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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 CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, 00002 $ LDVS, WORK, LWORK, RWORK, BWORK, INFO ) 00003 * 00004 * -- LAPACK driver routine (version 3.2) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * November 2006 00008 * 00009 * .. Scalar Arguments .. 00010 CHARACTER JOBVS, SORT 00011 INTEGER INFO, LDA, LDVS, LWORK, N, SDIM 00012 * .. 00013 * .. Array Arguments .. 00014 LOGICAL BWORK( * ) 00015 REAL RWORK( * ) 00016 COMPLEX A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * ) 00017 * .. 00018 * .. Function Arguments .. 00019 LOGICAL SELECT 00020 EXTERNAL SELECT 00021 * .. 00022 * 00023 * Purpose 00024 * ======= 00025 * 00026 * CGEES computes for an N-by-N complex nonsymmetric matrix A, the 00027 * eigenvalues, the Schur form T, and, optionally, the matrix of Schur 00028 * vectors Z. This gives the Schur factorization A = Z*T*(Z**H). 00029 * 00030 * Optionally, it also orders the eigenvalues on the diagonal of the 00031 * Schur form so that selected eigenvalues are at the top left. 00032 * The leading columns of Z then form an orthonormal basis for the 00033 * invariant subspace corresponding to the selected eigenvalues. 00034 00035 * A complex matrix is in Schur form if it is upper triangular. 00036 * 00037 * Arguments 00038 * ========= 00039 * 00040 * JOBVS (input) CHARACTER*1 00041 * = 'N': Schur vectors are not computed; 00042 * = 'V': Schur vectors are computed. 00043 * 00044 * SORT (input) CHARACTER*1 00045 * Specifies whether or not to order the eigenvalues on the 00046 * diagonal of the Schur form. 00047 * = 'N': Eigenvalues are not ordered: 00048 * = 'S': Eigenvalues are ordered (see SELECT). 00049 * 00050 * SELECT (external procedure) LOGICAL FUNCTION of one COMPLEX argument 00051 * SELECT must be declared EXTERNAL in the calling subroutine. 00052 * If SORT = 'S', SELECT is used to select eigenvalues to order 00053 * to the top left of the Schur form. 00054 * IF SORT = 'N', SELECT is not referenced. 00055 * The eigenvalue W(j) is selected if SELECT(W(j)) is true. 00056 * 00057 * N (input) INTEGER 00058 * The order of the matrix A. N >= 0. 00059 * 00060 * A (input/output) COMPLEX array, dimension (LDA,N) 00061 * On entry, the N-by-N matrix A. 00062 * On exit, A has been overwritten by its Schur form T. 00063 * 00064 * LDA (input) INTEGER 00065 * The leading dimension of the array A. LDA >= max(1,N). 00066 * 00067 * SDIM (output) INTEGER 00068 * If SORT = 'N', SDIM = 0. 00069 * If SORT = 'S', SDIM = number of eigenvalues for which 00070 * SELECT is true. 00071 * 00072 * W (output) COMPLEX array, dimension (N) 00073 * W contains the computed eigenvalues, in the same order that 00074 * they appear on the diagonal of the output Schur form T. 00075 * 00076 * VS (output) COMPLEX array, dimension (LDVS,N) 00077 * If JOBVS = 'V', VS contains the unitary matrix Z of Schur 00078 * vectors. 00079 * If JOBVS = 'N', VS is not referenced. 00080 * 00081 * LDVS (input) INTEGER 00082 * The leading dimension of the array VS. LDVS >= 1; if 00083 * JOBVS = 'V', LDVS >= N. 00084 * 00085 * WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) 00086 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00087 * 00088 * LWORK (input) INTEGER 00089 * The dimension of the array WORK. LWORK >= max(1,2*N). 00090 * For good performance, LWORK must generally be larger. 00091 * 00092 * If LWORK = -1, then a workspace query is assumed; the routine 00093 * only calculates the optimal size of the WORK array, returns 00094 * this value as the first entry of the WORK array, and no error 00095 * message related to LWORK is issued by XERBLA. 00096 * 00097 * RWORK (workspace) REAL array, dimension (N) 00098 * 00099 * BWORK (workspace) LOGICAL array, dimension (N) 00100 * Not referenced if SORT = 'N'. 00101 * 00102 * INFO (output) INTEGER 00103 * = 0: successful exit 00104 * < 0: if INFO = -i, the i-th argument had an illegal value. 00105 * > 0: if INFO = i, and i is 00106 * <= N: the QR algorithm failed to compute all the 00107 * eigenvalues; elements 1:ILO-1 and i+1:N of W 00108 * contain those eigenvalues which have converged; 00109 * if JOBVS = 'V', VS contains the matrix which 00110 * reduces A to its partially converged Schur form. 00111 * = N+1: the eigenvalues could not be reordered because 00112 * some eigenvalues were too close to separate (the 00113 * problem is very ill-conditioned); 00114 * = N+2: after reordering, roundoff changed values of 00115 * some complex eigenvalues so that leading 00116 * eigenvalues in the Schur form no longer satisfy 00117 * SELECT = .TRUE.. This could also be caused by 00118 * underflow due to scaling. 00119 * 00120 * ===================================================================== 00121 * 00122 * .. Parameters .. 00123 REAL ZERO, ONE 00124 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) 00125 * .. 00126 * .. Local Scalars .. 00127 LOGICAL LQUERY, SCALEA, WANTST, WANTVS 00128 INTEGER HSWORK, I, IBAL, ICOND, IERR, IEVAL, IHI, ILO, 00129 $ ITAU, IWRK, MAXWRK, MINWRK 00130 REAL ANRM, BIGNUM, CSCALE, EPS, S, SEP, SMLNUM 00131 * .. 00132 * .. Local Arrays .. 00133 REAL DUM( 1 ) 00134 * .. 00135 * .. External Subroutines .. 00136 EXTERNAL CCOPY, CGEBAK, CGEBAL, CGEHRD, CHSEQR, CLACPY, 00137 $ CLASCL, CTRSEN, CUNGHR, SLABAD, XERBLA 00138 * .. 00139 * .. External Functions .. 00140 LOGICAL LSAME 00141 INTEGER ILAENV 00142 REAL CLANGE, SLAMCH 00143 EXTERNAL LSAME, ILAENV, CLANGE, SLAMCH 00144 * .. 00145 * .. Intrinsic Functions .. 00146 INTRINSIC MAX, SQRT 00147 * .. 00148 * .. Executable Statements .. 00149 * 00150 * Test the input arguments 00151 * 00152 INFO = 0 00153 LQUERY = ( LWORK.EQ.-1 ) 00154 WANTVS = LSAME( JOBVS, 'V' ) 00155 WANTST = LSAME( SORT, 'S' ) 00156 IF( ( .NOT.WANTVS ) .AND. ( .NOT.LSAME( JOBVS, 'N' ) ) ) THEN 00157 INFO = -1 00158 ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN 00159 INFO = -2 00160 ELSE IF( N.LT.0 ) THEN 00161 INFO = -4 00162 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00163 INFO = -6 00164 ELSE IF( LDVS.LT.1 .OR. ( WANTVS .AND. LDVS.LT.N ) ) THEN 00165 INFO = -10 00166 END IF 00167 * 00168 * Compute workspace 00169 * (Note: Comments in the code beginning "Workspace:" describe the 00170 * minimal amount of workspace needed at that point in the code, 00171 * as well as the preferred amount for good performance. 00172 * CWorkspace refers to complex workspace, and RWorkspace to real 00173 * workspace. NB refers to the optimal block size for the 00174 * immediately following subroutine, as returned by ILAENV. 00175 * HSWORK refers to the workspace preferred by CHSEQR, as 00176 * calculated below. HSWORK is computed assuming ILO=1 and IHI=N, 00177 * the worst case.) 00178 * 00179 IF( INFO.EQ.0 ) THEN 00180 IF( N.EQ.0 ) THEN 00181 MINWRK = 1 00182 MAXWRK = 1 00183 ELSE 00184 MAXWRK = N + N*ILAENV( 1, 'CGEHRD', ' ', N, 1, N, 0 ) 00185 MINWRK = 2*N 00186 * 00187 CALL CHSEQR( 'S', JOBVS, N, 1, N, A, LDA, W, VS, LDVS, 00188 $ WORK, -1, IEVAL ) 00189 HSWORK = WORK( 1 ) 00190 * 00191 IF( .NOT.WANTVS ) THEN 00192 MAXWRK = MAX( MAXWRK, HSWORK ) 00193 ELSE 00194 MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'CUNGHR', 00195 $ ' ', N, 1, N, -1 ) ) 00196 MAXWRK = MAX( MAXWRK, HSWORK ) 00197 END IF 00198 END IF 00199 WORK( 1 ) = MAXWRK 00200 * 00201 IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN 00202 INFO = -12 00203 END IF 00204 END IF 00205 * 00206 IF( INFO.NE.0 ) THEN 00207 CALL XERBLA( 'CGEES ', -INFO ) 00208 RETURN 00209 ELSE IF( LQUERY ) THEN 00210 RETURN 00211 END IF 00212 * 00213 * Quick return if possible 00214 * 00215 IF( N.EQ.0 ) THEN 00216 SDIM = 0 00217 RETURN 00218 END IF 00219 * 00220 * Get machine constants 00221 * 00222 EPS = SLAMCH( 'P' ) 00223 SMLNUM = SLAMCH( 'S' ) 00224 BIGNUM = ONE / SMLNUM 00225 CALL SLABAD( SMLNUM, BIGNUM ) 00226 SMLNUM = SQRT( SMLNUM ) / EPS 00227 BIGNUM = ONE / SMLNUM 00228 * 00229 * Scale A if max element outside range [SMLNUM,BIGNUM] 00230 * 00231 ANRM = CLANGE( 'M', N, N, A, LDA, DUM ) 00232 SCALEA = .FALSE. 00233 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 00234 SCALEA = .TRUE. 00235 CSCALE = SMLNUM 00236 ELSE IF( ANRM.GT.BIGNUM ) THEN 00237 SCALEA = .TRUE. 00238 CSCALE = BIGNUM 00239 END IF 00240 IF( SCALEA ) 00241 $ CALL CLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR ) 00242 * 00243 * Permute the matrix to make it more nearly triangular 00244 * (CWorkspace: none) 00245 * (RWorkspace: need N) 00246 * 00247 IBAL = 1 00248 CALL CGEBAL( 'P', N, A, LDA, ILO, IHI, RWORK( IBAL ), IERR ) 00249 * 00250 * Reduce to upper Hessenberg form 00251 * (CWorkspace: need 2*N, prefer N+N*NB) 00252 * (RWorkspace: none) 00253 * 00254 ITAU = 1 00255 IWRK = N + ITAU 00256 CALL CGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ), 00257 $ LWORK-IWRK+1, IERR ) 00258 * 00259 IF( WANTVS ) THEN 00260 * 00261 * Copy Householder vectors to VS 00262 * 00263 CALL CLACPY( 'L', N, N, A, LDA, VS, LDVS ) 00264 * 00265 * Generate unitary matrix in VS 00266 * (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) 00267 * (RWorkspace: none) 00268 * 00269 CALL CUNGHR( N, ILO, IHI, VS, LDVS, WORK( ITAU ), WORK( IWRK ), 00270 $ LWORK-IWRK+1, IERR ) 00271 END IF 00272 * 00273 SDIM = 0 00274 * 00275 * Perform QR iteration, accumulating Schur vectors in VS if desired 00276 * (CWorkspace: need 1, prefer HSWORK (see comments) ) 00277 * (RWorkspace: none) 00278 * 00279 IWRK = ITAU 00280 CALL CHSEQR( 'S', JOBVS, N, ILO, IHI, A, LDA, W, VS, LDVS, 00281 $ WORK( IWRK ), LWORK-IWRK+1, IEVAL ) 00282 IF( IEVAL.GT.0 ) 00283 $ INFO = IEVAL 00284 * 00285 * Sort eigenvalues if desired 00286 * 00287 IF( WANTST .AND. INFO.EQ.0 ) THEN 00288 IF( SCALEA ) 00289 $ CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, N, 1, W, N, IERR ) 00290 DO 10 I = 1, N 00291 BWORK( I ) = SELECT( W( I ) ) 00292 10 CONTINUE 00293 * 00294 * Reorder eigenvalues and transform Schur vectors 00295 * (CWorkspace: none) 00296 * (RWorkspace: none) 00297 * 00298 CALL CTRSEN( 'N', JOBVS, BWORK, N, A, LDA, VS, LDVS, W, SDIM, 00299 $ S, SEP, WORK( IWRK ), LWORK-IWRK+1, ICOND ) 00300 END IF 00301 * 00302 IF( WANTVS ) THEN 00303 * 00304 * Undo balancing 00305 * (CWorkspace: none) 00306 * (RWorkspace: need N) 00307 * 00308 CALL CGEBAK( 'P', 'R', N, ILO, IHI, RWORK( IBAL ), N, VS, LDVS, 00309 $ IERR ) 00310 END IF 00311 * 00312 IF( SCALEA ) THEN 00313 * 00314 * Undo scaling for the Schur form of A 00315 * 00316 CALL CLASCL( 'U', 0, 0, CSCALE, ANRM, N, N, A, LDA, IERR ) 00317 CALL CCOPY( N, A, LDA+1, W, 1 ) 00318 END IF 00319 * 00320 WORK( 1 ) = MAXWRK 00321 RETURN 00322 * 00323 * End of CGEES 00324 * 00325 END
1.7.3 
