1*> \brief <b> CHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b> 2* 3* @generated from zheev_2stage.f, fortran z -> c, Sat Nov 5 23:18:06 2016 4* 5* =========== DOCUMENTATION =========== 6* 7* Online html documentation available at 8* http://www.netlib.org/lapack/explore-html/ 9* 10*> \htmlonly 11*> Download CHEEV_2STAGE + dependencies 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheev_2stage.f"> 13*> [TGZ]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheev_2stage.f"> 15*> [ZIP]</a> 16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheev_2stage.f"> 17*> [TXT]</a> 18*> \endhtmlonly 19* 20* Definition: 21* =========== 22* 23* SUBROUTINE CHEEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, 24* RWORK, INFO ) 25* 26* IMPLICIT NONE 27* 28* .. Scalar Arguments .. 29* CHARACTER JOBZ, UPLO 30* INTEGER INFO, LDA, LWORK, N 31* .. 32* .. Array Arguments .. 33* REAL RWORK( * ), W( * ) 34* COMPLEX A( LDA, * ), WORK( * ) 35* .. 36* 37* 38*> \par Purpose: 39* ============= 40*> 41*> \verbatim 42*> 43*> CHEEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a 44*> complex Hermitian matrix A using the 2stage technique for 45*> the reduction to tridiagonal. 46*> \endverbatim 47* 48* Arguments: 49* ========== 50* 51*> \param[in] JOBZ 52*> \verbatim 53*> JOBZ is CHARACTER*1 54*> = 'N': Compute eigenvalues only; 55*> = 'V': Compute eigenvalues and eigenvectors. 56*> Not available in this release. 57*> \endverbatim 58*> 59*> \param[in] UPLO 60*> \verbatim 61*> UPLO is CHARACTER*1 62*> = 'U': Upper triangle of A is stored; 63*> = 'L': Lower triangle of A is stored. 64*> \endverbatim 65*> 66*> \param[in] N 67*> \verbatim 68*> N is INTEGER 69*> The order of the matrix A. N >= 0. 70*> \endverbatim 71*> 72*> \param[in,out] A 73*> \verbatim 74*> A is COMPLEX array, dimension (LDA, N) 75*> On entry, the Hermitian matrix A. If UPLO = 'U', the 76*> leading N-by-N upper triangular part of A contains the 77*> upper triangular part of the matrix A. If UPLO = 'L', 78*> the leading N-by-N lower triangular part of A contains 79*> the lower triangular part of the matrix A. 80*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the 81*> orthonormal eigenvectors of the matrix A. 82*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') 83*> or the upper triangle (if UPLO='U') of A, including the 84*> diagonal, is destroyed. 85*> \endverbatim 86*> 87*> \param[in] LDA 88*> \verbatim 89*> LDA is INTEGER 90*> The leading dimension of the array A. LDA >= max(1,N). 91*> \endverbatim 92*> 93*> \param[out] W 94*> \verbatim 95*> W is REAL array, dimension (N) 96*> If INFO = 0, the eigenvalues in ascending order. 97*> \endverbatim 98*> 99*> \param[out] WORK 100*> \verbatim 101*> WORK is COMPLEX array, dimension (MAX(1,LWORK)) 102*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 103*> \endverbatim 104*> 105*> \param[in] LWORK 106*> \verbatim 107*> LWORK is INTEGER 108*> The length of the array WORK. LWORK >= 1, when N <= 1; 109*> otherwise 110*> If JOBZ = 'N' and N > 1, LWORK must be queried. 111*> LWORK = MAX(1, dimension) where 112*> dimension = max(stage1,stage2) + (KD+1)*N + N 113*> = N*KD + N*max(KD+1,FACTOPTNB) 114*> + max(2*KD*KD, KD*NTHREADS) 115*> + (KD+1)*N + N 116*> where KD is the blocking size of the reduction, 117*> FACTOPTNB is the blocking used by the QR or LQ 118*> algorithm, usually FACTOPTNB=128 is a good choice 119*> NTHREADS is the number of threads used when 120*> openMP compilation is enabled, otherwise =1. 121*> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available 122*> 123*> If LWORK = -1, then a workspace query is assumed; the routine 124*> only calculates the optimal size of the WORK array, returns 125*> this value as the first entry of the WORK array, and no error 126*> message related to LWORK is issued by XERBLA. 127*> \endverbatim 128*> 129*> \param[out] RWORK 130*> \verbatim 131*> RWORK is REAL array, dimension (max(1, 3*N-2)) 132*> \endverbatim 133*> 134*> \param[out] INFO 135*> \verbatim 136*> INFO is INTEGER 137*> = 0: successful exit 138*> < 0: if INFO = -i, the i-th argument had an illegal value 139*> > 0: if INFO = i, the algorithm failed to converge; i 140*> off-diagonal elements of an intermediate tridiagonal 141*> form did not converge to zero. 142*> \endverbatim 143* 144* Authors: 145* ======== 146* 147*> \author Univ. of Tennessee 148*> \author Univ. of California Berkeley 149*> \author Univ. of Colorado Denver 150*> \author NAG Ltd. 151* 152*> \date November 2017 153* 154*> \ingroup complexHEeigen 155* 156*> \par Further Details: 157* ===================== 158*> 159*> \verbatim 160*> 161*> All details about the 2stage techniques are available in: 162*> 163*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra. 164*> Parallel reduction to condensed forms for symmetric eigenvalue problems 165*> using aggregated fine-grained and memory-aware kernels. In Proceedings 166*> of 2011 International Conference for High Performance Computing, 167*> Networking, Storage and Analysis (SC '11), New York, NY, USA, 168*> Article 8 , 11 pages. 169*> http://doi.acm.org/10.1145/2063384.2063394 170*> 171*> A. Haidar, J. Kurzak, P. Luszczek, 2013. 172*> An improved parallel singular value algorithm and its implementation 173*> for multicore hardware, In Proceedings of 2013 International Conference 174*> for High Performance Computing, Networking, Storage and Analysis (SC '13). 175*> Denver, Colorado, USA, 2013. 176*> Article 90, 12 pages. 177*> http://doi.acm.org/10.1145/2503210.2503292 178*> 179*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. 180*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure 181*> calculations based on fine-grained memory aware tasks. 182*> International Journal of High Performance Computing Applications. 183*> Volume 28 Issue 2, Pages 196-209, May 2014. 184*> http://hpc.sagepub.com/content/28/2/196 185*> 186*> \endverbatim 187* 188* ===================================================================== 189 SUBROUTINE CHEEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, 190 $ RWORK, INFO ) 191* 192 IMPLICIT NONE 193* 194* -- LAPACK driver routine (version 3.8.0) -- 195* -- LAPACK is a software package provided by Univ. of Tennessee, -- 196* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 197* November 2017 198* 199* .. Scalar Arguments .. 200 CHARACTER JOBZ, UPLO 201 INTEGER INFO, LDA, LWORK, N 202* .. 203* .. Array Arguments .. 204 REAL RWORK( * ), W( * ) 205 COMPLEX A( LDA, * ), WORK( * ) 206* .. 207* 208* ===================================================================== 209* 210* .. Parameters .. 211 REAL ZERO, ONE 212 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) 213 COMPLEX CONE 214 PARAMETER ( CONE = ( 1.0E0, 0.0E0 ) ) 215* .. 216* .. Local Scalars .. 217 LOGICAL LOWER, LQUERY, WANTZ 218 INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE, 219 $ LLWORK, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS 220 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, 221 $ SMLNUM 222* .. 223* .. External Functions .. 224 LOGICAL LSAME 225 INTEGER ILAENV2STAGE 226 REAL SLAMCH, CLANHE 227 EXTERNAL LSAME, SLAMCH, CLANHE, ILAENV2STAGE 228* .. 229* .. External Subroutines .. 230 EXTERNAL SSCAL, SSTERF, XERBLA, CLASCL, CSTEQR, 231 $ CUNGTR, CHETRD_2STAGE 232* .. 233* .. Intrinsic Functions .. 234 INTRINSIC REAL, MAX, SQRT 235* .. 236* .. Executable Statements .. 237* 238* Test the input parameters. 239* 240 WANTZ = LSAME( JOBZ, 'V' ) 241 LOWER = LSAME( UPLO, 'L' ) 242 LQUERY = ( LWORK.EQ.-1 ) 243* 244 INFO = 0 245 IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN 246 INFO = -1 247 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN 248 INFO = -2 249 ELSE IF( N.LT.0 ) THEN 250 INFO = -3 251 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 252 INFO = -5 253 END IF 254* 255 IF( INFO.EQ.0 ) THEN 256 KD = ILAENV2STAGE( 1, 'CHETRD_2STAGE', JOBZ, N, -1, -1, -1 ) 257 IB = ILAENV2STAGE( 2, 'CHETRD_2STAGE', JOBZ, N, KD, -1, -1 ) 258 LHTRD = ILAENV2STAGE( 3, 'CHETRD_2STAGE', JOBZ, N, KD, IB, -1 ) 259 LWTRD = ILAENV2STAGE( 4, 'CHETRD_2STAGE', JOBZ, N, KD, IB, -1 ) 260 LWMIN = N + LHTRD + LWTRD 261 WORK( 1 ) = LWMIN 262* 263 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) 264 $ INFO = -8 265 END IF 266* 267 IF( INFO.NE.0 ) THEN 268 CALL XERBLA( 'CHEEV_2STAGE ', -INFO ) 269 RETURN 270 ELSE IF( LQUERY ) THEN 271 RETURN 272 END IF 273* 274* Quick return if possible 275* 276 IF( N.EQ.0 ) THEN 277 RETURN 278 END IF 279* 280 IF( N.EQ.1 ) THEN 281 W( 1 ) = REAL( A( 1, 1 ) ) 282 WORK( 1 ) = 1 283 IF( WANTZ ) 284 $ A( 1, 1 ) = CONE 285 RETURN 286 END IF 287* 288* Get machine constants. 289* 290 SAFMIN = SLAMCH( 'Safe minimum' ) 291 EPS = SLAMCH( 'Precision' ) 292 SMLNUM = SAFMIN / EPS 293 BIGNUM = ONE / SMLNUM 294 RMIN = SQRT( SMLNUM ) 295 RMAX = SQRT( BIGNUM ) 296* 297* Scale matrix to allowable range, if necessary. 298* 299 ANRM = CLANHE( 'M', UPLO, N, A, LDA, RWORK ) 300 ISCALE = 0 301 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN 302 ISCALE = 1 303 SIGMA = RMIN / ANRM 304 ELSE IF( ANRM.GT.RMAX ) THEN 305 ISCALE = 1 306 SIGMA = RMAX / ANRM 307 END IF 308 IF( ISCALE.EQ.1 ) 309 $ CALL CLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) 310* 311* Call CHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form. 312* 313 INDE = 1 314 INDTAU = 1 315 INDHOUS = INDTAU + N 316 INDWRK = INDHOUS + LHTRD 317 LLWORK = LWORK - INDWRK + 1 318* 319 CALL CHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, W, RWORK( INDE ), 320 $ WORK( INDTAU ), WORK( INDHOUS ), LHTRD, 321 $ WORK( INDWRK ), LLWORK, IINFO ) 322* 323* For eigenvalues only, call SSTERF. For eigenvectors, first call 324* CUNGTR to generate the unitary matrix, then call CSTEQR. 325* 326 IF( .NOT.WANTZ ) THEN 327 CALL SSTERF( N, W, RWORK( INDE ), INFO ) 328 ELSE 329 CALL CUNGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), 330 $ LLWORK, IINFO ) 331 INDWRK = INDE + N 332 CALL CSTEQR( JOBZ, N, W, RWORK( INDE ), A, LDA, 333 $ RWORK( INDWRK ), INFO ) 334 END IF 335* 336* If matrix was scaled, then rescale eigenvalues appropriately. 337* 338 IF( ISCALE.EQ.1 ) THEN 339 IF( INFO.EQ.0 ) THEN 340 IMAX = N 341 ELSE 342 IMAX = INFO - 1 343 END IF 344 CALL SSCAL( IMAX, ONE / SIGMA, W, 1 ) 345 END IF 346* 347* Set WORK(1) to optimal complex workspace size. 348* 349 WORK( 1 ) = LWMIN 350* 351 RETURN 352* 353* End of CHEEV_2STAGE 354* 355 END 356