00001 /* chseqr.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 complex c_b1 = {0.f,0.f}; 00019 static complex c_b2 = {1.f,0.f}; 00020 static integer c__1 = 1; 00021 static integer c__12 = 12; 00022 static integer c__2 = 2; 00023 static integer c__49 = 49; 00024 00025 /* Subroutine */ int chseqr_(char *job, char *compz, integer *n, integer *ilo, 00026 integer *ihi, complex *h__, integer *ldh, complex *w, complex *z__, 00027 integer *ldz, complex *work, integer *lwork, integer *info) 00028 { 00029 /* System generated locals */ 00030 address a__1[2]; 00031 integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3[2]; 00032 real r__1, r__2, r__3; 00033 complex q__1; 00034 char ch__1[2]; 00035 00036 /* Builtin functions */ 00037 /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); 00038 00039 /* Local variables */ 00040 complex hl[2401] /* was [49][49] */; 00041 integer kbot, nmin; 00042 extern logical lsame_(char *, char *); 00043 extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 00044 complex *, integer *); 00045 logical initz; 00046 complex workl[49]; 00047 logical wantt, wantz; 00048 extern /* Subroutine */ int claqr0_(logical *, logical *, integer *, 00049 integer *, integer *, complex *, integer *, complex *, integer *, 00050 integer *, complex *, integer *, complex *, integer *, integer *), 00051 clahqr_(logical *, logical *, integer *, integer *, integer *, 00052 complex *, integer *, complex *, integer *, integer *, complex *, 00053 integer *, integer *), clacpy_(char *, integer *, integer *, 00054 complex *, integer *, complex *, integer *), claset_(char 00055 *, integer *, integer *, complex *, complex *, complex *, integer 00056 *), xerbla_(char *, integer *); 00057 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00058 integer *, integer *); 00059 logical lquery; 00060 00061 00062 /* -- LAPACK driver routine (version 3.2) -- */ 00063 /* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */ 00064 /* November 2006 */ 00065 00066 /* .. Scalar Arguments .. */ 00067 /* .. */ 00068 /* .. Array Arguments .. */ 00069 /* .. */ 00070 /* Purpose */ 00071 /* ======= */ 00072 00073 /* CHSEQR computes the eigenvalues of a Hessenberg matrix H */ 00074 /* and, optionally, the matrices T and Z from the Schur decomposition */ 00075 /* H = Z T Z**H, where T is an upper triangular matrix (the */ 00076 /* Schur form), and Z is the unitary matrix of Schur vectors. */ 00077 00078 /* Optionally Z may be postmultiplied into an input unitary */ 00079 /* matrix Q so that this routine can give the Schur factorization */ 00080 /* of a matrix A which has been reduced to the Hessenberg form H */ 00081 /* by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H. */ 00082 00083 /* Arguments */ 00084 /* ========= */ 00085 00086 /* JOB (input) CHARACTER*1 */ 00087 /* = 'E': compute eigenvalues only; */ 00088 /* = 'S': compute eigenvalues and the Schur form T. */ 00089 00090 /* COMPZ (input) CHARACTER*1 */ 00091 /* = 'N': no Schur vectors are computed; */ 00092 /* = 'I': Z is initialized to the unit matrix and the matrix Z */ 00093 /* of Schur vectors of H is returned; */ 00094 /* = 'V': Z must contain an unitary matrix Q on entry, and */ 00095 /* the product Q*Z is returned. */ 00096 00097 /* N (input) INTEGER */ 00098 /* The order of the matrix H. N .GE. 0. */ 00099 00100 /* ILO (input) INTEGER */ 00101 /* IHI (input) INTEGER */ 00102 /* It is assumed that H is already upper triangular in rows */ 00103 /* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */ 00104 /* set by a previous call to CGEBAL, and then passed to CGEHRD */ 00105 /* when the matrix output by CGEBAL is reduced to Hessenberg */ 00106 /* form. Otherwise ILO and IHI should be set to 1 and N */ 00107 /* respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N. */ 00108 /* If N = 0, then ILO = 1 and IHI = 0. */ 00109 00110 /* H (input/output) COMPLEX array, dimension (LDH,N) */ 00111 /* On entry, the upper Hessenberg matrix H. */ 00112 /* On exit, if INFO = 0 and JOB = 'S', H contains the upper */ 00113 /* triangular matrix T from the Schur decomposition (the */ 00114 /* Schur form). If INFO = 0 and JOB = 'E', the contents of */ 00115 /* H are unspecified on exit. (The output value of H when */ 00116 /* INFO.GT.0 is given under the description of INFO below.) */ 00117 00118 /* Unlike earlier versions of CHSEQR, this subroutine may */ 00119 /* explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 */ 00120 /* or j = IHI+1, IHI+2, ... N. */ 00121 00122 /* LDH (input) INTEGER */ 00123 /* The leading dimension of the array H. LDH .GE. max(1,N). */ 00124 00125 /* W (output) COMPLEX array, dimension (N) */ 00126 /* The computed eigenvalues. If JOB = 'S', the eigenvalues are */ 00127 /* stored in the same order as on the diagonal of the Schur */ 00128 /* form returned in H, with W(i) = H(i,i). */ 00129 00130 /* Z (input/output) COMPLEX array, dimension (LDZ,N) */ 00131 /* If COMPZ = 'N', Z is not referenced. */ 00132 /* If COMPZ = 'I', on entry Z need not be set and on exit, */ 00133 /* if INFO = 0, Z contains the unitary matrix Z of the Schur */ 00134 /* vectors of H. If COMPZ = 'V', on entry Z must contain an */ 00135 /* N-by-N matrix Q, which is assumed to be equal to the unit */ 00136 /* matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, */ 00137 /* if INFO = 0, Z contains Q*Z. */ 00138 /* Normally Q is the unitary matrix generated by CUNGHR */ 00139 /* after the call to CGEHRD which formed the Hessenberg matrix */ 00140 /* H. (The output value of Z when INFO.GT.0 is given under */ 00141 /* the description of INFO below.) */ 00142 00143 /* LDZ (input) INTEGER */ 00144 /* The leading dimension of the array Z. if COMPZ = 'I' or */ 00145 /* COMPZ = 'V', then LDZ.GE.MAX(1,N). Otherwize, LDZ.GE.1. */ 00146 00147 /* WORK (workspace/output) COMPLEX array, dimension (LWORK) */ 00148 /* On exit, if INFO = 0, WORK(1) returns an estimate of */ 00149 /* the optimal value for LWORK. */ 00150 00151 /* LWORK (input) INTEGER */ 00152 /* The dimension of the array WORK. LWORK .GE. max(1,N) */ 00153 /* is sufficient and delivers very good and sometimes */ 00154 /* optimal performance. However, LWORK as large as 11*N */ 00155 /* may be required for optimal performance. A workspace */ 00156 /* query is recommended to determine the optimal workspace */ 00157 /* size. */ 00158 00159 /* If LWORK = -1, then CHSEQR does a workspace query. */ 00160 /* In this case, CHSEQR checks the input parameters and */ 00161 /* estimates the optimal workspace size for the given */ 00162 /* values of N, ILO and IHI. The estimate is returned */ 00163 /* in WORK(1). No error message related to LWORK is */ 00164 /* issued by XERBLA. Neither H nor Z are accessed. */ 00165 00166 00167 /* INFO (output) INTEGER */ 00168 /* = 0: successful exit */ 00169 /* .LT. 0: if INFO = -i, the i-th argument had an illegal */ 00170 /* value */ 00171 /* .GT. 0: if INFO = i, CHSEQR failed to compute all of */ 00172 /* the eigenvalues. Elements 1:ilo-1 and i+1:n of WR */ 00173 /* and WI contain those eigenvalues which have been */ 00174 /* successfully computed. (Failures are rare.) */ 00175 00176 /* If INFO .GT. 0 and JOB = 'E', then on exit, the */ 00177 /* remaining unconverged eigenvalues are the eigen- */ 00178 /* values of the upper Hessenberg matrix rows and */ 00179 /* columns ILO through INFO of the final, output */ 00180 /* value of H. */ 00181 00182 /* If INFO .GT. 0 and JOB = 'S', then on exit */ 00183 00184 /* (*) (initial value of H)*U = U*(final value of H) */ 00185 00186 /* where U is a unitary matrix. The final */ 00187 /* value of H is upper Hessenberg and triangular in */ 00188 /* rows and columns INFO+1 through IHI. */ 00189 00190 /* If INFO .GT. 0 and COMPZ = 'V', then on exit */ 00191 00192 /* (final value of Z) = (initial value of Z)*U */ 00193 00194 /* where U is the unitary matrix in (*) (regard- */ 00195 /* less of the value of JOB.) */ 00196 00197 /* If INFO .GT. 0 and COMPZ = 'I', then on exit */ 00198 /* (final value of Z) = U */ 00199 /* where U is the unitary matrix in (*) (regard- */ 00200 /* less of the value of JOB.) */ 00201 00202 /* If INFO .GT. 0 and COMPZ = 'N', then Z is not */ 00203 /* accessed. */ 00204 00205 /* ================================================================ */ 00206 /* Default values supplied by */ 00207 /* ILAENV(ISPEC,'CHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK). */ 00208 /* It is suggested that these defaults be adjusted in order */ 00209 /* to attain best performance in each particular */ 00210 /* computational environment. */ 00211 00212 /* ISPEC=12: The CLAHQR vs CLAQR0 crossover point. */ 00213 /* Default: 75. (Must be at least 11.) */ 00214 00215 /* ISPEC=13: Recommended deflation window size. */ 00216 /* This depends on ILO, IHI and NS. NS is the */ 00217 /* number of simultaneous shifts returned */ 00218 /* by ILAENV(ISPEC=15). (See ISPEC=15 below.) */ 00219 /* The default for (IHI-ILO+1).LE.500 is NS. */ 00220 /* The default for (IHI-ILO+1).GT.500 is 3*NS/2. */ 00221 00222 /* ISPEC=14: Nibble crossover point. (See IPARMQ for */ 00223 /* details.) Default: 14% of deflation window */ 00224 /* size. */ 00225 00226 /* ISPEC=15: Number of simultaneous shifts in a multishift */ 00227 /* QR iteration. */ 00228 00229 /* If IHI-ILO+1 is ... */ 00230 00231 /* greater than ...but less ... the */ 00232 /* or equal to ... than default is */ 00233 00234 /* 1 30 NS = 2(+) */ 00235 /* 30 60 NS = 4(+) */ 00236 /* 60 150 NS = 10(+) */ 00237 /* 150 590 NS = ** */ 00238 /* 590 3000 NS = 64 */ 00239 /* 3000 6000 NS = 128 */ 00240 /* 6000 infinity NS = 256 */ 00241 00242 /* (+) By default some or all matrices of this order */ 00243 /* are passed to the implicit double shift routine */ 00244 /* CLAHQR and this parameter is ignored. See */ 00245 /* ISPEC=12 above and comments in IPARMQ for */ 00246 /* details. */ 00247 00248 /* (**) The asterisks (**) indicate an ad-hoc */ 00249 /* function of N increasing from 10 to 64. */ 00250 00251 /* ISPEC=16: Select structured matrix multiply. */ 00252 /* If the number of simultaneous shifts (specified */ 00253 /* by ISPEC=15) is less than 14, then the default */ 00254 /* for ISPEC=16 is 0. Otherwise the default for */ 00255 /* ISPEC=16 is 2. */ 00256 00257 /* ================================================================ */ 00258 /* Based on contributions by */ 00259 /* Karen Braman and Ralph Byers, Department of Mathematics, */ 00260 /* University of Kansas, USA */ 00261 00262 /* ================================================================ */ 00263 /* References: */ 00264 /* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */ 00265 /* Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */ 00266 /* Performance, SIAM Journal of Matrix Analysis, volume 23, pages */ 00267 /* 929--947, 2002. */ 00268 00269 /* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */ 00270 /* Algorithm Part II: Aggressive Early Deflation, SIAM Journal */ 00271 /* of Matrix Analysis, volume 23, pages 948--973, 2002. */ 00272 00273 /* ================================================================ */ 00274 /* .. Parameters .. */ 00275 00276 /* ==== Matrices of order NTINY or smaller must be processed by */ 00277 /* . CLAHQR because of insufficient subdiagonal scratch space. */ 00278 /* . (This is a hard limit.) ==== */ 00279 00280 /* ==== NL allocates some local workspace to help small matrices */ 00281 /* . through a rare CLAHQR failure. NL .GT. NTINY = 11 is */ 00282 /* . required and NL .LE. NMIN = ILAENV(ISPEC=12,...) is recom- */ 00283 /* . mended. (The default value of NMIN is 75.) Using NL = 49 */ 00284 /* . allows up to six simultaneous shifts and a 16-by-16 */ 00285 /* . deflation window. ==== */ 00286 /* .. */ 00287 /* .. Local Arrays .. */ 00288 /* .. */ 00289 /* .. Local Scalars .. */ 00290 /* .. */ 00291 /* .. External Functions .. */ 00292 /* .. */ 00293 /* .. External Subroutines .. */ 00294 /* .. */ 00295 /* .. Intrinsic Functions .. */ 00296 /* .. */ 00297 /* .. Executable Statements .. */ 00298 00299 /* ==== Decode and check the input parameters. ==== */ 00300 00301 /* Parameter adjustments */ 00302 h_dim1 = *ldh; 00303 h_offset = 1 + h_dim1; 00304 h__ -= h_offset; 00305 --w; 00306 z_dim1 = *ldz; 00307 z_offset = 1 + z_dim1; 00308 z__ -= z_offset; 00309 --work; 00310 00311 /* Function Body */ 00312 wantt = lsame_(job, "S"); 00313 initz = lsame_(compz, "I"); 00314 wantz = initz || lsame_(compz, "V"); 00315 r__1 = (real) max(1,*n); 00316 q__1.r = r__1, q__1.i = 0.f; 00317 work[1].r = q__1.r, work[1].i = q__1.i; 00318 lquery = *lwork == -1; 00319 00320 *info = 0; 00321 if (! lsame_(job, "E") && ! wantt) { 00322 *info = -1; 00323 } else if (! lsame_(compz, "N") && ! wantz) { 00324 *info = -2; 00325 } else if (*n < 0) { 00326 *info = -3; 00327 } else if (*ilo < 1 || *ilo > max(1,*n)) { 00328 *info = -4; 00329 } else if (*ihi < min(*ilo,*n) || *ihi > *n) { 00330 *info = -5; 00331 } else if (*ldh < max(1,*n)) { 00332 *info = -7; 00333 } else if (*ldz < 1 || wantz && *ldz < max(1,*n)) { 00334 *info = -10; 00335 } else if (*lwork < max(1,*n) && ! lquery) { 00336 *info = -12; 00337 } 00338 00339 if (*info != 0) { 00340 00341 /* ==== Quick return in case of invalid argument. ==== */ 00342 00343 i__1 = -(*info); 00344 xerbla_("CHSEQR", &i__1); 00345 return 0; 00346 00347 } else if (*n == 0) { 00348 00349 /* ==== Quick return in case N = 0; nothing to do. ==== */ 00350 00351 return 0; 00352 00353 } else if (lquery) { 00354 00355 /* ==== Quick return in case of a workspace query ==== */ 00356 00357 claqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &w[1], ilo, 00358 ihi, &z__[z_offset], ldz, &work[1], lwork, info); 00359 /* ==== Ensure reported workspace size is backward-compatible with */ 00360 /* . previous LAPACK versions. ==== */ 00361 /* Computing MAX */ 00362 r__2 = work[1].r, r__3 = (real) max(1,*n); 00363 r__1 = dmax(r__2,r__3); 00364 q__1.r = r__1, q__1.i = 0.f; 00365 work[1].r = q__1.r, work[1].i = q__1.i; 00366 return 0; 00367 00368 } else { 00369 00370 /* ==== copy eigenvalues isolated by CGEBAL ==== */ 00371 00372 if (*ilo > 1) { 00373 i__1 = *ilo - 1; 00374 i__2 = *ldh + 1; 00375 ccopy_(&i__1, &h__[h_offset], &i__2, &w[1], &c__1); 00376 } 00377 if (*ihi < *n) { 00378 i__1 = *n - *ihi; 00379 i__2 = *ldh + 1; 00380 ccopy_(&i__1, &h__[*ihi + 1 + (*ihi + 1) * h_dim1], &i__2, &w[* 00381 ihi + 1], &c__1); 00382 } 00383 00384 /* ==== Initialize Z, if requested ==== */ 00385 00386 if (initz) { 00387 claset_("A", n, n, &c_b1, &c_b2, &z__[z_offset], ldz); 00388 } 00389 00390 /* ==== Quick return if possible ==== */ 00391 00392 if (*ilo == *ihi) { 00393 i__1 = *ilo; 00394 i__2 = *ilo + *ilo * h_dim1; 00395 w[i__1].r = h__[i__2].r, w[i__1].i = h__[i__2].i; 00396 return 0; 00397 } 00398 00399 /* ==== CLAHQR/CLAQR0 crossover point ==== */ 00400 00401 /* Writing concatenation */ 00402 i__3[0] = 1, a__1[0] = job; 00403 i__3[1] = 1, a__1[1] = compz; 00404 s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); 00405 nmin = ilaenv_(&c__12, "CHSEQR", ch__1, n, ilo, ihi, lwork); 00406 nmin = max(11,nmin); 00407 00408 /* ==== CLAQR0 for big matrices; CLAHQR for small ones ==== */ 00409 00410 if (*n > nmin) { 00411 claqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &w[1], 00412 ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info); 00413 } else { 00414 00415 /* ==== Small matrix ==== */ 00416 00417 clahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &w[1], 00418 ilo, ihi, &z__[z_offset], ldz, info); 00419 00420 if (*info > 0) { 00421 00422 /* ==== A rare CLAHQR failure! CLAQR0 sometimes succeeds */ 00423 /* . when CLAHQR fails. ==== */ 00424 00425 kbot = *info; 00426 00427 if (*n >= 49) { 00428 00429 /* ==== Larger matrices have enough subdiagonal scratch */ 00430 /* . space to call CLAQR0 directly. ==== */ 00431 00432 claqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset], 00433 ldh, &w[1], ilo, ihi, &z__[z_offset], ldz, &work[ 00434 1], lwork, info); 00435 00436 } else { 00437 00438 /* ==== Tiny matrices don't have enough subdiagonal */ 00439 /* . scratch space to benefit from CLAQR0. Hence, */ 00440 /* . tiny matrices must be copied into a larger */ 00441 /* . array before calling CLAQR0. ==== */ 00442 00443 clacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49); 00444 i__1 = *n + 1 + *n * 49 - 50; 00445 hl[i__1].r = 0.f, hl[i__1].i = 0.f; 00446 i__1 = 49 - *n; 00447 claset_("A", &c__49, &i__1, &c_b1, &c_b1, &hl[(*n + 1) * 00448 49 - 49], &c__49); 00449 claqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, & 00450 w[1], ilo, ihi, &z__[z_offset], ldz, workl, & 00451 c__49, info); 00452 if (wantt || *info != 0) { 00453 clacpy_("A", n, n, hl, &c__49, &h__[h_offset], ldh); 00454 } 00455 } 00456 } 00457 } 00458 00459 /* ==== Clear out the trash, if necessary. ==== */ 00460 00461 if ((wantt || *info != 0) && *n > 2) { 00462 i__1 = *n - 2; 00463 i__2 = *n - 2; 00464 claset_("L", &i__1, &i__2, &c_b1, &c_b1, &h__[h_dim1 + 3], ldh); 00465 } 00466 00467 /* ==== Ensure reported workspace size is backward-compatible with */ 00468 /* . previous LAPACK versions. ==== */ 00469 00470 /* Computing MAX */ 00471 r__2 = (real) max(1,*n), r__3 = work[1].r; 00472 r__1 = dmax(r__2,r__3); 00473 q__1.r = r__1, q__1.i = 0.f; 00474 work[1].r = q__1.r, work[1].i = q__1.i; 00475 } 00476 00477 /* ==== End of CHSEQR ==== */ 00478 00479 return 0; 00480 } /* chseqr_ */