1*> \brief <b> CGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b> 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download CGEEVX + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeevx.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeevx.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeevx.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL, 22* LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, 23* RCONDV, WORK, LWORK, RWORK, INFO ) 24* 25* .. Scalar Arguments .. 26* CHARACTER BALANC, JOBVL, JOBVR, SENSE 27* INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N 28* REAL ABNRM 29* .. 30* .. Array Arguments .. 31* REAL RCONDE( * ), RCONDV( * ), RWORK( * ), 32* $ SCALE( * ) 33* COMPLEX A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), 34* $ W( * ), WORK( * ) 35* .. 36* 37* 38*> \par Purpose: 39* ============= 40*> 41*> \verbatim 42*> 43*> CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the 44*> eigenvalues and, optionally, the left and/or right eigenvectors. 45*> 46*> Optionally also, it computes a balancing transformation to improve 47*> the conditioning of the eigenvalues and eigenvectors (ILO, IHI, 48*> SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues 49*> (RCONDE), and reciprocal condition numbers for the right 50*> eigenvectors (RCONDV). 51*> 52*> The right eigenvector v(j) of A satisfies 53*> A * v(j) = lambda(j) * v(j) 54*> where lambda(j) is its eigenvalue. 55*> The left eigenvector u(j) of A satisfies 56*> u(j)**H * A = lambda(j) * u(j)**H 57*> where u(j)**H denotes the conjugate transpose of u(j). 58*> 59*> The computed eigenvectors are normalized to have Euclidean norm 60*> equal to 1 and largest component real. 61*> 62*> Balancing a matrix means permuting the rows and columns to make it 63*> more nearly upper triangular, and applying a diagonal similarity 64*> transformation D * A * D**(-1), where D is a diagonal matrix, to 65*> make its rows and columns closer in norm and the condition numbers 66*> of its eigenvalues and eigenvectors smaller. The computed 67*> reciprocal condition numbers correspond to the balanced matrix. 68*> Permuting rows and columns will not change the condition numbers 69*> (in exact arithmetic) but diagonal scaling will. For further 70*> explanation of balancing, see section 4.10.2 of the LAPACK 71*> Users' Guide. 72*> \endverbatim 73* 74* Arguments: 75* ========== 76* 77*> \param[in] BALANC 78*> \verbatim 79*> BALANC is CHARACTER*1 80*> Indicates how the input matrix should be diagonally scaled 81*> and/or permuted to improve the conditioning of its 82*> eigenvalues. 83*> = 'N': Do not diagonally scale or permute; 84*> = 'P': Perform permutations to make the matrix more nearly 85*> upper triangular. Do not diagonally scale; 86*> = 'S': Diagonally scale the matrix, ie. replace A by 87*> D*A*D**(-1), where D is a diagonal matrix chosen 88*> to make the rows and columns of A more equal in 89*> norm. Do not permute; 90*> = 'B': Both diagonally scale and permute A. 91*> 92*> Computed reciprocal condition numbers will be for the matrix 93*> after balancing and/or permuting. Permuting does not change 94*> condition numbers (in exact arithmetic), but balancing does. 95*> \endverbatim 96*> 97*> \param[in] JOBVL 98*> \verbatim 99*> JOBVL is CHARACTER*1 100*> = 'N': left eigenvectors of A are not computed; 101*> = 'V': left eigenvectors of A are computed. 102*> If SENSE = 'E' or 'B', JOBVL must = 'V'. 103*> \endverbatim 104*> 105*> \param[in] JOBVR 106*> \verbatim 107*> JOBVR is CHARACTER*1 108*> = 'N': right eigenvectors of A are not computed; 109*> = 'V': right eigenvectors of A are computed. 110*> If SENSE = 'E' or 'B', JOBVR must = 'V'. 111*> \endverbatim 112*> 113*> \param[in] SENSE 114*> \verbatim 115*> SENSE is CHARACTER*1 116*> Determines which reciprocal condition numbers are computed. 117*> = 'N': None are computed; 118*> = 'E': Computed for eigenvalues only; 119*> = 'V': Computed for right eigenvectors only; 120*> = 'B': Computed for eigenvalues and right eigenvectors. 121*> 122*> If SENSE = 'E' or 'B', both left and right eigenvectors 123*> must also be computed (JOBVL = 'V' and JOBVR = 'V'). 124*> \endverbatim 125*> 126*> \param[in] N 127*> \verbatim 128*> N is INTEGER 129*> The order of the matrix A. N >= 0. 130*> \endverbatim 131*> 132*> \param[in,out] A 133*> \verbatim 134*> A is COMPLEX array, dimension (LDA,N) 135*> On entry, the N-by-N matrix A. 136*> On exit, A has been overwritten. If JOBVL = 'V' or 137*> JOBVR = 'V', A contains the Schur form of the balanced 138*> version of the matrix A. 139*> \endverbatim 140*> 141*> \param[in] LDA 142*> \verbatim 143*> LDA is INTEGER 144*> The leading dimension of the array A. LDA >= max(1,N). 145*> \endverbatim 146*> 147*> \param[out] W 148*> \verbatim 149*> W is COMPLEX array, dimension (N) 150*> W contains the computed eigenvalues. 151*> \endverbatim 152*> 153*> \param[out] VL 154*> \verbatim 155*> VL is COMPLEX array, dimension (LDVL,N) 156*> If JOBVL = 'V', the left eigenvectors u(j) are stored one 157*> after another in the columns of VL, in the same order 158*> as their eigenvalues. 159*> If JOBVL = 'N', VL is not referenced. 160*> u(j) = VL(:,j), the j-th column of VL. 161*> \endverbatim 162*> 163*> \param[in] LDVL 164*> \verbatim 165*> LDVL is INTEGER 166*> The leading dimension of the array VL. LDVL >= 1; if 167*> JOBVL = 'V', LDVL >= N. 168*> \endverbatim 169*> 170*> \param[out] VR 171*> \verbatim 172*> VR is COMPLEX array, dimension (LDVR,N) 173*> If JOBVR = 'V', the right eigenvectors v(j) are stored one 174*> after another in the columns of VR, in the same order 175*> as their eigenvalues. 176*> If JOBVR = 'N', VR is not referenced. 177*> v(j) = VR(:,j), the j-th column of VR. 178*> \endverbatim 179*> 180*> \param[in] LDVR 181*> \verbatim 182*> LDVR is INTEGER 183*> The leading dimension of the array VR. LDVR >= 1; if 184*> JOBVR = 'V', LDVR >= N. 185*> \endverbatim 186*> 187*> \param[out] ILO 188*> \verbatim 189*> ILO is INTEGER 190*> \endverbatim 191*> 192*> \param[out] IHI 193*> \verbatim 194*> IHI is INTEGER 195*> ILO and IHI are integer values determined when A was 196*> balanced. The balanced A(i,j) = 0 if I > J and 197*> J = 1,...,ILO-1 or I = IHI+1,...,N. 198*> \endverbatim 199*> 200*> \param[out] SCALE 201*> \verbatim 202*> SCALE is REAL array, dimension (N) 203*> Details of the permutations and scaling factors applied 204*> when balancing A. If P(j) is the index of the row and column 205*> interchanged with row and column j, and D(j) is the scaling 206*> factor applied to row and column j, then 207*> SCALE(J) = P(J), for J = 1,...,ILO-1 208*> = D(J), for J = ILO,...,IHI 209*> = P(J) for J = IHI+1,...,N. 210*> The order in which the interchanges are made is N to IHI+1, 211*> then 1 to ILO-1. 212*> \endverbatim 213*> 214*> \param[out] ABNRM 215*> \verbatim 216*> ABNRM is REAL 217*> The one-norm of the balanced matrix (the maximum 218*> of the sum of absolute values of elements of any column). 219*> \endverbatim 220*> 221*> \param[out] RCONDE 222*> \verbatim 223*> RCONDE is REAL array, dimension (N) 224*> RCONDE(j) is the reciprocal condition number of the j-th 225*> eigenvalue. 226*> \endverbatim 227*> 228*> \param[out] RCONDV 229*> \verbatim 230*> RCONDV is REAL array, dimension (N) 231*> RCONDV(j) is the reciprocal condition number of the j-th 232*> right eigenvector. 233*> \endverbatim 234*> 235*> \param[out] WORK 236*> \verbatim 237*> WORK is COMPLEX array, dimension (MAX(1,LWORK)) 238*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 239*> \endverbatim 240*> 241*> \param[in] LWORK 242*> \verbatim 243*> LWORK is INTEGER 244*> The dimension of the array WORK. If SENSE = 'N' or 'E', 245*> LWORK >= max(1,2*N), and if SENSE = 'V' or 'B', 246*> LWORK >= N*N+2*N. 247*> For good performance, LWORK must generally be larger. 248*> 249*> If LWORK = -1, then a workspace query is assumed; the routine 250*> only calculates the optimal size of the WORK array, returns 251*> this value as the first entry of the WORK array, and no error 252*> message related to LWORK is issued by XERBLA. 253*> \endverbatim 254*> 255*> \param[out] RWORK 256*> \verbatim 257*> RWORK is REAL array, dimension (2*N) 258*> \endverbatim 259*> 260*> \param[out] INFO 261*> \verbatim 262*> INFO is INTEGER 263*> = 0: successful exit 264*> < 0: if INFO = -i, the i-th argument had an illegal value. 265*> > 0: if INFO = i, the QR algorithm failed to compute all the 266*> eigenvalues, and no eigenvectors or condition numbers 267*> have been computed; elements 1:ILO-1 and i+1:N of W 268*> contain eigenvalues which have converged. 269*> \endverbatim 270* 271* Authors: 272* ======== 273* 274*> \author Univ. of Tennessee 275*> \author Univ. of California Berkeley 276*> \author Univ. of Colorado Denver 277*> \author NAG Ltd. 278* 279* 280* @generated from zgeevx.f, fortran z -> c, Tue Apr 19 01:47:44 2016 281* 282*> \ingroup complexGEeigen 283* 284* ===================================================================== 285 SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL, 286 $ LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, 287 $ RCONDV, WORK, LWORK, RWORK, INFO ) 288 implicit none 289* 290* -- LAPACK driver routine -- 291* -- LAPACK is a software package provided by Univ. of Tennessee, -- 292* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 293* 294* .. Scalar Arguments .. 295 CHARACTER BALANC, JOBVL, JOBVR, SENSE 296 INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N 297 REAL ABNRM 298* .. 299* .. Array Arguments .. 300 REAL RCONDE( * ), RCONDV( * ), RWORK( * ), 301 $ SCALE( * ) 302 COMPLEX A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), 303 $ W( * ), WORK( * ) 304* .. 305* 306* ===================================================================== 307* 308* .. Parameters .. 309 REAL ZERO, ONE 310 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) 311* .. 312* .. Local Scalars .. 313 LOGICAL LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE, 314 $ WNTSNN, WNTSNV 315 CHARACTER JOB, SIDE 316 INTEGER HSWORK, I, ICOND, IERR, ITAU, IWRK, K, 317 $ LWORK_TREVC, MAXWRK, MINWRK, NOUT 318 REAL ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM 319 COMPLEX TMP 320* .. 321* .. Local Arrays .. 322 LOGICAL SELECT( 1 ) 323 REAL DUM( 1 ) 324* .. 325* .. External Subroutines .. 326 EXTERNAL SLABAD, SLASCL, XERBLA, CSSCAL, CGEBAK, CGEBAL, 327 $ CGEHRD, CHSEQR, CLACPY, CLASCL, CSCAL, CTREVC3, 328 $ CTRSNA, CUNGHR 329* .. 330* .. External Functions .. 331 LOGICAL LSAME 332 INTEGER ISAMAX, ILAENV 333 REAL SLAMCH, SCNRM2, CLANGE 334 EXTERNAL LSAME, ISAMAX, ILAENV, SLAMCH, SCNRM2, CLANGE 335* .. 336* .. Intrinsic Functions .. 337 INTRINSIC REAL, CMPLX, CONJG, AIMAG, MAX, SQRT 338* .. 339* .. Executable Statements .. 340* 341* Test the input arguments 342* 343 INFO = 0 344 LQUERY = ( LWORK.EQ.-1 ) 345 WANTVL = LSAME( JOBVL, 'V' ) 346 WANTVR = LSAME( JOBVR, 'V' ) 347 WNTSNN = LSAME( SENSE, 'N' ) 348 WNTSNE = LSAME( SENSE, 'E' ) 349 WNTSNV = LSAME( SENSE, 'V' ) 350 WNTSNB = LSAME( SENSE, 'B' ) 351 IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 'S' ) .OR. 352 $ LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) ) THEN 353 INFO = -1 354 ELSE IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN 355 INFO = -2 356 ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN 357 INFO = -3 358 ELSE IF( .NOT.( WNTSNN .OR. WNTSNE .OR. WNTSNB .OR. WNTSNV ) .OR. 359 $ ( ( WNTSNE .OR. WNTSNB ) .AND. .NOT.( WANTVL .AND. 360 $ WANTVR ) ) ) THEN 361 INFO = -4 362 ELSE IF( N.LT.0 ) THEN 363 INFO = -5 364 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 365 INFO = -7 366 ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN 367 INFO = -10 368 ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN 369 INFO = -12 370 END IF 371* 372* Compute workspace 373* (Note: Comments in the code beginning "Workspace:" describe the 374* minimal amount of workspace needed at that point in the code, 375* as well as the preferred amount for good performance. 376* CWorkspace refers to complex workspace, and RWorkspace to real 377* workspace. NB refers to the optimal block size for the 378* immediately following subroutine, as returned by ILAENV. 379* HSWORK refers to the workspace preferred by CHSEQR, as 380* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, 381* the worst case.) 382* 383 IF( INFO.EQ.0 ) THEN 384 IF( N.EQ.0 ) THEN 385 MINWRK = 1 386 MAXWRK = 1 387 ELSE 388 MAXWRK = N + N*ILAENV( 1, 'CGEHRD', ' ', N, 1, N, 0 ) 389* 390 IF( WANTVL ) THEN 391 CALL CTREVC3( 'L', 'B', SELECT, N, A, LDA, 392 $ VL, LDVL, VR, LDVR, 393 $ N, NOUT, WORK, -1, RWORK, -1, IERR ) 394 LWORK_TREVC = INT( WORK(1) ) 395 MAXWRK = MAX( MAXWRK, LWORK_TREVC ) 396 CALL CHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL, 397 $ WORK, -1, INFO ) 398 ELSE IF( WANTVR ) THEN 399 CALL CTREVC3( 'R', 'B', SELECT, N, A, LDA, 400 $ VL, LDVL, VR, LDVR, 401 $ N, NOUT, WORK, -1, RWORK, -1, IERR ) 402 LWORK_TREVC = INT( WORK(1) ) 403 MAXWRK = MAX( MAXWRK, LWORK_TREVC ) 404 CALL CHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR, 405 $ WORK, -1, INFO ) 406 ELSE 407 IF( WNTSNN ) THEN 408 CALL CHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR, 409 $ WORK, -1, INFO ) 410 ELSE 411 CALL CHSEQR( 'S', 'N', N, 1, N, A, LDA, W, VR, LDVR, 412 $ WORK, -1, INFO ) 413 END IF 414 END IF 415 HSWORK = INT( WORK(1) ) 416* 417 IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN 418 MINWRK = 2*N 419 IF( .NOT.( WNTSNN .OR. WNTSNE ) ) 420 $ MINWRK = MAX( MINWRK, N*N + 2*N ) 421 MAXWRK = MAX( MAXWRK, HSWORK ) 422 IF( .NOT.( WNTSNN .OR. WNTSNE ) ) 423 $ MAXWRK = MAX( MAXWRK, N*N + 2*N ) 424 ELSE 425 MINWRK = 2*N 426 IF( .NOT.( WNTSNN .OR. WNTSNE ) ) 427 $ MINWRK = MAX( MINWRK, N*N + 2*N ) 428 MAXWRK = MAX( MAXWRK, HSWORK ) 429 MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'CUNGHR', 430 $ ' ', N, 1, N, -1 ) ) 431 IF( .NOT.( WNTSNN .OR. WNTSNE ) ) 432 $ MAXWRK = MAX( MAXWRK, N*N + 2*N ) 433 MAXWRK = MAX( MAXWRK, 2*N ) 434 END IF 435 MAXWRK = MAX( MAXWRK, MINWRK ) 436 END IF 437 WORK( 1 ) = MAXWRK 438* 439 IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN 440 INFO = -20 441 END IF 442 END IF 443* 444 IF( INFO.NE.0 ) THEN 445 CALL XERBLA( 'CGEEVX', -INFO ) 446 RETURN 447 ELSE IF( LQUERY ) THEN 448 RETURN 449 END IF 450* 451* Quick return if possible 452* 453 IF( N.EQ.0 ) 454 $ RETURN 455* 456* Get machine constants 457* 458 EPS = SLAMCH( 'P' ) 459 SMLNUM = SLAMCH( 'S' ) 460 BIGNUM = ONE / SMLNUM 461 CALL SLABAD( SMLNUM, BIGNUM ) 462 SMLNUM = SQRT( SMLNUM ) / EPS 463 BIGNUM = ONE / SMLNUM 464* 465* Scale A if max element outside range [SMLNUM,BIGNUM] 466* 467 ICOND = 0 468 ANRM = CLANGE( 'M', N, N, A, LDA, DUM ) 469 SCALEA = .FALSE. 470 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 471 SCALEA = .TRUE. 472 CSCALE = SMLNUM 473 ELSE IF( ANRM.GT.BIGNUM ) THEN 474 SCALEA = .TRUE. 475 CSCALE = BIGNUM 476 END IF 477 IF( SCALEA ) 478 $ CALL CLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR ) 479* 480* Balance the matrix and compute ABNRM 481* 482 CALL CGEBAL( BALANC, N, A, LDA, ILO, IHI, SCALE, IERR ) 483 ABNRM = CLANGE( '1', N, N, A, LDA, DUM ) 484 IF( SCALEA ) THEN 485 DUM( 1 ) = ABNRM 486 CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, 1, 1, DUM, 1, IERR ) 487 ABNRM = DUM( 1 ) 488 END IF 489* 490* Reduce to upper Hessenberg form 491* (CWorkspace: need 2*N, prefer N+N*NB) 492* (RWorkspace: none) 493* 494 ITAU = 1 495 IWRK = ITAU + N 496 CALL CGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ), 497 $ LWORK-IWRK+1, IERR ) 498* 499 IF( WANTVL ) THEN 500* 501* Want left eigenvectors 502* Copy Householder vectors to VL 503* 504 SIDE = 'L' 505 CALL CLACPY( 'L', N, N, A, LDA, VL, LDVL ) 506* 507* Generate unitary matrix in VL 508* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) 509* (RWorkspace: none) 510* 511 CALL CUNGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ), 512 $ LWORK-IWRK+1, IERR ) 513* 514* Perform QR iteration, accumulating Schur vectors in VL 515* (CWorkspace: need 1, prefer HSWORK (see comments) ) 516* (RWorkspace: none) 517* 518 IWRK = ITAU 519 CALL CHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VL, LDVL, 520 $ WORK( IWRK ), LWORK-IWRK+1, INFO ) 521* 522 IF( WANTVR ) THEN 523* 524* Want left and right eigenvectors 525* Copy Schur vectors to VR 526* 527 SIDE = 'B' 528 CALL CLACPY( 'F', N, N, VL, LDVL, VR, LDVR ) 529 END IF 530* 531 ELSE IF( WANTVR ) THEN 532* 533* Want right eigenvectors 534* Copy Householder vectors to VR 535* 536 SIDE = 'R' 537 CALL CLACPY( 'L', N, N, A, LDA, VR, LDVR ) 538* 539* Generate unitary matrix in VR 540* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) 541* (RWorkspace: none) 542* 543 CALL CUNGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ), 544 $ LWORK-IWRK+1, IERR ) 545* 546* Perform QR iteration, accumulating Schur vectors in VR 547* (CWorkspace: need 1, prefer HSWORK (see comments) ) 548* (RWorkspace: none) 549* 550 IWRK = ITAU 551 CALL CHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VR, LDVR, 552 $ WORK( IWRK ), LWORK-IWRK+1, INFO ) 553* 554 ELSE 555* 556* Compute eigenvalues only 557* If condition numbers desired, compute Schur form 558* 559 IF( WNTSNN ) THEN 560 JOB = 'E' 561 ELSE 562 JOB = 'S' 563 END IF 564* 565* (CWorkspace: need 1, prefer HSWORK (see comments) ) 566* (RWorkspace: none) 567* 568 IWRK = ITAU 569 CALL CHSEQR( JOB, 'N', N, ILO, IHI, A, LDA, W, VR, LDVR, 570 $ WORK( IWRK ), LWORK-IWRK+1, INFO ) 571 END IF 572* 573* If INFO .NE. 0 from CHSEQR, then quit 574* 575 IF( INFO.NE.0 ) 576 $ GO TO 50 577* 578 IF( WANTVL .OR. WANTVR ) THEN 579* 580* Compute left and/or right eigenvectors 581* (CWorkspace: need 2*N, prefer N + 2*N*NB) 582* (RWorkspace: need N) 583* 584 CALL CTREVC3( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, 585 $ N, NOUT, WORK( IWRK ), LWORK-IWRK+1, 586 $ RWORK, N, IERR ) 587 END IF 588* 589* Compute condition numbers if desired 590* (CWorkspace: need N*N+2*N unless SENSE = 'E') 591* (RWorkspace: need 2*N unless SENSE = 'E') 592* 593 IF( .NOT.WNTSNN ) THEN 594 CALL CTRSNA( SENSE, 'A', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, 595 $ RCONDE, RCONDV, N, NOUT, WORK( IWRK ), N, RWORK, 596 $ ICOND ) 597 END IF 598* 599 IF( WANTVL ) THEN 600* 601* Undo balancing of left eigenvectors 602* 603 CALL CGEBAK( BALANC, 'L', N, ILO, IHI, SCALE, N, VL, LDVL, 604 $ IERR ) 605* 606* Normalize left eigenvectors and make largest component real 607* 608 DO 20 I = 1, N 609 SCL = ONE / SCNRM2( N, VL( 1, I ), 1 ) 610 CALL CSSCAL( N, SCL, VL( 1, I ), 1 ) 611 DO 10 K = 1, N 612 RWORK( K ) = REAL( VL( K, I ) )**2 + 613 $ AIMAG( VL( K, I ) )**2 614 10 CONTINUE 615 K = ISAMAX( N, RWORK, 1 ) 616 TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( K ) ) 617 CALL CSCAL( N, TMP, VL( 1, I ), 1 ) 618 VL( K, I ) = CMPLX( REAL( VL( K, I ) ), ZERO ) 619 20 CONTINUE 620 END IF 621* 622 IF( WANTVR ) THEN 623* 624* Undo balancing of right eigenvectors 625* 626 CALL CGEBAK( BALANC, 'R', N, ILO, IHI, SCALE, N, VR, LDVR, 627 $ IERR ) 628* 629* Normalize right eigenvectors and make largest component real 630* 631 DO 40 I = 1, N 632 SCL = ONE / SCNRM2( N, VR( 1, I ), 1 ) 633 CALL CSSCAL( N, SCL, VR( 1, I ), 1 ) 634 DO 30 K = 1, N 635 RWORK( K ) = REAL( VR( K, I ) )**2 + 636 $ AIMAG( VR( K, I ) )**2 637 30 CONTINUE 638 K = ISAMAX( N, RWORK, 1 ) 639 TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( K ) ) 640 CALL CSCAL( N, TMP, VR( 1, I ), 1 ) 641 VR( K, I ) = CMPLX( REAL( VR( K, I ) ), ZERO ) 642 40 CONTINUE 643 END IF 644* 645* Undo scaling if necessary 646* 647 50 CONTINUE 648 IF( SCALEA ) THEN 649 CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, W( INFO+1 ), 650 $ MAX( N-INFO, 1 ), IERR ) 651 IF( INFO.EQ.0 ) THEN 652 IF( ( WNTSNV .OR. WNTSNB ) .AND. ICOND.EQ.0 ) 653 $ CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, N, 1, RCONDV, N, 654 $ IERR ) 655 ELSE 656 CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR ) 657 END IF 658 END IF 659* 660 WORK( 1 ) = MAXWRK 661 RETURN 662* 663* End of CGEEVX 664* 665 END 666