 |
LAPACK 3.3.1
Linear Algebra PACKage
|
|
LAPACK 3.3.1
Linear Algebra PACKage
|
00001 SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, 00002 $ VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, 00003 $ INFO ) 00004 * 00005 * -- LAPACK driver routine (version 3.2) -- 00006 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00007 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00008 * November 2006 00009 * 00010 * .. Scalar Arguments .. 00011 CHARACTER JOBVSL, JOBVSR 00012 INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N 00013 * .. 00014 * .. Array Arguments .. 00015 DOUBLE PRECISION RWORK( * ) 00016 COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ), 00017 $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ), 00018 $ WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * This routine is deprecated and has been replaced by routine ZGGES. 00025 * 00026 * ZGEGS computes the eigenvalues, Schur form, and, optionally, the 00027 * left and or/right Schur vectors of a complex matrix pair (A,B). 00028 * Given two square matrices A and B, the generalized Schur 00029 * factorization has the form 00030 * 00031 * A = Q*S*Z**H, B = Q*T*Z**H 00032 * 00033 * where Q and Z are unitary matrices and S and T are upper triangular. 00034 * The columns of Q are the left Schur vectors 00035 * and the columns of Z are the right Schur vectors. 00036 * 00037 * If only the eigenvalues of (A,B) are needed, the driver routine 00038 * ZGEGV should be used instead. See ZGEGV for a description of the 00039 * eigenvalues of the generalized nonsymmetric eigenvalue problem 00040 * (GNEP). 00041 * 00042 * Arguments 00043 * ========= 00044 * 00045 * JOBVSL (input) CHARACTER*1 00046 * = 'N': do not compute the left Schur vectors; 00047 * = 'V': compute the left Schur vectors (returned in VSL). 00048 * 00049 * JOBVSR (input) CHARACTER*1 00050 * = 'N': do not compute the right Schur vectors; 00051 * = 'V': compute the right Schur vectors (returned in VSR). 00052 * 00053 * N (input) INTEGER 00054 * The order of the matrices A, B, VSL, and VSR. N >= 0. 00055 * 00056 * A (input/output) COMPLEX*16 array, dimension (LDA, N) 00057 * On entry, the matrix A. 00058 * On exit, the upper triangular matrix S from the generalized 00059 * Schur factorization. 00060 * 00061 * LDA (input) INTEGER 00062 * The leading dimension of A. LDA >= max(1,N). 00063 * 00064 * B (input/output) COMPLEX*16 array, dimension (LDB, N) 00065 * On entry, the matrix B. 00066 * On exit, the upper triangular matrix T from the generalized 00067 * Schur factorization. 00068 * 00069 * LDB (input) INTEGER 00070 * The leading dimension of B. LDB >= max(1,N). 00071 * 00072 * ALPHA (output) COMPLEX*16 array, dimension (N) 00073 * The complex scalars alpha that define the eigenvalues of 00074 * GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur 00075 * form of A. 00076 * 00077 * BETA (output) COMPLEX*16 array, dimension (N) 00078 * The non-negative real scalars beta that define the 00079 * eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element 00080 * of the triangular factor T. 00081 * 00082 * Together, the quantities alpha = ALPHA(j) and beta = BETA(j) 00083 * represent the j-th eigenvalue of the matrix pair (A,B), in 00084 * one of the forms lambda = alpha/beta or mu = beta/alpha. 00085 * Since either lambda or mu may overflow, they should not, 00086 * in general, be computed. 00087 * 00088 * 00089 * VSL (output) COMPLEX*16 array, dimension (LDVSL,N) 00090 * If JOBVSL = 'V', the matrix of left Schur vectors Q. 00091 * Not referenced if JOBVSL = 'N'. 00092 * 00093 * LDVSL (input) INTEGER 00094 * The leading dimension of the matrix VSL. LDVSL >= 1, and 00095 * if JOBVSL = 'V', LDVSL >= N. 00096 * 00097 * VSR (output) COMPLEX*16 array, dimension (LDVSR,N) 00098 * If JOBVSR = 'V', the matrix of right Schur vectors Z. 00099 * Not referenced if JOBVSR = 'N'. 00100 * 00101 * LDVSR (input) INTEGER 00102 * The leading dimension of the matrix VSR. LDVSR >= 1, and 00103 * if JOBVSR = 'V', LDVSR >= N. 00104 * 00105 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 00106 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00107 * 00108 * LWORK (input) INTEGER 00109 * The dimension of the array WORK. LWORK >= max(1,2*N). 00110 * For good performance, LWORK must generally be larger. 00111 * To compute the optimal value of LWORK, call ILAENV to get 00112 * blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.) Then compute: 00113 * NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR; 00114 * the optimal LWORK is N*(NB+1). 00115 * 00116 * If LWORK = -1, then a workspace query is assumed; the routine 00117 * only calculates the optimal size of the WORK array, returns 00118 * this value as the first entry of the WORK array, and no error 00119 * message related to LWORK is issued by XERBLA. 00120 * 00121 * RWORK (workspace) DOUBLE PRECISION array, dimension (3*N) 00122 * 00123 * INFO (output) INTEGER 00124 * = 0: successful exit 00125 * < 0: if INFO = -i, the i-th argument had an illegal value. 00126 * =1,...,N: 00127 * The QZ iteration failed. (A,B) are not in Schur 00128 * form, but ALPHA(j) and BETA(j) should be correct for 00129 * j=INFO+1,...,N. 00130 * > N: errors that usually indicate LAPACK problems: 00131 * =N+1: error return from ZGGBAL 00132 * =N+2: error return from ZGEQRF 00133 * =N+3: error return from ZUNMQR 00134 * =N+4: error return from ZUNGQR 00135 * =N+5: error return from ZGGHRD 00136 * =N+6: error return from ZHGEQZ (other than failed 00137 * iteration) 00138 * =N+7: error return from ZGGBAK (computing VSL) 00139 * =N+8: error return from ZGGBAK (computing VSR) 00140 * =N+9: error return from ZLASCL (various places) 00141 * 00142 * ===================================================================== 00143 * 00144 * .. Parameters .. 00145 DOUBLE PRECISION ZERO, ONE 00146 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) 00147 COMPLEX*16 CZERO, CONE 00148 PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), 00149 $ CONE = ( 1.0D0, 0.0D0 ) ) 00150 * .. 00151 * .. Local Scalars .. 00152 LOGICAL ILASCL, ILBSCL, ILVSL, ILVSR, LQUERY 00153 INTEGER ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, ILO, 00154 $ IRIGHT, IROWS, IRWORK, ITAU, IWORK, LOPT, 00155 $ LWKMIN, LWKOPT, NB, NB1, NB2, NB3 00156 DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, 00157 $ SAFMIN, SMLNUM 00158 * .. 00159 * .. External Subroutines .. 00160 EXTERNAL XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD, ZHGEQZ, 00161 $ ZLACPY, ZLASCL, ZLASET, ZUNGQR, ZUNMQR 00162 * .. 00163 * .. External Functions .. 00164 LOGICAL LSAME 00165 INTEGER ILAENV 00166 DOUBLE PRECISION DLAMCH, ZLANGE 00167 EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE 00168 * .. 00169 * .. Intrinsic Functions .. 00170 INTRINSIC INT, MAX 00171 * .. 00172 * .. Executable Statements .. 00173 * 00174 * Decode the input arguments 00175 * 00176 IF( LSAME( JOBVSL, 'N' ) ) THEN 00177 IJOBVL = 1 00178 ILVSL = .FALSE. 00179 ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN 00180 IJOBVL = 2 00181 ILVSL = .TRUE. 00182 ELSE 00183 IJOBVL = -1 00184 ILVSL = .FALSE. 00185 END IF 00186 * 00187 IF( LSAME( JOBVSR, 'N' ) ) THEN 00188 IJOBVR = 1 00189 ILVSR = .FALSE. 00190 ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN 00191 IJOBVR = 2 00192 ILVSR = .TRUE. 00193 ELSE 00194 IJOBVR = -1 00195 ILVSR = .FALSE. 00196 END IF 00197 * 00198 * Test the input arguments 00199 * 00200 LWKMIN = MAX( 2*N, 1 ) 00201 LWKOPT = LWKMIN 00202 WORK( 1 ) = LWKOPT 00203 LQUERY = ( LWORK.EQ.-1 ) 00204 INFO = 0 00205 IF( IJOBVL.LE.0 ) THEN 00206 INFO = -1 00207 ELSE IF( IJOBVR.LE.0 ) THEN 00208 INFO = -2 00209 ELSE IF( N.LT.0 ) THEN 00210 INFO = -3 00211 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00212 INFO = -5 00213 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00214 INFO = -7 00215 ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN 00216 INFO = -11 00217 ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN 00218 INFO = -13 00219 ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN 00220 INFO = -15 00221 END IF 00222 * 00223 IF( INFO.EQ.0 ) THEN 00224 NB1 = ILAENV( 1, 'ZGEQRF', ' ', N, N, -1, -1 ) 00225 NB2 = ILAENV( 1, 'ZUNMQR', ' ', N, N, N, -1 ) 00226 NB3 = ILAENV( 1, 'ZUNGQR', ' ', N, N, N, -1 ) 00227 NB = MAX( NB1, NB2, NB3 ) 00228 LOPT = N*( NB+1 ) 00229 WORK( 1 ) = LOPT 00230 END IF 00231 * 00232 IF( INFO.NE.0 ) THEN 00233 CALL XERBLA( 'ZGEGS ', -INFO ) 00234 RETURN 00235 ELSE IF( LQUERY ) THEN 00236 RETURN 00237 END IF 00238 * 00239 * Quick return if possible 00240 * 00241 IF( N.EQ.0 ) 00242 $ RETURN 00243 * 00244 * Get machine constants 00245 * 00246 EPS = DLAMCH( 'E' )*DLAMCH( 'B' ) 00247 SAFMIN = DLAMCH( 'S' ) 00248 SMLNUM = N*SAFMIN / EPS 00249 BIGNUM = ONE / SMLNUM 00250 * 00251 * Scale A if max element outside range [SMLNUM,BIGNUM] 00252 * 00253 ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK ) 00254 ILASCL = .FALSE. 00255 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 00256 ANRMTO = SMLNUM 00257 ILASCL = .TRUE. 00258 ELSE IF( ANRM.GT.BIGNUM ) THEN 00259 ANRMTO = BIGNUM 00260 ILASCL = .TRUE. 00261 END IF 00262 * 00263 IF( ILASCL ) THEN 00264 CALL ZLASCL( 'G', -1, -1, ANRM, ANRMTO, N, N, A, LDA, IINFO ) 00265 IF( IINFO.NE.0 ) THEN 00266 INFO = N + 9 00267 RETURN 00268 END IF 00269 END IF 00270 * 00271 * Scale B if max element outside range [SMLNUM,BIGNUM] 00272 * 00273 BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK ) 00274 ILBSCL = .FALSE. 00275 IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN 00276 BNRMTO = SMLNUM 00277 ILBSCL = .TRUE. 00278 ELSE IF( BNRM.GT.BIGNUM ) THEN 00279 BNRMTO = BIGNUM 00280 ILBSCL = .TRUE. 00281 END IF 00282 * 00283 IF( ILBSCL ) THEN 00284 CALL ZLASCL( 'G', -1, -1, BNRM, BNRMTO, N, N, B, LDB, IINFO ) 00285 IF( IINFO.NE.0 ) THEN 00286 INFO = N + 9 00287 RETURN 00288 END IF 00289 END IF 00290 * 00291 * Permute the matrix to make it more nearly triangular 00292 * 00293 ILEFT = 1 00294 IRIGHT = N + 1 00295 IRWORK = IRIGHT + N 00296 IWORK = 1 00297 CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ), 00298 $ RWORK( IRIGHT ), RWORK( IRWORK ), IINFO ) 00299 IF( IINFO.NE.0 ) THEN 00300 INFO = N + 1 00301 GO TO 10 00302 END IF 00303 * 00304 * Reduce B to triangular form, and initialize VSL and/or VSR 00305 * 00306 IROWS = IHI + 1 - ILO 00307 ICOLS = N + 1 - ILO 00308 ITAU = IWORK 00309 IWORK = ITAU + IROWS 00310 CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ), 00311 $ WORK( IWORK ), LWORK+1-IWORK, IINFO ) 00312 IF( IINFO.GE.0 ) 00313 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 ) 00314 IF( IINFO.NE.0 ) THEN 00315 INFO = N + 2 00316 GO TO 10 00317 END IF 00318 * 00319 CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB, 00320 $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ), 00321 $ LWORK+1-IWORK, IINFO ) 00322 IF( IINFO.GE.0 ) 00323 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 ) 00324 IF( IINFO.NE.0 ) THEN 00325 INFO = N + 3 00326 GO TO 10 00327 END IF 00328 * 00329 IF( ILVSL ) THEN 00330 CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL ) 00331 CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB, 00332 $ VSL( ILO+1, ILO ), LDVSL ) 00333 CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL, 00334 $ WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK, 00335 $ IINFO ) 00336 IF( IINFO.GE.0 ) 00337 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 ) 00338 IF( IINFO.NE.0 ) THEN 00339 INFO = N + 4 00340 GO TO 10 00341 END IF 00342 END IF 00343 * 00344 IF( ILVSR ) 00345 $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR ) 00346 * 00347 * Reduce to generalized Hessenberg form 00348 * 00349 CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL, 00350 $ LDVSL, VSR, LDVSR, IINFO ) 00351 IF( IINFO.NE.0 ) THEN 00352 INFO = N + 5 00353 GO TO 10 00354 END IF 00355 * 00356 * Perform QZ algorithm, computing Schur vectors if desired 00357 * 00358 IWORK = ITAU 00359 CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, 00360 $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWORK ), 00361 $ LWORK+1-IWORK, RWORK( IRWORK ), IINFO ) 00362 IF( IINFO.GE.0 ) 00363 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 ) 00364 IF( IINFO.NE.0 ) THEN 00365 IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN 00366 INFO = IINFO 00367 ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN 00368 INFO = IINFO - N 00369 ELSE 00370 INFO = N + 6 00371 END IF 00372 GO TO 10 00373 END IF 00374 * 00375 * Apply permutation to VSL and VSR 00376 * 00377 IF( ILVSL ) THEN 00378 CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ), 00379 $ RWORK( IRIGHT ), N, VSL, LDVSL, IINFO ) 00380 IF( IINFO.NE.0 ) THEN 00381 INFO = N + 7 00382 GO TO 10 00383 END IF 00384 END IF 00385 IF( ILVSR ) THEN 00386 CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ), 00387 $ RWORK( IRIGHT ), N, VSR, LDVSR, IINFO ) 00388 IF( IINFO.NE.0 ) THEN 00389 INFO = N + 8 00390 GO TO 10 00391 END IF 00392 END IF 00393 * 00394 * Undo scaling 00395 * 00396 IF( ILASCL ) THEN 00397 CALL ZLASCL( 'U', -1, -1, ANRMTO, ANRM, N, N, A, LDA, IINFO ) 00398 IF( IINFO.NE.0 ) THEN 00399 INFO = N + 9 00400 RETURN 00401 END IF 00402 CALL ZLASCL( 'G', -1, -1, ANRMTO, ANRM, N, 1, ALPHA, N, IINFO ) 00403 IF( IINFO.NE.0 ) THEN 00404 INFO = N + 9 00405 RETURN 00406 END IF 00407 END IF 00408 * 00409 IF( ILBSCL ) THEN 00410 CALL ZLASCL( 'U', -1, -1, BNRMTO, BNRM, N, N, B, LDB, IINFO ) 00411 IF( IINFO.NE.0 ) THEN 00412 INFO = N + 9 00413 RETURN 00414 END IF 00415 CALL ZLASCL( 'G', -1, -1, BNRMTO, BNRM, N, 1, BETA, N, IINFO ) 00416 IF( IINFO.NE.0 ) THEN 00417 INFO = N + 9 00418 RETURN 00419 END IF 00420 END IF 00421 * 00422 10 CONTINUE 00423 WORK( 1 ) = LWKOPT 00424 * 00425 RETURN 00426 * 00427 * End of ZGEGS 00428 * 00429 END
1.7.3 
