00001 /* ztgsen.f -- translated by f2c (version 20061008). 00002 You must link the resulting object file with libf2c: 00003 on Microsoft Windows system, link with libf2c.lib; 00004 on Linux or Unix systems, link with .../path/to/libf2c.a -lm 00005 or, if you install libf2c.a in a standard place, with -lf2c -lm 00006 -- in that order, at the end of the command line, as in 00007 cc *.o -lf2c -lm 00008 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., 00009 00010 http://www.netlib.org/f2c/libf2c.zip 00011 */ 00012 00013 #include "f2c.h" 00014 #include "blaswrap.h" 00015 00016 /* Table of constant values */ 00017 00018 static integer c__1 = 1; 00019 00020 /* Subroutine */ int ztgsen_(integer *ijob, logical *wantq, logical *wantz, 00021 logical *select, integer *n, doublecomplex *a, integer *lda, 00022 doublecomplex *b, integer *ldb, doublecomplex *alpha, doublecomplex * 00023 beta, doublecomplex *q, integer *ldq, doublecomplex *z__, integer * 00024 ldz, integer *m, doublereal *pl, doublereal *pr, doublereal *dif, 00025 doublecomplex *work, integer *lwork, integer *iwork, integer *liwork, 00026 integer *info) 00027 { 00028 /* System generated locals */ 00029 integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, 00030 z_offset, i__1, i__2, i__3; 00031 doublecomplex z__1, z__2; 00032 00033 /* Builtin functions */ 00034 double sqrt(doublereal), z_abs(doublecomplex *); 00035 void d_cnjg(doublecomplex *, doublecomplex *); 00036 00037 /* Local variables */ 00038 integer i__, k, n1, n2, ks, mn2, ijb, kase, ierr; 00039 doublereal dsum; 00040 logical swap; 00041 doublecomplex temp1, temp2; 00042 integer isave[3]; 00043 extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 00044 doublecomplex *, integer *); 00045 logical wantd; 00046 integer lwmin; 00047 logical wantp; 00048 extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, 00049 doublecomplex *, doublereal *, integer *, integer *); 00050 logical wantd1, wantd2; 00051 extern doublereal dlamch_(char *); 00052 doublereal dscale, rdscal, safmin; 00053 extern /* Subroutine */ int xerbla_(char *, integer *); 00054 integer liwmin; 00055 extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 00056 doublecomplex *, integer *, doublecomplex *, integer *), 00057 ztgexc_(logical *, logical *, integer *, doublecomplex *, integer 00058 *, doublecomplex *, integer *, doublecomplex *, integer *, 00059 doublecomplex *, integer *, integer *, integer *, integer *), 00060 zlassq_(integer *, doublecomplex *, integer *, doublereal *, 00061 doublereal *); 00062 logical lquery; 00063 extern /* Subroutine */ int ztgsyl_(char *, integer *, integer *, integer 00064 *, doublecomplex *, integer *, doublecomplex *, integer *, 00065 doublecomplex *, integer *, doublecomplex *, integer *, 00066 doublecomplex *, integer *, doublecomplex *, integer *, 00067 doublereal *, doublereal *, doublecomplex *, integer *, integer *, 00068 integer *); 00069 00070 00071 /* -- LAPACK routine (version 3.2) -- */ 00072 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00073 /* January 2007 */ 00074 00075 /* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */ 00076 00077 /* .. Scalar Arguments .. */ 00078 /* .. */ 00079 /* .. Array Arguments .. */ 00080 /* .. */ 00081 00082 /* Purpose */ 00083 /* ======= */ 00084 00085 /* ZTGSEN reorders the generalized Schur decomposition of a complex */ 00086 /* matrix pair (A, B) (in terms of an unitary equivalence trans- */ 00087 /* formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues */ 00088 /* appears in the leading diagonal blocks of the pair (A,B). The leading */ 00089 /* columns of Q and Z form unitary bases of the corresponding left and */ 00090 /* right eigenspaces (deflating subspaces). (A, B) must be in */ 00091 /* generalized Schur canonical form, that is, A and B are both upper */ 00092 /* triangular. */ 00093 00094 /* ZTGSEN also computes the generalized eigenvalues */ 00095 00096 /* w(j)= ALPHA(j) / BETA(j) */ 00097 00098 /* of the reordered matrix pair (A, B). */ 00099 00100 /* Optionally, the routine computes estimates of reciprocal condition */ 00101 /* numbers for eigenvalues and eigenspaces. These are Difu[(A11,B11), */ 00102 /* (A22,B22)] and Difl[(A11,B11), (A22,B22)], i.e. the separation(s) */ 00103 /* between the matrix pairs (A11, B11) and (A22,B22) that correspond to */ 00104 /* the selected cluster and the eigenvalues outside the cluster, resp., */ 00105 /* and norms of "projections" onto left and right eigenspaces w.r.t. */ 00106 /* the selected cluster in the (1,1)-block. */ 00107 00108 00109 /* Arguments */ 00110 /* ========= */ 00111 00112 /* IJOB (input) integer */ 00113 /* Specifies whether condition numbers are required for the */ 00114 /* cluster of eigenvalues (PL and PR) or the deflating subspaces */ 00115 /* (Difu and Difl): */ 00116 /* =0: Only reorder w.r.t. SELECT. No extras. */ 00117 /* =1: Reciprocal of norms of "projections" onto left and right */ 00118 /* eigenspaces w.r.t. the selected cluster (PL and PR). */ 00119 /* =2: Upper bounds on Difu and Difl. F-norm-based estimate */ 00120 /* (DIF(1:2)). */ 00121 /* =3: Estimate of Difu and Difl. 1-norm-based estimate */ 00122 /* (DIF(1:2)). */ 00123 /* About 5 times as expensive as IJOB = 2. */ 00124 /* =4: Compute PL, PR and DIF (i.e. 0, 1 and 2 above): Economic */ 00125 /* version to get it all. */ 00126 /* =5: Compute PL, PR and DIF (i.e. 0, 1 and 3 above) */ 00127 00128 /* WANTQ (input) LOGICAL */ 00129 /* .TRUE. : update the left transformation matrix Q; */ 00130 /* .FALSE.: do not update Q. */ 00131 00132 /* WANTZ (input) LOGICAL */ 00133 /* .TRUE. : update the right transformation matrix Z; */ 00134 /* .FALSE.: do not update Z. */ 00135 00136 /* SELECT (input) LOGICAL array, dimension (N) */ 00137 /* SELECT specifies the eigenvalues in the selected cluster. To */ 00138 /* select an eigenvalue w(j), SELECT(j) must be set to */ 00139 /* .TRUE.. */ 00140 00141 /* N (input) INTEGER */ 00142 /* The order of the matrices A and B. N >= 0. */ 00143 00144 /* A (input/output) COMPLEX*16 array, dimension(LDA,N) */ 00145 /* On entry, the upper triangular matrix A, in generalized */ 00146 /* Schur canonical form. */ 00147 /* On exit, A is overwritten by the reordered matrix A. */ 00148 00149 /* LDA (input) INTEGER */ 00150 /* The leading dimension of the array A. LDA >= max(1,N). */ 00151 00152 /* B (input/output) COMPLEX*16 array, dimension(LDB,N) */ 00153 /* On entry, the upper triangular matrix B, in generalized */ 00154 /* Schur canonical form. */ 00155 /* On exit, B is overwritten by the reordered matrix B. */ 00156 00157 /* LDB (input) INTEGER */ 00158 /* The leading dimension of the array B. LDB >= max(1,N). */ 00159 00160 /* ALPHA (output) COMPLEX*16 array, dimension (N) */ 00161 /* BETA (output) COMPLEX*16 array, dimension (N) */ 00162 /* The diagonal elements of A and B, respectively, */ 00163 /* when the pair (A,B) has been reduced to generalized Schur */ 00164 /* form. ALPHA(i)/BETA(i) i=1,...,N are the generalized */ 00165 /* eigenvalues. */ 00166 00167 /* Q (input/output) COMPLEX*16 array, dimension (LDQ,N) */ 00168 /* On entry, if WANTQ = .TRUE., Q is an N-by-N matrix. */ 00169 /* On exit, Q has been postmultiplied by the left unitary */ 00170 /* transformation matrix which reorder (A, B); The leading M */ 00171 /* columns of Q form orthonormal bases for the specified pair of */ 00172 /* left eigenspaces (deflating subspaces). */ 00173 /* If WANTQ = .FALSE., Q is not referenced. */ 00174 00175 /* LDQ (input) INTEGER */ 00176 /* The leading dimension of the array Q. LDQ >= 1. */ 00177 /* If WANTQ = .TRUE., LDQ >= N. */ 00178 00179 /* Z (input/output) COMPLEX*16 array, dimension (LDZ,N) */ 00180 /* On entry, if WANTZ = .TRUE., Z is an N-by-N matrix. */ 00181 /* On exit, Z has been postmultiplied by the left unitary */ 00182 /* transformation matrix which reorder (A, B); The leading M */ 00183 /* columns of Z form orthonormal bases for the specified pair of */ 00184 /* left eigenspaces (deflating subspaces). */ 00185 /* If WANTZ = .FALSE., Z is not referenced. */ 00186 00187 /* LDZ (input) INTEGER */ 00188 /* The leading dimension of the array Z. LDZ >= 1. */ 00189 /* If WANTZ = .TRUE., LDZ >= N. */ 00190 00191 /* M (output) INTEGER */ 00192 /* The dimension of the specified pair of left and right */ 00193 /* eigenspaces, (deflating subspaces) 0 <= M <= N. */ 00194 00195 /* PL (output) DOUBLE PRECISION */ 00196 /* PR (output) DOUBLE PRECISION */ 00197 /* If IJOB = 1, 4 or 5, PL, PR are lower bounds on the */ 00198 /* reciprocal of the norm of "projections" onto left and right */ 00199 /* eigenspace with respect to the selected cluster. */ 00200 /* 0 < PL, PR <= 1. */ 00201 /* If M = 0 or M = N, PL = PR = 1. */ 00202 /* If IJOB = 0, 2 or 3 PL, PR are not referenced. */ 00203 00204 /* DIF (output) DOUBLE PRECISION array, dimension (2). */ 00205 /* If IJOB >= 2, DIF(1:2) store the estimates of Difu and Difl. */ 00206 /* If IJOB = 2 or 4, DIF(1:2) are F-norm-based upper bounds on */ 00207 /* Difu and Difl. If IJOB = 3 or 5, DIF(1:2) are 1-norm-based */ 00208 /* estimates of Difu and Difl, computed using reversed */ 00209 /* communication with ZLACN2. */ 00210 /* If M = 0 or N, DIF(1:2) = F-norm([A, B]). */ 00211 /* If IJOB = 0 or 1, DIF is not referenced. */ 00212 00213 /* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */ 00214 /* IF IJOB = 0, WORK is not referenced. Otherwise, */ 00215 /* on exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00216 00217 /* LWORK (input) INTEGER */ 00218 /* The dimension of the array WORK. LWORK >= 1 */ 00219 /* If IJOB = 1, 2 or 4, LWORK >= 2*M*(N-M) */ 00220 /* If IJOB = 3 or 5, LWORK >= 4*M*(N-M) */ 00221 00222 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00223 /* only calculates the optimal size of the WORK array, returns */ 00224 /* this value as the first entry of the WORK array, and no error */ 00225 /* message related to LWORK is issued by XERBLA. */ 00226 00227 /* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */ 00228 /* IF IJOB = 0, IWORK is not referenced. Otherwise, */ 00229 /* on exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ 00230 00231 /* LIWORK (input) INTEGER */ 00232 /* The dimension of the array IWORK. LIWORK >= 1. */ 00233 /* If IJOB = 1, 2 or 4, LIWORK >= N+2; */ 00234 /* If IJOB = 3 or 5, LIWORK >= MAX(N+2, 2*M*(N-M)); */ 00235 00236 /* If LIWORK = -1, then a workspace query is assumed; the */ 00237 /* routine only calculates the optimal size of the IWORK array, */ 00238 /* returns this value as the first entry of the IWORK array, and */ 00239 /* no error message related to LIWORK is issued by XERBLA. */ 00240 00241 /* INFO (output) INTEGER */ 00242 /* =0: Successful exit. */ 00243 /* <0: If INFO = -i, the i-th argument had an illegal value. */ 00244 /* =1: Reordering of (A, B) failed because the transformed */ 00245 /* matrix pair (A, B) would be too far from generalized */ 00246 /* Schur form; the problem is very ill-conditioned. */ 00247 /* (A, B) may have been partially reordered. */ 00248 /* If requested, 0 is returned in DIF(*), PL and PR. */ 00249 00250 00251 /* Further Details */ 00252 /* =============== */ 00253 00254 /* ZTGSEN first collects the selected eigenvalues by computing unitary */ 00255 /* U and W that move them to the top left corner of (A, B). In other */ 00256 /* words, the selected eigenvalues are the eigenvalues of (A11, B11) in */ 00257 00258 /* U'*(A, B)*W = (A11 A12) (B11 B12) n1 */ 00259 /* ( 0 A22),( 0 B22) n2 */ 00260 /* n1 n2 n1 n2 */ 00261 00262 /* where N = n1+n2 and U' means the conjugate transpose of U. The first */ 00263 /* n1 columns of U and W span the specified pair of left and right */ 00264 /* eigenspaces (deflating subspaces) of (A, B). */ 00265 00266 /* If (A, B) has been obtained from the generalized real Schur */ 00267 /* decomposition of a matrix pair (C, D) = Q*(A, B)*Z', then the */ 00268 /* reordered generalized Schur form of (C, D) is given by */ 00269 00270 /* (C, D) = (Q*U)*(U'*(A, B)*W)*(Z*W)', */ 00271 00272 /* and the first n1 columns of Q*U and Z*W span the corresponding */ 00273 /* deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.). */ 00274 00275 /* Note that if the selected eigenvalue is sufficiently ill-conditioned, */ 00276 /* then its value may differ significantly from its value before */ 00277 /* reordering. */ 00278 00279 /* The reciprocal condition numbers of the left and right eigenspaces */ 00280 /* spanned by the first n1 columns of U and W (or Q*U and Z*W) may */ 00281 /* be returned in DIF(1:2), corresponding to Difu and Difl, resp. */ 00282 00283 /* The Difu and Difl are defined as: */ 00284 00285 /* Difu[(A11, B11), (A22, B22)] = sigma-min( Zu ) */ 00286 /* and */ 00287 /* Difl[(A11, B11), (A22, B22)] = Difu[(A22, B22), (A11, B11)], */ 00288 00289 /* where sigma-min(Zu) is the smallest singular value of the */ 00290 /* (2*n1*n2)-by-(2*n1*n2) matrix */ 00291 00292 /* Zu = [ kron(In2, A11) -kron(A22', In1) ] */ 00293 /* [ kron(In2, B11) -kron(B22', In1) ]. */ 00294 00295 /* Here, Inx is the identity matrix of size nx and A22' is the */ 00296 /* transpose of A22. kron(X, Y) is the Kronecker product between */ 00297 /* the matrices X and Y. */ 00298 00299 /* When DIF(2) is small, small changes in (A, B) can cause large changes */ 00300 /* in the deflating subspace. An approximate (asymptotic) bound on the */ 00301 /* maximum angular error in the computed deflating subspaces is */ 00302 00303 /* EPS * norm((A, B)) / DIF(2), */ 00304 00305 /* where EPS is the machine precision. */ 00306 00307 /* The reciprocal norm of the projectors on the left and right */ 00308 /* eigenspaces associated with (A11, B11) may be returned in PL and PR. */ 00309 /* They are computed as follows. First we compute L and R so that */ 00310 /* P*(A, B)*Q is block diagonal, where */ 00311 00312 /* P = ( I -L ) n1 Q = ( I R ) n1 */ 00313 /* ( 0 I ) n2 and ( 0 I ) n2 */ 00314 /* n1 n2 n1 n2 */ 00315 00316 /* and (L, R) is the solution to the generalized Sylvester equation */ 00317 00318 /* A11*R - L*A22 = -A12 */ 00319 /* B11*R - L*B22 = -B12 */ 00320 00321 /* Then PL = (F-norm(L)**2+1)**(-1/2) and PR = (F-norm(R)**2+1)**(-1/2). */ 00322 /* An approximate (asymptotic) bound on the average absolute error of */ 00323 /* the selected eigenvalues is */ 00324 00325 /* EPS * norm((A, B)) / PL. */ 00326 00327 /* There are also global error bounds which valid for perturbations up */ 00328 /* to a certain restriction: A lower bound (x) on the smallest */ 00329 /* F-norm(E,F) for which an eigenvalue of (A11, B11) may move and */ 00330 /* coalesce with an eigenvalue of (A22, B22) under perturbation (E,F), */ 00331 /* (i.e. (A + E, B + F), is */ 00332 00333 /* x = min(Difu,Difl)/((1/(PL*PL)+1/(PR*PR))**(1/2)+2*max(1/PL,1/PR)). */ 00334 00335 /* An approximate bound on x can be computed from DIF(1:2), PL and PR. */ 00336 00337 /* If y = ( F-norm(E,F) / x) <= 1, the angles between the perturbed */ 00338 /* (L', R') and unperturbed (L, R) left and right deflating subspaces */ 00339 /* associated with the selected cluster in the (1,1)-blocks can be */ 00340 /* bounded as */ 00341 00342 /* max-angle(L, L') <= arctan( y * PL / (1 - y * (1 - PL * PL)**(1/2)) */ 00343 /* max-angle(R, R') <= arctan( y * PR / (1 - y * (1 - PR * PR)**(1/2)) */ 00344 00345 /* See LAPACK User's Guide section 4.11 or the following references */ 00346 /* for more information. */ 00347 00348 /* Note that if the default method for computing the Frobenius-norm- */ 00349 /* based estimate DIF is not wanted (see ZLATDF), then the parameter */ 00350 /* IDIFJB (see below) should be changed from 3 to 4 (routine ZLATDF */ 00351 /* (IJOB = 2 will be used)). See ZTGSYL for more details. */ 00352 00353 /* Based on contributions by */ 00354 /* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */ 00355 /* Umea University, S-901 87 Umea, Sweden. */ 00356 00357 /* References */ 00358 /* ========== */ 00359 00360 /* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */ 00361 /* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */ 00362 /* M.S. Moonen et al (eds), Linear Algebra for Large Scale and */ 00363 /* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */ 00364 00365 /* [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */ 00366 /* Eigenvalues of a Regular Matrix Pair (A, B) and Condition */ 00367 /* Estimation: Theory, Algorithms and Software, Report */ 00368 /* UMINF - 94.04, Department of Computing Science, Umea University, */ 00369 /* S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. */ 00370 /* To appear in Numerical Algorithms, 1996. */ 00371 00372 /* [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */ 00373 /* for Solving the Generalized Sylvester Equation and Estimating the */ 00374 /* Separation between Regular Matrix Pairs, Report UMINF - 93.23, */ 00375 /* Department of Computing Science, Umea University, S-901 87 Umea, */ 00376 /* Sweden, December 1993, Revised April 1994, Also as LAPACK working */ 00377 /* Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, */ 00378 /* 1996. */ 00379 00380 /* ===================================================================== */ 00381 00382 /* .. Parameters .. */ 00383 /* .. */ 00384 /* .. Local Scalars .. */ 00385 /* .. */ 00386 /* .. Local Arrays .. */ 00387 /* .. */ 00388 /* .. External Subroutines .. */ 00389 /* .. */ 00390 /* .. Intrinsic Functions .. */ 00391 /* .. */ 00392 /* .. External Functions .. */ 00393 /* .. */ 00394 /* .. Executable Statements .. */ 00395 00396 /* Decode and test the input parameters */ 00397 00398 /* Parameter adjustments */ 00399 --select; 00400 a_dim1 = *lda; 00401 a_offset = 1 + a_dim1; 00402 a -= a_offset; 00403 b_dim1 = *ldb; 00404 b_offset = 1 + b_dim1; 00405 b -= b_offset; 00406 --alpha; 00407 --beta; 00408 q_dim1 = *ldq; 00409 q_offset = 1 + q_dim1; 00410 q -= q_offset; 00411 z_dim1 = *ldz; 00412 z_offset = 1 + z_dim1; 00413 z__ -= z_offset; 00414 --dif; 00415 --work; 00416 --iwork; 00417 00418 /* Function Body */ 00419 *info = 0; 00420 lquery = *lwork == -1 || *liwork == -1; 00421 00422 if (*ijob < 0 || *ijob > 5) { 00423 *info = -1; 00424 } else if (*n < 0) { 00425 *info = -5; 00426 } else if (*lda < max(1,*n)) { 00427 *info = -7; 00428 } else if (*ldb < max(1,*n)) { 00429 *info = -9; 00430 } else if (*ldq < 1 || *wantq && *ldq < *n) { 00431 *info = -13; 00432 } else if (*ldz < 1 || *wantz && *ldz < *n) { 00433 *info = -15; 00434 } 00435 00436 if (*info != 0) { 00437 i__1 = -(*info); 00438 xerbla_("ZTGSEN", &i__1); 00439 return 0; 00440 } 00441 00442 ierr = 0; 00443 00444 wantp = *ijob == 1 || *ijob >= 4; 00445 wantd1 = *ijob == 2 || *ijob == 4; 00446 wantd2 = *ijob == 3 || *ijob == 5; 00447 wantd = wantd1 || wantd2; 00448 00449 /* Set M to the dimension of the specified pair of deflating */ 00450 /* subspaces. */ 00451 00452 *m = 0; 00453 i__1 = *n; 00454 for (k = 1; k <= i__1; ++k) { 00455 i__2 = k; 00456 i__3 = k + k * a_dim1; 00457 alpha[i__2].r = a[i__3].r, alpha[i__2].i = a[i__3].i; 00458 i__2 = k; 00459 i__3 = k + k * b_dim1; 00460 beta[i__2].r = b[i__3].r, beta[i__2].i = b[i__3].i; 00461 if (k < *n) { 00462 if (select[k]) { 00463 ++(*m); 00464 } 00465 } else { 00466 if (select[*n]) { 00467 ++(*m); 00468 } 00469 } 00470 /* L10: */ 00471 } 00472 00473 if (*ijob == 1 || *ijob == 2 || *ijob == 4) { 00474 /* Computing MAX */ 00475 i__1 = 1, i__2 = (*m << 1) * (*n - *m); 00476 lwmin = max(i__1,i__2); 00477 /* Computing MAX */ 00478 i__1 = 1, i__2 = *n + 2; 00479 liwmin = max(i__1,i__2); 00480 } else if (*ijob == 3 || *ijob == 5) { 00481 /* Computing MAX */ 00482 i__1 = 1, i__2 = (*m << 2) * (*n - *m); 00483 lwmin = max(i__1,i__2); 00484 /* Computing MAX */ 00485 i__1 = 1, i__2 = (*m << 1) * (*n - *m), i__1 = max(i__1,i__2), i__2 = 00486 *n + 2; 00487 liwmin = max(i__1,i__2); 00488 } else { 00489 lwmin = 1; 00490 liwmin = 1; 00491 } 00492 00493 work[1].r = (doublereal) lwmin, work[1].i = 0.; 00494 iwork[1] = liwmin; 00495 00496 if (*lwork < lwmin && ! lquery) { 00497 *info = -21; 00498 } else if (*liwork < liwmin && ! lquery) { 00499 *info = -23; 00500 } 00501 00502 if (*info != 0) { 00503 i__1 = -(*info); 00504 xerbla_("ZTGSEN", &i__1); 00505 return 0; 00506 } else if (lquery) { 00507 return 0; 00508 } 00509 00510 /* Quick return if possible. */ 00511 00512 if (*m == *n || *m == 0) { 00513 if (wantp) { 00514 *pl = 1.; 00515 *pr = 1.; 00516 } 00517 if (wantd) { 00518 dscale = 0.; 00519 dsum = 1.; 00520 i__1 = *n; 00521 for (i__ = 1; i__ <= i__1; ++i__) { 00522 zlassq_(n, &a[i__ * a_dim1 + 1], &c__1, &dscale, &dsum); 00523 zlassq_(n, &b[i__ * b_dim1 + 1], &c__1, &dscale, &dsum); 00524 /* L20: */ 00525 } 00526 dif[1] = dscale * sqrt(dsum); 00527 dif[2] = dif[1]; 00528 } 00529 goto L70; 00530 } 00531 00532 /* Get machine constant */ 00533 00534 safmin = dlamch_("S"); 00535 00536 /* Collect the selected blocks at the top-left corner of (A, B). */ 00537 00538 ks = 0; 00539 i__1 = *n; 00540 for (k = 1; k <= i__1; ++k) { 00541 swap = select[k]; 00542 if (swap) { 00543 ++ks; 00544 00545 /* Swap the K-th block to position KS. Compute unitary Q */ 00546 /* and Z that will swap adjacent diagonal blocks in (A, B). */ 00547 00548 if (k != ks) { 00549 ztgexc_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, 00550 &q[q_offset], ldq, &z__[z_offset], ldz, &k, &ks, & 00551 ierr); 00552 } 00553 00554 if (ierr > 0) { 00555 00556 /* Swap is rejected: exit. */ 00557 00558 *info = 1; 00559 if (wantp) { 00560 *pl = 0.; 00561 *pr = 0.; 00562 } 00563 if (wantd) { 00564 dif[1] = 0.; 00565 dif[2] = 0.; 00566 } 00567 goto L70; 00568 } 00569 } 00570 /* L30: */ 00571 } 00572 if (wantp) { 00573 00574 /* Solve generalized Sylvester equation for R and L: */ 00575 /* A11 * R - L * A22 = A12 */ 00576 /* B11 * R - L * B22 = B12 */ 00577 00578 n1 = *m; 00579 n2 = *n - *m; 00580 i__ = n1 + 1; 00581 zlacpy_("Full", &n1, &n2, &a[i__ * a_dim1 + 1], lda, &work[1], &n1); 00582 zlacpy_("Full", &n1, &n2, &b[i__ * b_dim1 + 1], ldb, &work[n1 * n2 + 00583 1], &n1); 00584 ijb = 0; 00585 i__1 = *lwork - (n1 << 1) * n2; 00586 ztgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ * a_dim1] 00587 , lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ + i__ * 00588 b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &dif[1], & 00589 work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], &ierr); 00590 00591 /* Estimate the reciprocal of norms of "projections" onto */ 00592 /* left and right eigenspaces */ 00593 00594 rdscal = 0.; 00595 dsum = 1.; 00596 i__1 = n1 * n2; 00597 zlassq_(&i__1, &work[1], &c__1, &rdscal, &dsum); 00598 *pl = rdscal * sqrt(dsum); 00599 if (*pl == 0.) { 00600 *pl = 1.; 00601 } else { 00602 *pl = dscale / (sqrt(dscale * dscale / *pl + *pl) * sqrt(*pl)); 00603 } 00604 rdscal = 0.; 00605 dsum = 1.; 00606 i__1 = n1 * n2; 00607 zlassq_(&i__1, &work[n1 * n2 + 1], &c__1, &rdscal, &dsum); 00608 *pr = rdscal * sqrt(dsum); 00609 if (*pr == 0.) { 00610 *pr = 1.; 00611 } else { 00612 *pr = dscale / (sqrt(dscale * dscale / *pr + *pr) * sqrt(*pr)); 00613 } 00614 } 00615 if (wantd) { 00616 00617 /* Compute estimates Difu and Difl. */ 00618 00619 if (wantd1) { 00620 n1 = *m; 00621 n2 = *n - *m; 00622 i__ = n1 + 1; 00623 ijb = 3; 00624 00625 /* Frobenius norm-based Difu estimate. */ 00626 00627 i__1 = *lwork - (n1 << 1) * n2; 00628 ztgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ * 00629 a_dim1], lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ + 00630 i__ * b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, & 00631 dif[1], &work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], & 00632 ierr); 00633 00634 /* Frobenius norm-based Difl estimate. */ 00635 00636 i__1 = *lwork - (n1 << 1) * n2; 00637 ztgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, &a[ 00638 a_offset], lda, &work[1], &n2, &b[i__ + i__ * b_dim1], 00639 ldb, &b[b_offset], ldb, &work[n1 * n2 + 1], &n2, &dscale, 00640 &dif[2], &work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], & 00641 ierr); 00642 } else { 00643 00644 /* Compute 1-norm-based estimates of Difu and Difl using */ 00645 /* reversed communication with ZLACN2. In each step a */ 00646 /* generalized Sylvester equation or a transposed variant */ 00647 /* is solved. */ 00648 00649 kase = 0; 00650 n1 = *m; 00651 n2 = *n - *m; 00652 i__ = n1 + 1; 00653 ijb = 0; 00654 mn2 = (n1 << 1) * n2; 00655 00656 /* 1-norm-based estimate of Difu. */ 00657 00658 L40: 00659 zlacn2_(&mn2, &work[mn2 + 1], &work[1], &dif[1], &kase, isave); 00660 if (kase != 0) { 00661 if (kase == 1) { 00662 00663 /* Solve generalized Sylvester equation */ 00664 00665 i__1 = *lwork - (n1 << 1) * n2; 00666 ztgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + 00667 i__ * a_dim1], lda, &work[1], &n1, &b[b_offset], 00668 ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 + 00669 1], &n1, &dscale, &dif[1], &work[(n1 * n2 << 1) + 00670 1], &i__1, &iwork[1], &ierr); 00671 } else { 00672 00673 /* Solve the transposed variant. */ 00674 00675 i__1 = *lwork - (n1 << 1) * n2; 00676 ztgsyl_("C", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + 00677 i__ * a_dim1], lda, &work[1], &n1, &b[b_offset], 00678 ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 + 00679 1], &n1, &dscale, &dif[1], &work[(n1 * n2 << 1) + 00680 1], &i__1, &iwork[1], &ierr); 00681 } 00682 goto L40; 00683 } 00684 dif[1] = dscale / dif[1]; 00685 00686 /* 1-norm-based estimate of Difl. */ 00687 00688 L50: 00689 zlacn2_(&mn2, &work[mn2 + 1], &work[1], &dif[2], &kase, isave); 00690 if (kase != 0) { 00691 if (kase == 1) { 00692 00693 /* Solve generalized Sylvester equation */ 00694 00695 i__1 = *lwork - (n1 << 1) * n2; 00696 ztgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, 00697 &a[a_offset], lda, &work[1], &n2, &b[i__ + i__ * 00698 b_dim1], ldb, &b[b_offset], ldb, &work[n1 * n2 + 00699 1], &n2, &dscale, &dif[2], &work[(n1 * n2 << 1) + 00700 1], &i__1, &iwork[1], &ierr); 00701 } else { 00702 00703 /* Solve the transposed variant. */ 00704 00705 i__1 = *lwork - (n1 << 1) * n2; 00706 ztgsyl_("C", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, 00707 &a[a_offset], lda, &work[1], &n2, &b[b_offset], 00708 ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 + 00709 1], &n2, &dscale, &dif[2], &work[(n1 * n2 << 1) + 00710 1], &i__1, &iwork[1], &ierr); 00711 } 00712 goto L50; 00713 } 00714 dif[2] = dscale / dif[2]; 00715 } 00716 } 00717 00718 /* If B(K,K) is complex, make it real and positive (normalization */ 00719 /* of the generalized Schur form) and Store the generalized */ 00720 /* eigenvalues of reordered pair (A, B) */ 00721 00722 i__1 = *n; 00723 for (k = 1; k <= i__1; ++k) { 00724 dscale = z_abs(&b[k + k * b_dim1]); 00725 if (dscale > safmin) { 00726 i__2 = k + k * b_dim1; 00727 z__2.r = b[i__2].r / dscale, z__2.i = b[i__2].i / dscale; 00728 d_cnjg(&z__1, &z__2); 00729 temp1.r = z__1.r, temp1.i = z__1.i; 00730 i__2 = k + k * b_dim1; 00731 z__1.r = b[i__2].r / dscale, z__1.i = b[i__2].i / dscale; 00732 temp2.r = z__1.r, temp2.i = z__1.i; 00733 i__2 = k + k * b_dim1; 00734 b[i__2].r = dscale, b[i__2].i = 0.; 00735 i__2 = *n - k; 00736 zscal_(&i__2, &temp1, &b[k + (k + 1) * b_dim1], ldb); 00737 i__2 = *n - k + 1; 00738 zscal_(&i__2, &temp1, &a[k + k * a_dim1], lda); 00739 if (*wantq) { 00740 zscal_(n, &temp2, &q[k * q_dim1 + 1], &c__1); 00741 } 00742 } else { 00743 i__2 = k + k * b_dim1; 00744 b[i__2].r = 0., b[i__2].i = 0.; 00745 } 00746 00747 i__2 = k; 00748 i__3 = k + k * a_dim1; 00749 alpha[i__2].r = a[i__3].r, alpha[i__2].i = a[i__3].i; 00750 i__2 = k; 00751 i__3 = k + k * b_dim1; 00752 beta[i__2].r = b[i__3].r, beta[i__2].i = b[i__3].i; 00753 00754 /* L60: */ 00755 } 00756 00757 L70: 00758 00759 work[1].r = (doublereal) lwmin, work[1].i = 0.; 00760 iwork[1] = liwmin; 00761 00762 return 0; 00763 00764 /* End of ZTGSEN */ 00765 00766 } /* ztgsen_ */