00278 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN 00279 INFO = -2 00280 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN 00281 INFO = -3 00282 ELSE IF( N.LT.0 ) THEN 00283 INFO = -4 00284 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00285 INFO = -6 00286 ELSE 00287 IF( VALEIG ) THEN 00288 IF( N.GT.0 .AND. VU.LE.VL ) 00289 $ INFO = -8 00290 ELSE IF( INDEIG ) THEN 00291 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN 00292 INFO = -9 00293 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN 00294 INFO = -10 00295 END IF 00296 END IF 00297 END IF 00298 IF( INFO.EQ.0 ) THEN 00299 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00300 INFO = -15 00301 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 00302 INFO = -18 00303 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 00304 INFO = -20 00305 END IF 00306 END IF 00307 * 00308 IF( INFO.EQ.0 ) THEN 00309 NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) 00310 NB = MAX( NB, ILAENV( 1, 'DORMTR', UPLO, N, -1, -1, -1 ) ) 00311 LWKOPT = MAX( ( NB+1 )*N, LWMIN ) 00312 WORK( 1 ) = LWKOPT 00313 IWORK( 1 ) = LIWMIN 00314 END IF 00315 * 00316 IF( INFO.NE.0 ) THEN 00317 CALL XERBLA( 'DSYEVR', -INFO ) 00318 RETURN 00319 ELSE IF( LQUERY ) THEN 00320 RETURN 00321 END IF 00322 * 00323 * Quick return if possible 00324 * 00325 M = 0 00326 IF( N.EQ.0 ) THEN 00327 WORK( 1 ) = 1 00328 RETURN 00329 END IF 00330 * 00331 IF( N.EQ.1 ) THEN 00332 WORK( 1 ) = 7 00333 IF( ALLEIG .OR. INDEIG ) THEN 00334 M = 1 00335 W( 1 ) = A( 1, 1 ) 00336 ELSE 00337 IF( VL.LT.A( 1, 1 ) .AND. VU.GE.A( 1, 1 ) ) THEN 00338 M = 1 00339 W( 1 ) = A( 1, 1 ) 00340 END IF 00341 END IF 00342 IF( WANTZ ) THEN 00343 Z( 1, 1 ) = ONE 00344 ISUPPZ( 1 ) = 1 00345 ISUPPZ( 2 ) = 1 00346 END IF 00347 RETURN 00348 END IF 00349 * 00350 * Get machine constants. 00351 * 00352 SAFMIN = DLAMCH( 'Safe minimum' ) 00353 EPS = DLAMCH( 'Precision' ) 00354 SMLNUM = SAFMIN / EPS 00355 BIGNUM = ONE / SMLNUM 00356 RMIN = SQRT( SMLNUM ) 00357 RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) 00358 * 00359 * Scale matrix to allowable range, if necessary. 00360 * 00361 ISCALE = 0 00362 ABSTLL = ABSTOL 00363 IF (VALEIG) THEN 00364 VLL = VL 00365 VUU = VU 00366 END IF 00367 ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) 00368 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN 00369 ISCALE = 1 00370 SIGMA = RMIN / ANRM 00371 ELSE IF( ANRM.GT.RMAX ) THEN 00372 ISCALE = 1 00373 SIGMA = RMAX / ANRM 00374 END IF 00375 IF( ISCALE.EQ.1 ) THEN 00376 IF( LOWER ) THEN 00377 DO 10 J = 1, N 00378 CALL DSCAL( N-J+1, SIGMA, A( J, J ), 1 ) 00379 10 CONTINUE 00380 ELSE 00381 DO 20 J = 1, N 00382 CALL DSCAL( J, SIGMA, A( 1, J ), 1 ) 00383 20 CONTINUE 00384 END IF 00385 IF( ABSTOL.GT.0 ) 00386 $ ABSTLL = ABSTOL*SIGMA 00387 IF( VALEIG ) THEN 00388 VLL = VL*SIGMA 00389 VUU = VU*SIGMA 00390 END IF 00391 END IF 00392 00393 * Initialize indices into workspaces. Note: The IWORK indices are 00394 * used only if DSTERF or DSTEMR fail. 00395 00396 * WORK(INDTAU:INDTAU+N-1) stores the scalar factors of the 00397 * elementary reflectors used in DSYTRD. 00398 INDTAU = 1 00399 * WORK(INDD:INDD+N-1) stores the tridiagonal's diagonal entries. 00400 INDD = INDTAU + N 00401 * WORK(INDE:INDE+N-1) stores the off-diagonal entries of the 00402 * tridiagonal matrix from DSYTRD. 00403 INDE = INDD + N 00404 * WORK(INDDD:INDDD+N-1) is a copy of the diagonal entries over 00405 * -written by DSTEMR (the DSTERF path copies the diagonal to W). 00406 INDDD = INDE + N 00407 * WORK(INDEE:INDEE+N-1) is a copy of the off-diagonal entries over 00408 * -written while computing the eigenvalues in DSTERF and DSTEMR. 00409 INDEE = INDDD + N 00410 * INDWK is the starting offset of the left-over workspace, and 00411 * LLWORK is the remaining workspace size. 00412 INDWK = INDEE + N 00413 LLWORK = LWORK - INDWK + 1 00414 00415 * IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and 00416 * stores the block indices of each of the M<=N eigenvalues. 00417 INDIBL = 1 00418 * IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ and 00419 * stores the starting and finishing indices of each block. 00420 INDISP = INDIBL + N 00421 * IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors 00422 * that corresponding to eigenvectors that fail to converge in 00423 * DSTEIN. This information is discarded; if any fail, the driver 00424 * returns INFO > 0. 00425 INDIFL = INDISP + N 00426 * INDIWO is the offset of the remaining integer workspace. 00427 INDIWO = INDISP + N 00428 00429 * 00430 * Call DSYTRD to reduce symmetric matrix to tridiagonal form. 00431 * 00432 CALL DSYTRD( UPLO, N, A, LDA, WORK( INDD ), WORK( INDE ), 00433 $ WORK( INDTAU ), WORK( INDWK ), LLWORK, IINFO ) 00434 * 00435 * If all eigenvalues are desired 00436 * then call DSTERF or DSTEMR and DORMTR. 00437 * 00438 IF( ( ALLEIG .OR. ( INDEIG .AND. IL.EQ.1 .AND. IU.EQ.N ) ) .AND. 00439 $ IEEEOK.EQ.1 ) THEN 00440 IF( .NOT.WANTZ ) THEN 00441 CALL DCOPY( N, WORK( INDD ), 1, W, 1 ) 00442 CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 ) 00443 CALL DSTERF( N, W, WORK( INDEE ), INFO ) 00444 ELSE 00445 CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 ) 00446 CALL DCOPY( N, WORK( INDD ), 1, WORK( INDDD ), 1 ) 00447 * 00448 IF (ABSTOL .LE. TWO*N*EPS) THEN 00449 TRYRAC = .TRUE. 00450 ELSE 00451 TRYRAC = .FALSE. 00452 END IF 00453 CALL DSTEMR( JOBZ, 'A', N, WORK( INDDD ), WORK( INDEE ), 00454 $ VL, VU, IL, IU, M, W, Z, LDZ, N, ISUPPZ, 00455 $ TRYRAC, WORK( INDWK ), LWORK, IWORK, LIWORK, 00456 $ INFO ) 00457 * 00458 * 00459 * 00460 * Apply orthogonal matrix used in reduction to tridiagonal 00461 * form to eigenvectors returned by DSTEIN. 00462 * 00463 IF( WANTZ .AND. INFO.EQ.0 ) THEN 00464 INDWKN = INDE 00465 LLWRKN = LWORK - INDWKN + 1 00466 CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA, 00467 $ WORK( INDTAU ), Z, LDZ, WORK( INDWKN ), 00468 $ LLWRKN, IINFO ) 00469 END IF 00470 END IF 00471 * 00472 * 00473 IF( INFO.EQ.0 ) THEN 00474 * Everything worked. Skip DSTEBZ/DSTEIN. IWORK(:) are 00475 * undefined. 00476 M = N 00477 GO TO 30 00478 END IF 00479 INFO = 0 00480 END IF 00481 * 00482 * Otherwise, call DSTEBZ and, if eigenvectors are desired, DSTEIN. 00483 * Also call DSTEBZ and DSTEIN if DSTEMR fails. 00484 * 00485 IF( WANTZ ) THEN 00486 ORDER = 'B' 00487 ELSE 00488 ORDER = 'E' 00489 END IF 00490 00491 CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, 00492 $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W, 00493 $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWK ), 00494 $ IWORK( INDIWO ), INFO ) 00495 * 00496 IF( WANTZ ) THEN 00497 CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W, 00498 $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, 00499 $ WORK( INDWK ), IWORK( INDIWO ), IWORK( INDIFL ), 00500 $ INFO ) 00501 * 00502 * Apply orthogonal matrix used in reduction to tridiagonal 00503 * form to eigenvectors returned by DSTEIN. 00504 * 00505 INDWKN = INDE 00506 LLWRKN = LWORK - INDWKN + 1 00507 CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z, 00508 $ LDZ, WORK( INDWKN ), LLWRKN, IINFO ) 00509 END IF 00510 * 00511 * If matrix was scaled, then rescale eigenvalues appropriately. 00512 * 00513 * Jump here if DSTEMR/DSTEIN succeeded. 00514 30 CONTINUE 00515 IF( ISCALE.EQ.1 ) THEN 00516 IF( INFO.EQ.0 ) THEN 00517 IMAX = M 00518 ELSE 00519 IMAX = INFO - 1 00520 END IF 00521 CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) 00522 END IF 00523 * 00524 * If eigenvalues are not in order, then sort them, along with 00525 * eigenvectors. Note: We do not sort the IFAIL portion of IWORK. 00526 * It may not be initialized (if DSTEMR/DSTEIN succeeded), and we do 00527 * not return this detailed information to the user. 00528 * 00529 IF( WANTZ ) THEN 00530 DO 50 J = 1, M - 1 00531 I = 0 00532 TMP1 = W( J ) 00533 DO 40 JJ = J + 1, M 00534 IF( W( JJ ).LT.TMP1 ) THEN 00535 I = JJ 00536 TMP1 = W( JJ ) 00537 END IF 00538 40 CONTINUE 00539 * 00540 IF( I.NE.0 ) THEN 00541 W( I ) = W( J ) 00542 W( J ) = TMP1 00543 CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) 00544 END IF 00545 50 CONTINUE 00546 END IF 00547 * 00548 * Set WORK(1) to optimal workspace size. 00549 * 00550 WORK( 1 ) = LWKOPT 00551 IWORK( 1 ) = LIWMIN 00552 * 00553 RETURN 00554 * 00555 * End of DSYEVR 00556 * 00557 END
1.7.2