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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE CGEGS( 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 REAL RWORK( * ) 00016 COMPLEX 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00018 $ WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * This routine is deprecated and has been replaced by routine CGGES. 00025 * 00026 * CGEGS computes the eigenvalues, Schur form, and, optionally, the 00027 * left and or/right Schur vectors of a complex matrix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 * CGEGV should be used instead. See CGEGV 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 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 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 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 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 * VSL (output) COMPLEX array, dimension (LDVSL,N) 00089 * If JOBVSL = 'V', the matrix of left Schur vectors Q. 00090 * Not referenced if JOBVSL = 'N'. 00091 * 00092 * LDVSL (input) INTEGER 00093 * The leading dimension of the matrix VSL. LDVSL >= 1, and 00094 * if JOBVSL = 'V', LDVSL >= N. 00095 * 00096 * VSR (output) COMPLEX array, dimension (LDVSR,N) 00097 * If JOBVSR = 'V', the matrix of right Schur vectors Z. 00098 * Not referenced if JOBVSR = 'N'. 00099 * 00100 * LDVSR (input) INTEGER 00101 * The leading dimension of the matrix VSR. LDVSR >= 1, and 00102 * if JOBVSR = 'V', LDVSR >= N. 00103 * 00104 * WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) 00105 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00106 * 00107 * LWORK (input) INTEGER 00108 * The dimension of the array WORK. LWORK >= max(1,2*N). 00109 * For good performance, LWORK must generally be larger. 00110 * To compute the optimal value of LWORK, call ILAENV to get 00111 * blocksizes (for CGEQRF, CUNMQR, and CUNGQR.) Then compute: 00112 * NB -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR; 00113 * the optimal LWORK is N*(NB+1). 00114 * 00115 * If LWORK = -1, then a workspace query is assumed; the routine 00116 * only calculates the optimal size of the WORK array, returns 00117 * this value as the first entry of the WORK array, and no error 00118 * message related to LWORK is issued by XERBLA. 00119 * 00120 * RWORK (workspace) REAL array, dimension (3*N) 00121 * 00122 * INFO (output) INTEGER 00123 * = 0: successful exit 00124 * < 0: if INFO = -i, the i-th argument had an illegal value. 00125 * =1,...,N: 00126 * The QZ iteration failed. (A,B) are not in Schur 00127 * form, but ALPHA(j) and BETA(j) should be correct for 00128 * j=INFO+1,...,N. 00129 * > N: errors that usually indicate LAPACK problems: 00130 * =N+1: error return from CGGBAL 00131 * =N+2: error return from CGEQRF 00132 * =N+3: error return from CUNMQR 00133 * =N+4: error return from CUNGQR 00134 * =N+5: error return from CGGHRD 00135 * =N+6: error return from CHGEQZ (other than failed 00136 * iteration) 00137 * =N+7: error return from CGGBAK (computing VSL) 00138 * =N+8: error return from CGGBAK (computing VSR) 00139 * =N+9: error return from CLASCL (various places) 00140 * 00141 * ===================================================================== 00142 * 00143 * .. Parameters .. 00144 REAL ZERO, ONE 00145 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) 00146 COMPLEX CZERO, CONE 00147 PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ), 00148 $ CONE = ( 1.0E0, 0.0E0 ) ) 00149 * .. 00150 * .. Local Scalars .. 00151 LOGICAL ILASCL, ILBSCL, ILVSL, ILVSR, LQUERY 00152 INTEGER ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, 00153 $ ILO, IRIGHT, IROWS, IRWORK, ITAU, IWORK, 00154 $ LOPT, LWKMIN, LWKOPT, NB, NB1, NB2, NB3 00155 REAL ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, 00156 $ SAFMIN, SMLNUM 00157 * .. 00158 * .. External Subroutines .. 00159 EXTERNAL CGEQRF, CGGBAK, CGGBAL, CGGHRD, CHGEQZ, CLACPY, 00160 $ CLASCL, CLASET, CUNGQR, CUNMQR, XERBLA 00161 * .. 00162 * .. External Functions .. 00163 LOGICAL LSAME 00164 INTEGER ILAENV 00165 REAL CLANGE, SLAMCH 00166 EXTERNAL ILAENV, LSAME, CLANGE, SLAMCH 00167 * .. 00168 * .. Intrinsic Functions .. 00169 INTRINSIC INT, MAX 00170 * .. 00171 * .. Executable Statements .. 00172 * 00173 * Decode the input arguments 00174 * 00175 IF( LSAME( JOBVSL, 'N' ) ) THEN 00176 IJOBVL = 1 00177 ILVSL = .FALSE. 00178 ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN 00179 IJOBVL = 2 00180 ILVSL = .TRUE. 00181 ELSE 00182 IJOBVL = -1 00183 ILVSL = .FALSE. 00184 END IF 00185 * 00186 IF( LSAME( JOBVSR, 'N' ) ) THEN 00187 IJOBVR = 1 00188 ILVSR = .FALSE. 00189 ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN 00190 IJOBVR = 2 00191 ILVSR = .TRUE. 00192 ELSE 00193 IJOBVR = -1 00194 ILVSR = .FALSE. 00195 END IF 00196 * 00197 * Test the input arguments 00198 * 00199 LWKMIN = MAX( 2*N, 1 ) 00200 LWKOPT = LWKMIN 00201 WORK( 1 ) = LWKOPT 00202 LQUERY = ( LWORK.EQ.-1 ) 00203 INFO = 0 00204 IF( IJOBVL.LE.0 ) THEN 00205 INFO = -1 00206 ELSE IF( IJOBVR.LE.0 ) THEN 00207 INFO = -2 00208 ELSE IF( N.LT.0 ) THEN 00209 INFO = -3 00210 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00211 INFO = -5 00212 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00213 INFO = -7 00214 ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN 00215 INFO = -11 00216 ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN 00217 INFO = -13 00218 ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN 00219 INFO = -15 00220 END IF 00221 * 00222 IF( INFO.EQ.0 ) THEN 00223 NB1 = ILAENV( 1, 'CGEQRF', ' ', N, N, -1, -1 ) 00224 NB2 = ILAENV( 1, 'CUNMQR', ' ', N, N, N, -1 ) 00225 NB3 = ILAENV( 1, 'CUNGQR', ' ', N, N, N, -1 ) 00226 NB = MAX( NB1, NB2, NB3 ) 00227 LOPT = N*(NB+1) 00228 WORK( 1 ) = LOPT 00229 END IF 00230 * 00231 IF( INFO.NE.0 ) THEN 00232 CALL XERBLA( 'CGEGS ', -INFO ) 00233 RETURN 00234 ELSE IF( LQUERY ) THEN 00235 RETURN 00236 END IF 00237 * 00238 * Quick return if possible 00239 * 00240 IF( N.EQ.0 ) 00241 $ RETURN 00242 * 00243 * Get machine constants 00244 * 00245 EPS = SLAMCH( 'E' )*SLAMCH( 'B' ) 00246 SAFMIN = SLAMCH( 'S' ) 00247 SMLNUM = N*SAFMIN / EPS 00248 BIGNUM = ONE / SMLNUM 00249 * 00250 * Scale A if max element outside range [SMLNUM,BIGNUM] 00251 * 00252 ANRM = CLANGE( 'M', N, N, A, LDA, RWORK ) 00253 ILASCL = .FALSE. 00254 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 00255 ANRMTO = SMLNUM 00256 ILASCL = .TRUE. 00257 ELSE IF( ANRM.GT.BIGNUM ) THEN 00258 ANRMTO = BIGNUM 00259 ILASCL = .TRUE. 00260 END IF 00261 * 00262 IF( ILASCL ) THEN 00263 CALL CLASCL( 'G', -1, -1, ANRM, ANRMTO, N, N, A, LDA, IINFO ) 00264 IF( IINFO.NE.0 ) THEN 00265 INFO = N + 9 00266 RETURN 00267 END IF 00268 END IF 00269 * 00270 * Scale B if max element outside range [SMLNUM,BIGNUM] 00271 * 00272 BNRM = CLANGE( 'M', N, N, B, LDB, RWORK ) 00273 ILBSCL = .FALSE. 00274 IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN 00275 BNRMTO = SMLNUM 00276 ILBSCL = .TRUE. 00277 ELSE IF( BNRM.GT.BIGNUM ) THEN 00278 BNRMTO = BIGNUM 00279 ILBSCL = .TRUE. 00280 END IF 00281 * 00282 IF( ILBSCL ) THEN 00283 CALL CLASCL( 'G', -1, -1, BNRM, BNRMTO, N, N, B, LDB, IINFO ) 00284 IF( IINFO.NE.0 ) THEN 00285 INFO = N + 9 00286 RETURN 00287 END IF 00288 END IF 00289 * 00290 * Permute the matrix to make it more nearly triangular 00291 * 00292 ILEFT = 1 00293 IRIGHT = N + 1 00294 IRWORK = IRIGHT + N 00295 IWORK = 1 00296 CALL CGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ), 00297 $ RWORK( IRIGHT ), RWORK( IRWORK ), IINFO ) 00298 IF( IINFO.NE.0 ) THEN 00299 INFO = N + 1 00300 GO TO 10 00301 END IF 00302 * 00303 * Reduce B to triangular form, and initialize VSL and/or VSR 00304 * 00305 IROWS = IHI + 1 - ILO 00306 ICOLS = N + 1 - ILO 00307 ITAU = IWORK 00308 IWORK = ITAU + IROWS 00309 CALL CGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ), 00310 $ WORK( IWORK ), LWORK+1-IWORK, IINFO ) 00311 IF( IINFO.GE.0 ) 00312 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 ) 00313 IF( IINFO.NE.0 ) THEN 00314 INFO = N + 2 00315 GO TO 10 00316 END IF 00317 * 00318 CALL CUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB, 00319 $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ), 00320 $ LWORK+1-IWORK, IINFO ) 00321 IF( IINFO.GE.0 ) 00322 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 ) 00323 IF( IINFO.NE.0 ) THEN 00324 INFO = N + 3 00325 GO TO 10 00326 END IF 00327 * 00328 IF( ILVSL ) THEN 00329 CALL CLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL ) 00330 CALL CLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB, 00331 $ VSL( ILO+1, ILO ), LDVSL ) 00332 CALL CUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL, 00333 $ WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK, 00334 $ IINFO ) 00335 IF( IINFO.GE.0 ) 00336 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 ) 00337 IF( IINFO.NE.0 ) THEN 00338 INFO = N + 4 00339 GO TO 10 00340 END IF 00341 END IF 00342 * 00343 IF( ILVSR ) 00344 $ CALL CLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR ) 00345 * 00346 * Reduce to generalized Hessenberg form 00347 * 00348 CALL CGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL, 00349 $ LDVSL, VSR, LDVSR, IINFO ) 00350 IF( IINFO.NE.0 ) THEN 00351 INFO = N + 5 00352 GO TO 10 00353 END IF 00354 * 00355 * Perform QZ algorithm, computing Schur vectors if desired 00356 * 00357 IWORK = ITAU 00358 CALL CHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, 00359 $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWORK ), 00360 $ LWORK+1-IWORK, RWORK( IRWORK ), IINFO ) 00361 IF( IINFO.GE.0 ) 00362 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 ) 00363 IF( IINFO.NE.0 ) THEN 00364 IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN 00365 INFO = IINFO 00366 ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN 00367 INFO = IINFO - N 00368 ELSE 00369 INFO = N + 6 00370 END IF 00371 GO TO 10 00372 END IF 00373 * 00374 * Apply permutation to VSL and VSR 00375 * 00376 IF( ILVSL ) THEN 00377 CALL CGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ), 00378 $ RWORK( IRIGHT ), N, VSL, LDVSL, IINFO ) 00379 IF( IINFO.NE.0 ) THEN 00380 INFO = N + 7 00381 GO TO 10 00382 END IF 00383 END IF 00384 IF( ILVSR ) THEN 00385 CALL CGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ), 00386 $ RWORK( IRIGHT ), N, VSR, LDVSR, IINFO ) 00387 IF( IINFO.NE.0 ) THEN 00388 INFO = N + 8 00389 GO TO 10 00390 END IF 00391 END IF 00392 * 00393 * Undo scaling 00394 * 00395 IF( ILASCL ) THEN 00396 CALL CLASCL( 'U', -1, -1, ANRMTO, ANRM, N, N, A, LDA, IINFO ) 00397 IF( IINFO.NE.0 ) THEN 00398 INFO = N + 9 00399 RETURN 00400 END IF 00401 CALL CLASCL( 'G', -1, -1, ANRMTO, ANRM, N, 1, ALPHA, N, IINFO ) 00402 IF( IINFO.NE.0 ) THEN 00403 INFO = N + 9 00404 RETURN 00405 END IF 00406 END IF 00407 * 00408 IF( ILBSCL ) THEN 00409 CALL CLASCL( 'U', -1, -1, BNRMTO, BNRM, N, N, B, LDB, IINFO ) 00410 IF( IINFO.NE.0 ) THEN 00411 INFO = N + 9 00412 RETURN 00413 END IF 00414 CALL CLASCL( 'G', -1, -1, BNRMTO, BNRM, N, 1, BETA, N, IINFO ) 00415 IF( IINFO.NE.0 ) THEN 00416 INFO = N + 9 00417 RETURN 00418 END IF 00419 END IF 00420 * 00421 10 CONTINUE 00422 WORK( 1 ) = LWKOPT 00423 * 00424 RETURN 00425 * 00426 * End of CGEGS 00427 * 00428 END
1.7.3 
