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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI, 00002 $ VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, 00003 $ RCONDE, RCONDV, WORK, LWORK, IWORK, INFO ) 00004 * 00005 * -- LAPACK driver routine (version 3.3.1) -- 00006 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00007 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00008 * -- April 2011 -- 00009 * 00010 * .. Scalar Arguments .. 00011 CHARACTER BALANC, JOBVL, JOBVR, SENSE 00012 INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N 00013 DOUBLE PRECISION ABNRM 00014 * .. 00015 * .. Array Arguments .. 00016 INTEGER IWORK( * ) 00017 DOUBLE PRECISION A( LDA, * ), RCONDE( * ), RCONDV( * ), 00018 $ SCALE( * ), VL( LDVL, * ), VR( LDVR, * ), 00019 $ WI( * ), WORK( * ), WR( * ) 00020 * .. 00021 * 00022 * Purpose 00023 * ======= 00024 * 00025 * DGEEVX computes for an N-by-N real nonsymmetric matrix A, the 00026 * eigenvalues and, optionally, the left and/or right eigenvectors. 00027 * 00028 * Optionally also, it computes a balancing transformation to improve 00029 * the conditioning of the eigenvalues and eigenvectors (ILO, IHI, 00030 * SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues 00031 * (RCONDE), and reciprocal condition numbers for the right 00032 * eigenvectors (RCONDV). 00033 * 00034 * The right eigenvector v(j) of A satisfies 00035 * A * v(j) = lambda(j) * v(j) 00036 * where lambda(j) is its eigenvalue. 00037 * The left eigenvector u(j) of A satisfies 00038 * u(j)**T * A = lambda(j) * u(j)**T 00039 * where u(j)**T denotes the transpose of u(j). 00040 * 00041 * The computed eigenvectors are normalized to have Euclidean norm 00042 * equal to 1 and largest component real. 00043 * 00044 * Balancing a matrix means permuting the rows and columns to make it 00045 * more nearly upper triangular, and applying a diagonal similarity 00046 * transformation D * A * D**(-1), where D is a diagonal matrix, to 00047 * make its rows and columns closer in norm and the condition numbers 00048 * of its eigenvalues and eigenvectors smaller. The computed 00049 * reciprocal condition numbers correspond to the balanced matrix. 00050 * Permuting rows and columns will not change the condition numbers 00051 * (in exact arithmetic) but diagonal scaling will. For further 00052 * explanation of balancing, see section 4.10.2 of the LAPACK 00053 * Users' Guide. 00054 * 00055 * Arguments 00056 * ========= 00057 * 00058 * BALANC (input) CHARACTER*1 00059 * Indicates how the input matrix should be diagonally scaled 00060 * and/or permuted to improve the conditioning of its 00061 * eigenvalues. 00062 * = 'N': Do not diagonally scale or permute; 00063 * = 'P': Perform permutations to make the matrix more nearly 00064 * upper triangular. Do not diagonally scale; 00065 * = 'S': Diagonally scale the matrix, i.e. replace A by 00066 * D*A*D**(-1), where D is a diagonal matrix chosen 00067 * to make the rows and columns of A more equal in 00068 * norm. Do not permute; 00069 * = 'B': Both diagonally scale and permute A. 00070 * 00071 * Computed reciprocal condition numbers will be for the matrix 00072 * after balancing and/or permuting. Permuting does not change 00073 * condition numbers (in exact arithmetic), but balancing does. 00074 * 00075 * JOBVL (input) CHARACTER*1 00076 * = 'N': left eigenvectors of A are not computed; 00077 * = 'V': left eigenvectors of A are computed. 00078 * If SENSE = 'E' or 'B', JOBVL must = 'V'. 00079 * 00080 * JOBVR (input) CHARACTER*1 00081 * = 'N': right eigenvectors of A are not computed; 00082 * = 'V': right eigenvectors of A are computed. 00083 * If SENSE = 'E' or 'B', JOBVR must = 'V'. 00084 * 00085 * SENSE (input) CHARACTER*1 00086 * Determines which reciprocal condition numbers are computed. 00087 * = 'N': None are computed; 00088 * = 'E': Computed for eigenvalues only; 00089 * = 'V': Computed for right eigenvectors only; 00090 * = 'B': Computed for eigenvalues and right eigenvectors. 00091 * 00092 * If SENSE = 'E' or 'B', both left and right eigenvectors 00093 * must also be computed (JOBVL = 'V' and JOBVR = 'V'). 00094 * 00095 * N (input) INTEGER 00096 * The order of the matrix A. N >= 0. 00097 * 00098 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) 00099 * On entry, the N-by-N matrix A. 00100 * On exit, A has been overwritten. If JOBVL = 'V' or 00101 * JOBVR = 'V', A contains the real Schur form of the balanced 00102 * version of the input matrix A. 00103 * 00104 * LDA (input) INTEGER 00105 * The leading dimension of the array A. LDA >= max(1,N). 00106 * 00107 * WR (output) DOUBLE PRECISION array, dimension (N) 00108 * WI (output) DOUBLE PRECISION array, dimension (N) 00109 * WR and WI contain the real and imaginary parts, 00110 * respectively, of the computed eigenvalues. Complex 00111 * conjugate pairs of eigenvalues will appear consecutively 00112 * with the eigenvalue having the positive imaginary part 00113 * first. 00114 * 00115 * VL (output) DOUBLE PRECISION array, dimension (LDVL,N) 00116 * If JOBVL = 'V', the left eigenvectors u(j) are stored one 00117 * after another in the columns of VL, in the same order 00118 * as their eigenvalues. 00119 * If JOBVL = 'N', VL is not referenced. 00120 * If the j-th eigenvalue is real, then u(j) = VL(:,j), 00121 * the j-th column of VL. 00122 * If the j-th and (j+1)-st eigenvalues form a complex 00123 * conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and 00124 * u(j+1) = VL(:,j) - i*VL(:,j+1). 00125 * 00126 * LDVL (input) INTEGER 00127 * The leading dimension of the array VL. LDVL >= 1; if 00128 * JOBVL = 'V', LDVL >= N. 00129 * 00130 * VR (output) DOUBLE PRECISION array, dimension (LDVR,N) 00131 * If JOBVR = 'V', the right eigenvectors v(j) are stored one 00132 * after another in the columns of VR, in the same order 00133 * as their eigenvalues. 00134 * If JOBVR = 'N', VR is not referenced. 00135 * If the j-th eigenvalue is real, then v(j) = VR(:,j), 00136 * the j-th column of VR. 00137 * If the j-th and (j+1)-st eigenvalues form a complex 00138 * conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and 00139 * v(j+1) = VR(:,j) - i*VR(:,j+1). 00140 * 00141 * LDVR (input) INTEGER 00142 * The leading dimension of the array VR. LDVR >= 1, and if 00143 * JOBVR = 'V', LDVR >= N. 00144 * 00145 * ILO (output) INTEGER 00146 * IHI (output) INTEGER 00147 * ILO and IHI are integer values determined when A was 00148 * balanced. The balanced A(i,j) = 0 if I > J and 00149 * J = 1,...,ILO-1 or I = IHI+1,...,N. 00150 * 00151 * SCALE (output) DOUBLE PRECISION array, dimension (N) 00152 * Details of the permutations and scaling factors applied 00153 * when balancing A. If P(j) is the index of the row and column 00154 * interchanged with row and column j, and D(j) is the scaling 00155 * factor applied to row and column j, then 00156 * SCALE(J) = P(J), for J = 1,...,ILO-1 00157 * = D(J), for J = ILO,...,IHI 00158 * = P(J) for J = IHI+1,...,N. 00159 * The order in which the interchanges are made is N to IHI+1, 00160 * then 1 to ILO-1. 00161 * 00162 * ABNRM (output) DOUBLE PRECISION 00163 * The one-norm of the balanced matrix (the maximum 00164 * of the sum of absolute values of elements of any column). 00165 * 00166 * RCONDE (output) DOUBLE PRECISION array, dimension (N) 00167 * RCONDE(j) is the reciprocal condition number of the j-th 00168 * eigenvalue. 00169 * 00170 * RCONDV (output) DOUBLE PRECISION array, dimension (N) 00171 * RCONDV(j) is the reciprocal condition number of the j-th 00172 * right eigenvector. 00173 * 00174 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00175 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00176 * 00177 * LWORK (input) INTEGER 00178 * The dimension of the array WORK. If SENSE = 'N' or 'E', 00179 * LWORK >= max(1,2*N), and if JOBVL = 'V' or JOBVR = 'V', 00180 * LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6). 00181 * For good performance, LWORK must generally be larger. 00182 * 00183 * If LWORK = -1, then a workspace query is assumed; the routine 00184 * only calculates the optimal size of the WORK array, returns 00185 * this value as the first entry of the WORK array, and no error 00186 * message related to LWORK is issued by XERBLA. 00187 * 00188 * IWORK (workspace) INTEGER array, dimension (2*N-2) 00189 * If SENSE = 'N' or 'E', not referenced. 00190 * 00191 * INFO (output) INTEGER 00192 * = 0: successful exit 00193 * < 0: if INFO = -i, the i-th argument had an illegal value. 00194 * > 0: if INFO = i, the QR algorithm failed to compute all the 00195 * eigenvalues, and no eigenvectors or condition numbers 00196 * have been computed; elements 1:ILO-1 and i+1:N of WR 00197 * and WI contain eigenvalues which have converged. 00198 * 00199 * ===================================================================== 00200 * 00201 * .. Parameters .. 00202 DOUBLE PRECISION ZERO, ONE 00203 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) 00204 * .. 00205 * .. Local Scalars .. 00206 LOGICAL LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE, 00207 $ WNTSNN, WNTSNV 00208 CHARACTER JOB, SIDE 00209 INTEGER HSWORK, I, ICOND, IERR, ITAU, IWRK, K, MAXWRK, 00210 $ MINWRK, NOUT 00211 DOUBLE PRECISION ANRM, BIGNUM, CS, CSCALE, EPS, R, SCL, SMLNUM, 00212 $ SN 00213 * .. 00214 * .. Local Arrays .. 00215 LOGICAL SELECT( 1 ) 00216 DOUBLE PRECISION DUM( 1 ) 00217 * .. 00218 * .. External Subroutines .. 00219 EXTERNAL DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLABAD, DLACPY, 00220 $ DLARTG, DLASCL, DORGHR, DROT, DSCAL, DTREVC, 00221 $ DTRSNA, XERBLA 00222 * .. 00223 * .. External Functions .. 00224 LOGICAL LSAME 00225 INTEGER IDAMAX, ILAENV 00226 DOUBLE PRECISION DLAMCH, DLANGE, DLAPY2, DNRM2 00227 EXTERNAL LSAME, IDAMAX, ILAENV, DLAMCH, DLANGE, DLAPY2, 00228 $ DNRM2 00229 * .. 00230 * .. Intrinsic Functions .. 00231 INTRINSIC MAX, SQRT 00232 * .. 00233 * .. Executable Statements .. 00234 * 00235 * Test the input arguments 00236 * 00237 INFO = 0 00238 LQUERY = ( LWORK.EQ.-1 ) 00239 WANTVL = LSAME( JOBVL, 'V' ) 00240 WANTVR = LSAME( JOBVR, 'V' ) 00241 WNTSNN = LSAME( SENSE, 'N' ) 00242 WNTSNE = LSAME( SENSE, 'E' ) 00243 WNTSNV = LSAME( SENSE, 'V' ) 00244 WNTSNB = LSAME( SENSE, 'B' ) 00245 IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 00246 $ 'S' ) .OR. LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) ) 00247 $ THEN 00248 INFO = -1 00249 ELSE IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN 00250 INFO = -2 00251 ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN 00252 INFO = -3 00253 ELSE IF( .NOT.( WNTSNN .OR. WNTSNE .OR. WNTSNB .OR. WNTSNV ) .OR. 00254 $ ( ( WNTSNE .OR. WNTSNB ) .AND. .NOT.( WANTVL .AND. 00255 $ WANTVR ) ) ) THEN 00256 INFO = -4 00257 ELSE IF( N.LT.0 ) THEN 00258 INFO = -5 00259 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00260 INFO = -7 00261 ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN 00262 INFO = -11 00263 ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN 00264 INFO = -13 00265 END IF 00266 * 00267 * Compute workspace 00268 * (Note: Comments in the code beginning "Workspace:" describe the 00269 * minimal amount of workspace needed at that point in the code, 00270 * as well as the preferred amount for good performance. 00271 * NB refers to the optimal block size for the immediately 00272 * following subroutine, as returned by ILAENV. 00273 * HSWORK refers to the workspace preferred by DHSEQR, as 00274 * calculated below. HSWORK is computed assuming ILO=1 and IHI=N, 00275 * the worst case.) 00276 * 00277 IF( INFO.EQ.0 ) THEN 00278 IF( N.EQ.0 ) THEN 00279 MINWRK = 1 00280 MAXWRK = 1 00281 ELSE 00282 MAXWRK = N + N*ILAENV( 1, 'DGEHRD', ' ', N, 1, N, 0 ) 00283 * 00284 IF( WANTVL ) THEN 00285 CALL DHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VL, LDVL, 00286 $ WORK, -1, INFO ) 00287 ELSE IF( WANTVR ) THEN 00288 CALL DHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VR, LDVR, 00289 $ WORK, -1, INFO ) 00290 ELSE 00291 IF( WNTSNN ) THEN 00292 CALL DHSEQR( 'E', 'N', N, 1, N, A, LDA, WR, WI, VR, 00293 $ LDVR, WORK, -1, INFO ) 00294 ELSE 00295 CALL DHSEQR( 'S', 'N', N, 1, N, A, LDA, WR, WI, VR, 00296 $ LDVR, WORK, -1, INFO ) 00297 END IF 00298 END IF 00299 HSWORK = WORK( 1 ) 00300 * 00301 IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN 00302 MINWRK = 2*N 00303 IF( .NOT.WNTSNN ) 00304 $ MINWRK = MAX( MINWRK, N*N+6*N ) 00305 MAXWRK = MAX( MAXWRK, HSWORK ) 00306 IF( .NOT.WNTSNN ) 00307 $ MAXWRK = MAX( MAXWRK, N*N + 6*N ) 00308 ELSE 00309 MINWRK = 3*N 00310 IF( ( .NOT.WNTSNN ) .AND. ( .NOT.WNTSNE ) ) 00311 $ MINWRK = MAX( MINWRK, N*N + 6*N ) 00312 MAXWRK = MAX( MAXWRK, HSWORK ) 00313 MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'DORGHR', 00314 $ ' ', N, 1, N, -1 ) ) 00315 IF( ( .NOT.WNTSNN ) .AND. ( .NOT.WNTSNE ) ) 00316 $ MAXWRK = MAX( MAXWRK, N*N + 6*N ) 00317 MAXWRK = MAX( MAXWRK, 3*N ) 00318 END IF 00319 MAXWRK = MAX( MAXWRK, MINWRK ) 00320 END IF 00321 WORK( 1 ) = MAXWRK 00322 * 00323 IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN 00324 INFO = -21 00325 END IF 00326 END IF 00327 * 00328 IF( INFO.NE.0 ) THEN 00329 CALL XERBLA( 'DGEEVX', -INFO ) 00330 RETURN 00331 ELSE IF( LQUERY ) THEN 00332 RETURN 00333 END IF 00334 * 00335 * Quick return if possible 00336 * 00337 IF( N.EQ.0 ) 00338 $ RETURN 00339 * 00340 * Get machine constants 00341 * 00342 EPS = DLAMCH( 'P' ) 00343 SMLNUM = DLAMCH( 'S' ) 00344 BIGNUM = ONE / SMLNUM 00345 CALL DLABAD( SMLNUM, BIGNUM ) 00346 SMLNUM = SQRT( SMLNUM ) / EPS 00347 BIGNUM = ONE / SMLNUM 00348 * 00349 * Scale A if max element outside range [SMLNUM,BIGNUM] 00350 * 00351 ICOND = 0 00352 ANRM = DLANGE( 'M', N, N, A, LDA, DUM ) 00353 SCALEA = .FALSE. 00354 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 00355 SCALEA = .TRUE. 00356 CSCALE = SMLNUM 00357 ELSE IF( ANRM.GT.BIGNUM ) THEN 00358 SCALEA = .TRUE. 00359 CSCALE = BIGNUM 00360 END IF 00361 IF( SCALEA ) 00362 $ CALL DLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR ) 00363 * 00364 * Balance the matrix and compute ABNRM 00365 * 00366 CALL DGEBAL( BALANC, N, A, LDA, ILO, IHI, SCALE, IERR ) 00367 ABNRM = DLANGE( '1', N, N, A, LDA, DUM ) 00368 IF( SCALEA ) THEN 00369 DUM( 1 ) = ABNRM 00370 CALL DLASCL( 'G', 0, 0, CSCALE, ANRM, 1, 1, DUM, 1, IERR ) 00371 ABNRM = DUM( 1 ) 00372 END IF 00373 * 00374 * Reduce to upper Hessenberg form 00375 * (Workspace: need 2*N, prefer N+N*NB) 00376 * 00377 ITAU = 1 00378 IWRK = ITAU + N 00379 CALL DGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ), 00380 $ LWORK-IWRK+1, IERR ) 00381 * 00382 IF( WANTVL ) THEN 00383 * 00384 * Want left eigenvectors 00385 * Copy Householder vectors to VL 00386 * 00387 SIDE = 'L' 00388 CALL DLACPY( 'L', N, N, A, LDA, VL, LDVL ) 00389 * 00390 * Generate orthogonal matrix in VL 00391 * (Workspace: need 2*N-1, prefer N+(N-1)*NB) 00392 * 00393 CALL DORGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ), 00394 $ LWORK-IWRK+1, IERR ) 00395 * 00396 * Perform QR iteration, accumulating Schur vectors in VL 00397 * (Workspace: need 1, prefer HSWORK (see comments) ) 00398 * 00399 IWRK = ITAU 00400 CALL DHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, WR, WI, VL, LDVL, 00401 $ WORK( IWRK ), LWORK-IWRK+1, INFO ) 00402 * 00403 IF( WANTVR ) THEN 00404 * 00405 * Want left and right eigenvectors 00406 * Copy Schur vectors to VR 00407 * 00408 SIDE = 'B' 00409 CALL DLACPY( 'F', N, N, VL, LDVL, VR, LDVR ) 00410 END IF 00411 * 00412 ELSE IF( WANTVR ) THEN 00413 * 00414 * Want right eigenvectors 00415 * Copy Householder vectors to VR 00416 * 00417 SIDE = 'R' 00418 CALL DLACPY( 'L', N, N, A, LDA, VR, LDVR ) 00419 * 00420 * Generate orthogonal matrix in VR 00421 * (Workspace: need 2*N-1, prefer N+(N-1)*NB) 00422 * 00423 CALL DORGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ), 00424 $ LWORK-IWRK+1, IERR ) 00425 * 00426 * Perform QR iteration, accumulating Schur vectors in VR 00427 * (Workspace: need 1, prefer HSWORK (see comments) ) 00428 * 00429 IWRK = ITAU 00430 CALL DHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, WR, WI, VR, LDVR, 00431 $ WORK( IWRK ), LWORK-IWRK+1, INFO ) 00432 * 00433 ELSE 00434 * 00435 * Compute eigenvalues only 00436 * If condition numbers desired, compute Schur form 00437 * 00438 IF( WNTSNN ) THEN 00439 JOB = 'E' 00440 ELSE 00441 JOB = 'S' 00442 END IF 00443 * 00444 * (Workspace: need 1, prefer HSWORK (see comments) ) 00445 * 00446 IWRK = ITAU 00447 CALL DHSEQR( JOB, 'N', N, ILO, IHI, A, LDA, WR, WI, VR, LDVR, 00448 $ WORK( IWRK ), LWORK-IWRK+1, INFO ) 00449 END IF 00450 * 00451 * If INFO > 0 from DHSEQR, then quit 00452 * 00453 IF( INFO.GT.0 ) 00454 $ GO TO 50 00455 * 00456 IF( WANTVL .OR. WANTVR ) THEN 00457 * 00458 * Compute left and/or right eigenvectors 00459 * (Workspace: need 3*N) 00460 * 00461 CALL DTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, 00462 $ N, NOUT, WORK( IWRK ), IERR ) 00463 END IF 00464 * 00465 * Compute condition numbers if desired 00466 * (Workspace: need N*N+6*N unless SENSE = 'E') 00467 * 00468 IF( .NOT.WNTSNN ) THEN 00469 CALL DTRSNA( SENSE, 'A', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, 00470 $ RCONDE, RCONDV, N, NOUT, WORK( IWRK ), N, IWORK, 00471 $ ICOND ) 00472 END IF 00473 * 00474 IF( WANTVL ) THEN 00475 * 00476 * Undo balancing of left eigenvectors 00477 * 00478 CALL DGEBAK( BALANC, 'L', N, ILO, IHI, SCALE, N, VL, LDVL, 00479 $ IERR ) 00480 * 00481 * Normalize left eigenvectors and make largest component real 00482 * 00483 DO 20 I = 1, N 00484 IF( WI( I ).EQ.ZERO ) THEN 00485 SCL = ONE / DNRM2( N, VL( 1, I ), 1 ) 00486 CALL DSCAL( N, SCL, VL( 1, I ), 1 ) 00487 ELSE IF( WI( I ).GT.ZERO ) THEN 00488 SCL = ONE / DLAPY2( DNRM2( N, VL( 1, I ), 1 ), 00489 $ DNRM2( N, VL( 1, I+1 ), 1 ) ) 00490 CALL DSCAL( N, SCL, VL( 1, I ), 1 ) 00491 CALL DSCAL( N, SCL, VL( 1, I+1 ), 1 ) 00492 DO 10 K = 1, N 00493 WORK( K ) = VL( K, I )**2 + VL( K, I+1 )**2 00494 10 CONTINUE 00495 K = IDAMAX( N, WORK, 1 ) 00496 CALL DLARTG( VL( K, I ), VL( K, I+1 ), CS, SN, R ) 00497 CALL DROT( N, VL( 1, I ), 1, VL( 1, I+1 ), 1, CS, SN ) 00498 VL( K, I+1 ) = ZERO 00499 END IF 00500 20 CONTINUE 00501 END IF 00502 * 00503 IF( WANTVR ) THEN 00504 * 00505 * Undo balancing of right eigenvectors 00506 * 00507 CALL DGEBAK( BALANC, 'R', N, ILO, IHI, SCALE, N, VR, LDVR, 00508 $ IERR ) 00509 * 00510 * Normalize right eigenvectors and make largest component real 00511 * 00512 DO 40 I = 1, N 00513 IF( WI( I ).EQ.ZERO ) THEN 00514 SCL = ONE / DNRM2( N, VR( 1, I ), 1 ) 00515 CALL DSCAL( N, SCL, VR( 1, I ), 1 ) 00516 ELSE IF( WI( I ).GT.ZERO ) THEN 00517 SCL = ONE / DLAPY2( DNRM2( N, VR( 1, I ), 1 ), 00518 $ DNRM2( N, VR( 1, I+1 ), 1 ) ) 00519 CALL DSCAL( N, SCL, VR( 1, I ), 1 ) 00520 CALL DSCAL( N, SCL, VR( 1, I+1 ), 1 ) 00521 DO 30 K = 1, N 00522 WORK( K ) = VR( K, I )**2 + VR( K, I+1 )**2 00523 30 CONTINUE 00524 K = IDAMAX( N, WORK, 1 ) 00525 CALL DLARTG( VR( K, I ), VR( K, I+1 ), CS, SN, R ) 00526 CALL DROT( N, VR( 1, I ), 1, VR( 1, I+1 ), 1, CS, SN ) 00527 VR( K, I+1 ) = ZERO 00528 END IF 00529 40 CONTINUE 00530 END IF 00531 * 00532 * Undo scaling if necessary 00533 * 00534 50 CONTINUE 00535 IF( SCALEA ) THEN 00536 CALL DLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, WR( INFO+1 ), 00537 $ MAX( N-INFO, 1 ), IERR ) 00538 CALL DLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, WI( INFO+1 ), 00539 $ MAX( N-INFO, 1 ), IERR ) 00540 IF( INFO.EQ.0 ) THEN 00541 IF( ( WNTSNV .OR. WNTSNB ) .AND. ICOND.EQ.0 ) 00542 $ CALL DLASCL( 'G', 0, 0, CSCALE, ANRM, N, 1, RCONDV, N, 00543 $ IERR ) 00544 ELSE 00545 CALL DLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, WR, N, 00546 $ IERR ) 00547 CALL DLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, WI, N, 00548 $ IERR ) 00549 END IF 00550 END IF 00551 * 00552 WORK( 1 ) = MAXWRK 00553 RETURN 00554 * 00555 * End of DGEEVX 00556 * 00557 END
1.7.3 
