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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 DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, 00002 $ LDZ, J1, N1, N2, WORK, LWORK, INFO ) 00003 * 00004 * -- LAPACK auxiliary routine (version 3.3.1) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * -- April 2011 -- 00008 * 00009 * .. Scalar Arguments .. 00010 LOGICAL WANTQ, WANTZ 00011 INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 00012 * .. 00013 * .. Array Arguments .. 00014 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), 00015 $ WORK( * ), Z( LDZ, * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) 00022 * of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair 00023 * (A, B) by an orthogonal equivalence transformation. 00024 * 00025 * (A, B) must be in generalized real Schur canonical form (as returned 00026 * by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 00027 * diagonal blocks. B is upper triangular. 00028 * 00029 * Optionally, the matrices Q and Z of generalized Schur vectors are 00030 * updated. 00031 * 00032 * Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T 00033 * Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T 00034 * 00035 * 00036 * Arguments 00037 * ========= 00038 * 00039 * WANTQ (input) LOGICAL 00040 * .TRUE. : update the left transformation matrix Q; 00041 * .FALSE.: do not update Q. 00042 * 00043 * WANTZ (input) LOGICAL 00044 * .TRUE. : update the right transformation matrix Z; 00045 * .FALSE.: do not update Z. 00046 * 00047 * N (input) INTEGER 00048 * The order of the matrices A and B. N >= 0. 00049 * 00050 * A (input/output) DOUBLE PRECISION array, dimensions (LDA,N) 00051 * On entry, the matrix A in the pair (A, B). 00052 * On exit, the updated matrix A. 00053 * 00054 * LDA (input) INTEGER 00055 * The leading dimension of the array A. LDA >= max(1,N). 00056 * 00057 * B (input/output) DOUBLE PRECISION array, dimensions (LDB,N) 00058 * On entry, the matrix B in the pair (A, B). 00059 * On exit, the updated matrix B. 00060 * 00061 * LDB (input) INTEGER 00062 * The leading dimension of the array B. LDB >= max(1,N). 00063 * 00064 * Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) 00065 * On entry, if WANTQ = .TRUE., the orthogonal matrix Q. 00066 * On exit, the updated matrix Q. 00067 * Not referenced if WANTQ = .FALSE.. 00068 * 00069 * LDQ (input) INTEGER 00070 * The leading dimension of the array Q. LDQ >= 1. 00071 * If WANTQ = .TRUE., LDQ >= N. 00072 * 00073 * Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N) 00074 * On entry, if WANTZ =.TRUE., the orthogonal matrix Z. 00075 * On exit, the updated matrix Z. 00076 * Not referenced if WANTZ = .FALSE.. 00077 * 00078 * LDZ (input) INTEGER 00079 * The leading dimension of the array Z. LDZ >= 1. 00080 * If WANTZ = .TRUE., LDZ >= N. 00081 * 00082 * J1 (input) INTEGER 00083 * The index to the first block (A11, B11). 1 <= J1 <= N. 00084 * 00085 * N1 (input) INTEGER 00086 * The order of the first block (A11, B11). N1 = 0, 1 or 2. 00087 * 00088 * N2 (input) INTEGER 00089 * The order of the second block (A22, B22). N2 = 0, 1 or 2. 00090 * 00091 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)). 00092 * 00093 * LWORK (input) INTEGER 00094 * The dimension of the array WORK. 00095 * LWORK >= MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 ) 00096 * 00097 * INFO (output) INTEGER 00098 * =0: Successful exit 00099 * >0: If INFO = 1, the transformed matrix (A, B) would be 00100 * too far from generalized Schur form; the blocks are 00101 * not swapped and (A, B) and (Q, Z) are unchanged. 00102 * The problem of swapping is too ill-conditioned. 00103 * <0: If INFO = -16: LWORK is too small. Appropriate value 00104 * for LWORK is returned in WORK(1). 00105 * 00106 * Further Details 00107 * =============== 00108 * 00109 * Based on contributions by 00110 * Bo Kagstrom and Peter Poromaa, Department of Computing Science, 00111 * Umea University, S-901 87 Umea, Sweden. 00112 * 00113 * In the current code both weak and strong stability tests are 00114 * performed. The user can omit the strong stability test by changing 00115 * the internal logical parameter WANDS to .FALSE.. See ref. [2] for 00116 * details. 00117 * 00118 * [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the 00119 * Generalized Real Schur Form of a Regular Matrix Pair (A, B), in 00120 * M.S. Moonen et al (eds), Linear Algebra for Large Scale and 00121 * Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. 00122 * 00123 * [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified 00124 * Eigenvalues of a Regular Matrix Pair (A, B) and Condition 00125 * Estimation: Theory, Algorithms and Software, 00126 * Report UMINF - 94.04, Department of Computing Science, Umea 00127 * University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working 00128 * Note 87. To appear in Numerical Algorithms, 1996. 00129 * 00130 * ===================================================================== 00131 * Replaced various illegal calls to DCOPY by calls to DLASET, or by DO 00132 * loops. Sven Hammarling, 1/5/02. 00133 * 00134 * .. Parameters .. 00135 DOUBLE PRECISION ZERO, ONE 00136 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00137 DOUBLE PRECISION TWENTY 00138 PARAMETER ( TWENTY = 2.0D+01 ) 00139 INTEGER LDST 00140 PARAMETER ( LDST = 4 ) 00141 LOGICAL WANDS 00142 PARAMETER ( WANDS = .TRUE. ) 00143 * .. 00144 * .. Local Scalars .. 00145 LOGICAL DTRONG, WEAK 00146 INTEGER I, IDUM, LINFO, M 00147 DOUBLE PRECISION BQRA21, BRQA21, DDUM, DNORM, DSCALE, DSUM, EPS, 00148 $ F, G, SA, SB, SCALE, SMLNUM, SS, THRESH, WS 00149 * .. 00150 * .. Local Arrays .. 00151 INTEGER IWORK( LDST ) 00152 DOUBLE PRECISION AI( 2 ), AR( 2 ), BE( 2 ), IR( LDST, LDST ), 00153 $ IRCOP( LDST, LDST ), LI( LDST, LDST ), 00154 $ LICOP( LDST, LDST ), S( LDST, LDST ), 00155 $ SCPY( LDST, LDST ), T( LDST, LDST ), 00156 $ TAUL( LDST ), TAUR( LDST ), TCPY( LDST, LDST ) 00157 * .. 00158 * .. External Functions .. 00159 DOUBLE PRECISION DLAMCH 00160 EXTERNAL DLAMCH 00161 * .. 00162 * .. External Subroutines .. 00163 EXTERNAL DGEMM, DGEQR2, DGERQ2, DLACPY, DLAGV2, DLARTG, 00164 $ DLASET, DLASSQ, DORG2R, DORGR2, DORM2R, DORMR2, 00165 $ DROT, DSCAL, DTGSY2 00166 * .. 00167 * .. Intrinsic Functions .. 00168 INTRINSIC ABS, MAX, SQRT 00169 * .. 00170 * .. Executable Statements .. 00171 * 00172 INFO = 0 00173 * 00174 * Quick return if possible 00175 * 00176 IF( N.LE.1 .OR. N1.LE.0 .OR. N2.LE.0 ) 00177 $ RETURN 00178 IF( N1.GT.N .OR. ( J1+N1 ).GT.N ) 00179 $ RETURN 00180 M = N1 + N2 00181 IF( LWORK.LT.MAX( 1, N*M, M*M*2 ) ) THEN 00182 INFO = -16 00183 WORK( 1 ) = MAX( 1, N*M, M*M*2 ) 00184 RETURN 00185 END IF 00186 * 00187 WEAK = .FALSE. 00188 DTRONG = .FALSE. 00189 * 00190 * Make a local copy of selected block 00191 * 00192 CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, LI, LDST ) 00193 CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, IR, LDST ) 00194 CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, S, LDST ) 00195 CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, T, LDST ) 00196 * 00197 * Compute threshold for testing acceptance of swapping. 00198 * 00199 EPS = DLAMCH( 'P' ) 00200 SMLNUM = DLAMCH( 'S' ) / EPS 00201 DSCALE = ZERO 00202 DSUM = ONE 00203 CALL DLACPY( 'Full', M, M, S, LDST, WORK, M ) 00204 CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM ) 00205 CALL DLACPY( 'Full', M, M, T, LDST, WORK, M ) 00206 CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM ) 00207 DNORM = DSCALE*SQRT( DSUM ) 00208 * 00209 * THRES has been changed from 00210 * THRESH = MAX( TEN*EPS*SA, SMLNUM ) 00211 * to 00212 * THRESH = MAX( TWENTY*EPS*SA, SMLNUM ) 00213 * on 04/01/10. 00214 * "Bug" reported by Ondra Kamenik, confirmed by Julie Langou, fixed by 00215 * Jim Demmel and Guillaume Revy. See forum post 1783. 00216 * 00217 THRESH = MAX( TWENTY*EPS*DNORM, SMLNUM ) 00218 * 00219 IF( M.EQ.2 ) THEN 00220 * 00221 * CASE 1: Swap 1-by-1 and 1-by-1 blocks. 00222 * 00223 * Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks 00224 * using Givens rotations and perform the swap tentatively. 00225 * 00226 F = S( 2, 2 )*T( 1, 1 ) - T( 2, 2 )*S( 1, 1 ) 00227 G = S( 2, 2 )*T( 1, 2 ) - T( 2, 2 )*S( 1, 2 ) 00228 SB = ABS( T( 2, 2 ) ) 00229 SA = ABS( S( 2, 2 ) ) 00230 CALL DLARTG( F, G, IR( 1, 2 ), IR( 1, 1 ), DDUM ) 00231 IR( 2, 1 ) = -IR( 1, 2 ) 00232 IR( 2, 2 ) = IR( 1, 1 ) 00233 CALL DROT( 2, S( 1, 1 ), 1, S( 1, 2 ), 1, IR( 1, 1 ), 00234 $ IR( 2, 1 ) ) 00235 CALL DROT( 2, T( 1, 1 ), 1, T( 1, 2 ), 1, IR( 1, 1 ), 00236 $ IR( 2, 1 ) ) 00237 IF( SA.GE.SB ) THEN 00238 CALL DLARTG( S( 1, 1 ), S( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ), 00239 $ DDUM ) 00240 ELSE 00241 CALL DLARTG( T( 1, 1 ), T( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ), 00242 $ DDUM ) 00243 END IF 00244 CALL DROT( 2, S( 1, 1 ), LDST, S( 2, 1 ), LDST, LI( 1, 1 ), 00245 $ LI( 2, 1 ) ) 00246 CALL DROT( 2, T( 1, 1 ), LDST, T( 2, 1 ), LDST, LI( 1, 1 ), 00247 $ LI( 2, 1 ) ) 00248 LI( 2, 2 ) = LI( 1, 1 ) 00249 LI( 1, 2 ) = -LI( 2, 1 ) 00250 * 00251 * Weak stability test: 00252 * |S21| + |T21| <= O(EPS * F-norm((S, T))) 00253 * 00254 WS = ABS( S( 2, 1 ) ) + ABS( T( 2, 1 ) ) 00255 WEAK = WS.LE.THRESH 00256 IF( .NOT.WEAK ) 00257 $ GO TO 70 00258 * 00259 IF( WANDS ) THEN 00260 * 00261 * Strong stability test: 00262 * F-norm((A-QL**T*S*QR, B-QL**T*T*QR)) <= O(EPS*F-norm((A,B))) 00263 * 00264 CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ), 00265 $ M ) 00266 CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, 00267 $ WORK, M ) 00268 CALL DGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE, 00269 $ WORK( M*M+1 ), M ) 00270 DSCALE = ZERO 00271 DSUM = ONE 00272 CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) 00273 * 00274 CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ), 00275 $ M ) 00276 CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, 00277 $ WORK, M ) 00278 CALL DGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE, 00279 $ WORK( M*M+1 ), M ) 00280 CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) 00281 SS = DSCALE*SQRT( DSUM ) 00282 DTRONG = SS.LE.THRESH 00283 IF( .NOT.DTRONG ) 00284 $ GO TO 70 00285 END IF 00286 * 00287 * Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and 00288 * (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). 00289 * 00290 CALL DROT( J1+1, A( 1, J1 ), 1, A( 1, J1+1 ), 1, IR( 1, 1 ), 00291 $ IR( 2, 1 ) ) 00292 CALL DROT( J1+1, B( 1, J1 ), 1, B( 1, J1+1 ), 1, IR( 1, 1 ), 00293 $ IR( 2, 1 ) ) 00294 CALL DROT( N-J1+1, A( J1, J1 ), LDA, A( J1+1, J1 ), LDA, 00295 $ LI( 1, 1 ), LI( 2, 1 ) ) 00296 CALL DROT( N-J1+1, B( J1, J1 ), LDB, B( J1+1, J1 ), LDB, 00297 $ LI( 1, 1 ), LI( 2, 1 ) ) 00298 * 00299 * Set N1-by-N2 (2,1) - blocks to ZERO. 00300 * 00301 A( J1+1, J1 ) = ZERO 00302 B( J1+1, J1 ) = ZERO 00303 * 00304 * Accumulate transformations into Q and Z if requested. 00305 * 00306 IF( WANTZ ) 00307 $ CALL DROT( N, Z( 1, J1 ), 1, Z( 1, J1+1 ), 1, IR( 1, 1 ), 00308 $ IR( 2, 1 ) ) 00309 IF( WANTQ ) 00310 $ CALL DROT( N, Q( 1, J1 ), 1, Q( 1, J1+1 ), 1, LI( 1, 1 ), 00311 $ LI( 2, 1 ) ) 00312 * 00313 * Exit with INFO = 0 if swap was successfully performed. 00314 * 00315 RETURN 00316 * 00317 ELSE 00318 * 00319 * CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2 00320 * and 2-by-2 blocks. 00321 * 00322 * Solve the generalized Sylvester equation 00323 * S11 * R - L * S22 = SCALE * S12 00324 * T11 * R - L * T22 = SCALE * T12 00325 * for R and L. Solutions in LI and IR. 00326 * 00327 CALL DLACPY( 'Full', N1, N2, T( 1, N1+1 ), LDST, LI, LDST ) 00328 CALL DLACPY( 'Full', N1, N2, S( 1, N1+1 ), LDST, 00329 $ IR( N2+1, N1+1 ), LDST ) 00330 CALL DTGSY2( 'N', 0, N1, N2, S, LDST, S( N1+1, N1+1 ), LDST, 00331 $ IR( N2+1, N1+1 ), LDST, T, LDST, T( N1+1, N1+1 ), 00332 $ LDST, LI, LDST, SCALE, DSUM, DSCALE, IWORK, IDUM, 00333 $ LINFO ) 00334 * 00335 * Compute orthogonal matrix QL: 00336 * 00337 * QL**T * LI = [ TL ] 00338 * [ 0 ] 00339 * where 00340 * LI = [ -L ] 00341 * [ SCALE * identity(N2) ] 00342 * 00343 DO 10 I = 1, N2 00344 CALL DSCAL( N1, -ONE, LI( 1, I ), 1 ) 00345 LI( N1+I, I ) = SCALE 00346 10 CONTINUE 00347 CALL DGEQR2( M, N2, LI, LDST, TAUL, WORK, LINFO ) 00348 IF( LINFO.NE.0 ) 00349 $ GO TO 70 00350 CALL DORG2R( M, M, N2, LI, LDST, TAUL, WORK, LINFO ) 00351 IF( LINFO.NE.0 ) 00352 $ GO TO 70 00353 * 00354 * Compute orthogonal matrix RQ: 00355 * 00356 * IR * RQ**T = [ 0 TR], 00357 * 00358 * where IR = [ SCALE * identity(N1), R ] 00359 * 00360 DO 20 I = 1, N1 00361 IR( N2+I, I ) = SCALE 00362 20 CONTINUE 00363 CALL DGERQ2( N1, M, IR( N2+1, 1 ), LDST, TAUR, WORK, LINFO ) 00364 IF( LINFO.NE.0 ) 00365 $ GO TO 70 00366 CALL DORGR2( M, M, N1, IR, LDST, TAUR, WORK, LINFO ) 00367 IF( LINFO.NE.0 ) 00368 $ GO TO 70 00369 * 00370 * Perform the swapping tentatively: 00371 * 00372 CALL DGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, 00373 $ WORK, M ) 00374 CALL DGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, S, 00375 $ LDST ) 00376 CALL DGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, 00377 $ WORK, M ) 00378 CALL DGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, T, 00379 $ LDST ) 00380 CALL DLACPY( 'F', M, M, S, LDST, SCPY, LDST ) 00381 CALL DLACPY( 'F', M, M, T, LDST, TCPY, LDST ) 00382 CALL DLACPY( 'F', M, M, IR, LDST, IRCOP, LDST ) 00383 CALL DLACPY( 'F', M, M, LI, LDST, LICOP, LDST ) 00384 * 00385 * Triangularize the B-part by an RQ factorization. 00386 * Apply transformation (from left) to A-part, giving S. 00387 * 00388 CALL DGERQ2( M, M, T, LDST, TAUR, WORK, LINFO ) 00389 IF( LINFO.NE.0 ) 00390 $ GO TO 70 00391 CALL DORMR2( 'R', 'T', M, M, M, T, LDST, TAUR, S, LDST, WORK, 00392 $ LINFO ) 00393 IF( LINFO.NE.0 ) 00394 $ GO TO 70 00395 CALL DORMR2( 'L', 'N', M, M, M, T, LDST, TAUR, IR, LDST, WORK, 00396 $ LINFO ) 00397 IF( LINFO.NE.0 ) 00398 $ GO TO 70 00399 * 00400 * Compute F-norm(S21) in BRQA21. (T21 is 0.) 00401 * 00402 DSCALE = ZERO 00403 DSUM = ONE 00404 DO 30 I = 1, N2 00405 CALL DLASSQ( N1, S( N2+1, I ), 1, DSCALE, DSUM ) 00406 30 CONTINUE 00407 BRQA21 = DSCALE*SQRT( DSUM ) 00408 * 00409 * Triangularize the B-part by a QR factorization. 00410 * Apply transformation (from right) to A-part, giving S. 00411 * 00412 CALL DGEQR2( M, M, TCPY, LDST, TAUL, WORK, LINFO ) 00413 IF( LINFO.NE.0 ) 00414 $ GO TO 70 00415 CALL DORM2R( 'L', 'T', M, M, M, TCPY, LDST, TAUL, SCPY, LDST, 00416 $ WORK, INFO ) 00417 CALL DORM2R( 'R', 'N', M, M, M, TCPY, LDST, TAUL, LICOP, LDST, 00418 $ WORK, INFO ) 00419 IF( LINFO.NE.0 ) 00420 $ GO TO 70 00421 * 00422 * Compute F-norm(S21) in BQRA21. (T21 is 0.) 00423 * 00424 DSCALE = ZERO 00425 DSUM = ONE 00426 DO 40 I = 1, N2 00427 CALL DLASSQ( N1, SCPY( N2+1, I ), 1, DSCALE, DSUM ) 00428 40 CONTINUE 00429 BQRA21 = DSCALE*SQRT( DSUM ) 00430 * 00431 * Decide which method to use. 00432 * Weak stability test: 00433 * F-norm(S21) <= O(EPS * F-norm((S, T))) 00434 * 00435 IF( BQRA21.LE.BRQA21 .AND. BQRA21.LE.THRESH ) THEN 00436 CALL DLACPY( 'F', M, M, SCPY, LDST, S, LDST ) 00437 CALL DLACPY( 'F', M, M, TCPY, LDST, T, LDST ) 00438 CALL DLACPY( 'F', M, M, IRCOP, LDST, IR, LDST ) 00439 CALL DLACPY( 'F', M, M, LICOP, LDST, LI, LDST ) 00440 ELSE IF( BRQA21.GE.THRESH ) THEN 00441 GO TO 70 00442 END IF 00443 * 00444 * Set lower triangle of B-part to zero 00445 * 00446 CALL DLASET( 'Lower', M-1, M-1, ZERO, ZERO, T(2,1), LDST ) 00447 * 00448 IF( WANDS ) THEN 00449 * 00450 * Strong stability test: 00451 * F-norm((A-QL*S*QR**T, B-QL*T*QR**T)) <= O(EPS*F-norm((A,B))) 00452 * 00453 CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ), 00454 $ M ) 00455 CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, 00456 $ WORK, M ) 00457 CALL DGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE, 00458 $ WORK( M*M+1 ), M ) 00459 DSCALE = ZERO 00460 DSUM = ONE 00461 CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) 00462 * 00463 CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ), 00464 $ M ) 00465 CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, 00466 $ WORK, M ) 00467 CALL DGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE, 00468 $ WORK( M*M+1 ), M ) 00469 CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) 00470 SS = DSCALE*SQRT( DSUM ) 00471 DTRONG = ( SS.LE.THRESH ) 00472 IF( .NOT.DTRONG ) 00473 $ GO TO 70 00474 * 00475 END IF 00476 * 00477 * If the swap is accepted ("weakly" and "strongly"), apply the 00478 * transformations and set N1-by-N2 (2,1)-block to zero. 00479 * 00480 CALL DLASET( 'Full', N1, N2, ZERO, ZERO, S(N2+1,1), LDST ) 00481 * 00482 * copy back M-by-M diagonal block starting at index J1 of (A, B) 00483 * 00484 CALL DLACPY( 'F', M, M, S, LDST, A( J1, J1 ), LDA ) 00485 CALL DLACPY( 'F', M, M, T, LDST, B( J1, J1 ), LDB ) 00486 CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, T, LDST ) 00487 * 00488 * Standardize existing 2-by-2 blocks. 00489 * 00490 DO 50 I = 1, M*M 00491 WORK(I) = ZERO 00492 50 CONTINUE 00493 WORK( 1 ) = ONE 00494 T( 1, 1 ) = ONE 00495 IDUM = LWORK - M*M - 2 00496 IF( N2.GT.1 ) THEN 00497 CALL DLAGV2( A( J1, J1 ), LDA, B( J1, J1 ), LDB, AR, AI, BE, 00498 $ WORK( 1 ), WORK( 2 ), T( 1, 1 ), T( 2, 1 ) ) 00499 WORK( M+1 ) = -WORK( 2 ) 00500 WORK( M+2 ) = WORK( 1 ) 00501 T( N2, N2 ) = T( 1, 1 ) 00502 T( 1, 2 ) = -T( 2, 1 ) 00503 END IF 00504 WORK( M*M ) = ONE 00505 T( M, M ) = ONE 00506 * 00507 IF( N1.GT.1 ) THEN 00508 CALL DLAGV2( A( J1+N2, J1+N2 ), LDA, B( J1+N2, J1+N2 ), LDB, 00509 $ TAUR, TAUL, WORK( M*M+1 ), WORK( N2*M+N2+1 ), 00510 $ WORK( N2*M+N2+2 ), T( N2+1, N2+1 ), 00511 $ T( M, M-1 ) ) 00512 WORK( M*M ) = WORK( N2*M+N2+1 ) 00513 WORK( M*M-1 ) = -WORK( N2*M+N2+2 ) 00514 T( M, M ) = T( N2+1, N2+1 ) 00515 T( M-1, M ) = -T( M, M-1 ) 00516 END IF 00517 CALL DGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, A( J1, J1+N2 ), 00518 $ LDA, ZERO, WORK( M*M+1 ), N2 ) 00519 CALL DLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, A( J1, J1+N2 ), 00520 $ LDA ) 00521 CALL DGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, B( J1, J1+N2 ), 00522 $ LDB, ZERO, WORK( M*M+1 ), N2 ) 00523 CALL DLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, B( J1, J1+N2 ), 00524 $ LDB ) 00525 CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, WORK, M, ZERO, 00526 $ WORK( M*M+1 ), M ) 00527 CALL DLACPY( 'Full', M, M, WORK( M*M+1 ), M, LI, LDST ) 00528 CALL DGEMM( 'N', 'N', N2, N1, N1, ONE, A( J1, J1+N2 ), LDA, 00529 $ T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 ) 00530 CALL DLACPY( 'Full', N2, N1, WORK, N2, A( J1, J1+N2 ), LDA ) 00531 CALL DGEMM( 'N', 'N', N2, N1, N1, ONE, B( J1, J1+N2 ), LDB, 00532 $ T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 ) 00533 CALL DLACPY( 'Full', N2, N1, WORK, N2, B( J1, J1+N2 ), LDB ) 00534 CALL DGEMM( 'T', 'N', M, M, M, ONE, IR, LDST, T, LDST, ZERO, 00535 $ WORK, M ) 00536 CALL DLACPY( 'Full', M, M, WORK, M, IR, LDST ) 00537 * 00538 * Accumulate transformations into Q and Z if requested. 00539 * 00540 IF( WANTQ ) THEN 00541 CALL DGEMM( 'N', 'N', N, M, M, ONE, Q( 1, J1 ), LDQ, LI, 00542 $ LDST, ZERO, WORK, N ) 00543 CALL DLACPY( 'Full', N, M, WORK, N, Q( 1, J1 ), LDQ ) 00544 * 00545 END IF 00546 * 00547 IF( WANTZ ) THEN 00548 CALL DGEMM( 'N', 'N', N, M, M, ONE, Z( 1, J1 ), LDZ, IR, 00549 $ LDST, ZERO, WORK, N ) 00550 CALL DLACPY( 'Full', N, M, WORK, N, Z( 1, J1 ), LDZ ) 00551 * 00552 END IF 00553 * 00554 * Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and 00555 * (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). 00556 * 00557 I = J1 + M 00558 IF( I.LE.N ) THEN 00559 CALL DGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST, 00560 $ A( J1, I ), LDA, ZERO, WORK, M ) 00561 CALL DLACPY( 'Full', M, N-I+1, WORK, M, A( J1, I ), LDA ) 00562 CALL DGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST, 00563 $ B( J1, I ), LDA, ZERO, WORK, M ) 00564 CALL DLACPY( 'Full', M, N-I+1, WORK, M, B( J1, I ), LDB ) 00565 END IF 00566 I = J1 - 1 00567 IF( I.GT.0 ) THEN 00568 CALL DGEMM( 'N', 'N', I, M, M, ONE, A( 1, J1 ), LDA, IR, 00569 $ LDST, ZERO, WORK, I ) 00570 CALL DLACPY( 'Full', I, M, WORK, I, A( 1, J1 ), LDA ) 00571 CALL DGEMM( 'N', 'N', I, M, M, ONE, B( 1, J1 ), LDB, IR, 00572 $ LDST, ZERO, WORK, I ) 00573 CALL DLACPY( 'Full', I, M, WORK, I, B( 1, J1 ), LDB ) 00574 END IF 00575 * 00576 * Exit with INFO = 0 if swap was successfully performed. 00577 * 00578 RETURN 00579 * 00580 END IF 00581 * 00582 * Exit with INFO = 1 if swap was rejected. 00583 * 00584 70 CONTINUE 00585 * 00586 INFO = 1 00587 RETURN 00588 * 00589 * End of DTGEX2 00590 * 00591 END
1.7.3 
