14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static integer c__1 = 1;
516 static integer c_n1 = -1;
517 static doublecomplex c_b14 = {1.,0.};
518 static doublecomplex c_b15 = {0.,0.};
519 static doublecomplex c_b23 = {-1.,0.};
521 /* > \brief \b ZHETRF_AA_2STAGE */
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
529 /* > Download ZHETRF_AA_2STAGE + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrf_
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetrf_
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrf_
544 /* SUBROUTINE ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, */
545 /* IPIV2, WORK, LWORK, INFO ) */
548 /* INTEGER N, LDA, LTB, LWORK, INFO */
549 /* INTEGER IPIV( * ), IPIV2( * ) */
550 /* COMPLEX*16 A( LDA, * ), TB( * ), WORK( * ) */
552 /* > \par Purpose: */
557 /* > ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A */
558 /* > using the Aasen's algorithm. The form of the factorization is */
560 /* > A = U**H*T*U or A = L*T*L**H */
562 /* > where U (or L) is a product of permutation and unit upper (lower) */
563 /* > triangular matrices, and T is a hermitian band matrix with the */
564 /* > bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is */
565 /* > LU factorized with partial pivoting). */
567 /* > This is the blocked version of the algorithm, calling Level 3 BLAS. */
573 /* > \param[in] UPLO */
575 /* > UPLO is CHARACTER*1 */
576 /* > = 'U': Upper triangle of A is stored; */
577 /* > = 'L': Lower triangle of A is stored. */
583 /* > The order of the matrix A. N >= 0. */
586 /* > \param[in,out] A */
588 /* > A is COMPLEX*16 array, dimension (LDA,N) */
589 /* > On entry, the hermitian matrix A. If UPLO = 'U', the leading */
590 /* > N-by-N upper triangular part of A contains the upper */
591 /* > triangular part of the matrix A, and the strictly lower */
592 /* > triangular part of A is not referenced. If UPLO = 'L', the */
593 /* > leading N-by-N lower triangular part of A contains the lower */
594 /* > triangular part of the matrix A, and the strictly upper */
595 /* > triangular part of A is not referenced. */
597 /* > On exit, L is stored below (or above) the subdiaonal blocks, */
598 /* > when UPLO is 'L' (or 'U'). */
601 /* > \param[in] LDA */
603 /* > LDA is INTEGER */
604 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
607 /* > \param[out] TB */
609 /* > TB is COMPLEX*16 array, dimension (LTB) */
610 /* > On exit, details of the LU factorization of the band matrix. */
613 /* > \param[in] LTB */
615 /* > LTB is INTEGER */
616 /* > The size of the array TB. LTB >= 4*N, internally */
617 /* > used to select NB such that LTB >= (3*NB+1)*N. */
619 /* > If LTB = -1, then a workspace query is assumed; the */
620 /* > routine only calculates the optimal size of LTB, */
621 /* > returns this value as the first entry of TB, and */
622 /* > no error message related to LTB is issued by XERBLA. */
625 /* > \param[out] IPIV */
627 /* > IPIV is INTEGER array, dimension (N) */
628 /* > On exit, it contains the details of the interchanges, i.e., */
629 /* > the row and column k of A were interchanged with the */
630 /* > row and column IPIV(k). */
633 /* > \param[out] IPIV2 */
635 /* > IPIV2 is INTEGER array, dimension (N) */
636 /* > On exit, it contains the details of the interchanges, i.e., */
637 /* > the row and column k of T were interchanged with the */
638 /* > row and column IPIV(k). */
641 /* > \param[out] WORK */
643 /* > WORK is COMPLEX*16 workspace of size LWORK */
646 /* > \param[in] LWORK */
648 /* > LWORK is INTEGER */
649 /* > The size of WORK. LWORK >= N, internally used to select NB */
650 /* > such that LWORK >= N*NB. */
652 /* > If LWORK = -1, then a workspace query is assumed; the */
653 /* > routine only calculates the optimal size of the WORK array, */
654 /* > returns this value as the first entry of the WORK array, and */
655 /* > no error message related to LWORK is issued by XERBLA. */
658 /* > \param[out] INFO */
660 /* > INFO is INTEGER */
661 /* > = 0: successful exit */
662 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
663 /* > > 0: if INFO = i, band LU factorization failed on i-th column */
669 /* > \author Univ. of Tennessee */
670 /* > \author Univ. of California Berkeley */
671 /* > \author Univ. of Colorado Denver */
672 /* > \author NAG Ltd. */
674 /* > \date November 2017 */
676 /* > \ingroup complex16SYcomputational */
678 /* ===================================================================== */
679 /* Subroutine */ int zhetrf_aa_2stage_(char *uplo, integer *n, doublecomplex
680 *a, integer *lda, doublecomplex *tb, integer *ltb, integer *ipiv,
681 integer *ipiv2, doublecomplex *work, integer *lwork, integer *info)
683 /* System generated locals */
684 integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
688 /* Local variables */
689 integer ldtb, i__, j, k;
690 extern logical lsame_(char *, char *);
692 extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
693 integer *, doublecomplex *, doublecomplex *, integer *,
694 doublecomplex *, integer *, doublecomplex *, doublecomplex *,
699 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
700 doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
701 integer *, doublecomplex *, integer *), ztrsm_(char *, char *,
702 char *, char *, integer *, integer *, doublecomplex *,
703 doublecomplex *, integer *, doublecomplex *, integer *);
704 integer jb, kb, nb, td, nt;
705 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
706 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
707 integer *, integer *, ftnlen, ftnlen);
708 extern /* Subroutine */ int zlacgv_(integer *, doublecomplex *, integer *)
709 , zgbtrf_(integer *, integer *, integer *, integer *,
710 doublecomplex *, integer *, integer *, integer *), zgetrf_(
711 integer *, integer *, doublecomplex *, integer *, integer *,
712 integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
713 integer *, doublecomplex *, integer *), zlaset_(char *,
714 integer *, integer *, doublecomplex *, doublecomplex *,
715 doublecomplex *, integer *), zhegst_(integer *, char *,
716 integer *, doublecomplex *, integer *, doublecomplex *, integer *,
718 logical tquery, wquery;
722 /* -- LAPACK computational routine (version 3.8.0) -- */
723 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
724 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
729 /* ===================================================================== */
732 /* Test the input parameters. */
734 /* Parameter adjustments */
736 a_offset = 1 + a_dim1 * 1;
745 upper = lsame_(uplo, "U");
746 wquery = *lwork == -1;
748 if (! upper && ! lsame_(uplo, "L")) {
752 } else if (*lda < f2cmax(1,*n)) {
754 } else if (*ltb < *n << 2 && ! tquery) {
756 } else if (*lwork < *n && ! wquery) {
762 xerbla_("ZHETRF_AA_2STAGE", &i__1, (ftnlen)16);
766 /* Answer the query */
768 nb = ilaenv_(&c__1, "ZHETRF_AA_2STAGE", uplo, n, &c_n1, &c_n1, &c_n1, (
769 ftnlen)16, (ftnlen)1);
772 i__1 = (nb * 3 + 1) * *n;
773 tb[1].r = (doublereal) i__1, tb[1].i = 0.;
777 work[1].r = (doublereal) i__1, work[1].i = 0.;
780 if (tquery || wquery) {
790 /* Determine the number of the block size */
793 if (ldtb < nb * 3 + 1) {
796 if (*lwork < nb * *n) {
800 /* Determine the number of the block columns */
802 nt = (*n + nb - 1) / nb;
806 /* Initialize vectors/matrices */
809 for (j = 1; j <= i__1; ++j) {
815 tb[1].r = (doublereal) nb, tb[1].i = 0.;
819 /* ..................................................... */
820 /* Factorize A as U**H*D*U using the upper triangle of A */
821 /* ..................................................... */
824 for (j = 0; j <= i__1; ++j) {
826 /* Generate Jth column of W and H */
829 i__2 = nb, i__3 = *n - j * nb;
830 kb = f2cmin(i__2,i__3);
832 for (i__ = 1; i__ <= i__2; ++i__) {
834 /* H(I,J) = T(I,I)*U(I,J) + T(I+1,I)*U(I+1,J) */
841 zgemm_("NoTranspose", "NoTranspose", &nb, &kb, &jb, &
842 c_b14, &tb[td + 1 + i__ * nb * ldtb], &i__3, &a[(
843 i__ - 1) * nb + 1 + (j * nb + 1) * a_dim1], lda, &
844 c_b15, &work[i__ * nb + 1], n);
846 /* H(I,J) = T(I,I-1)*U(I-1,J) + T(I,I)*U(I,J) + T(I,I+1)*U(I+1,J) */
853 zgemm_("NoTranspose", "NoTranspose", &nb, &kb, &jb, &
854 c_b14, &tb[td + nb + 1 + (i__ - 1) * nb * ldtb], &
855 i__3, &a[(i__ - 2) * nb + 1 + (j * nb + 1) *
856 a_dim1], lda, &c_b15, &work[i__ * nb + 1], n);
863 zlacpy_("Upper", &kb, &kb, &a[j * nb + 1 + (j * nb + 1) * a_dim1],
864 lda, &tb[td + 1 + j * nb * ldtb], &i__2);
866 /* T(J,J) = U(1:J,J)'*H(1:J) */
869 zgemm_("Conjugate transpose", "NoTranspose", &kb, &kb, &i__2,
870 &c_b23, &a[(j * nb + 1) * a_dim1 + 1], lda, &work[nb
871 + 1], n, &c_b14, &tb[td + 1 + j * nb * ldtb], &i__3);
872 /* T(J,J) += U(J,J)'*T(J,J-1)*U(J-1,J) */
874 zgemm_("Conjugate transpose", "NoTranspose", &kb, &nb, &kb, &
875 c_b14, &a[(j - 1) * nb + 1 + (j * nb + 1) * a_dim1],
876 lda, &tb[td + nb + 1 + (j - 1) * nb * ldtb], &i__2, &
879 zgemm_("NoTranspose", "NoTranspose", &kb, &kb, &nb, &c_b23, &
880 work[1], n, &a[(j - 2) * nb + 1 + (j * nb + 1) *
881 a_dim1], lda, &c_b14, &tb[td + 1 + j * nb * ldtb], &
886 zhegst_(&c__1, "Upper", &kb, &tb[td + 1 + j * nb * ldtb], &
887 i__2, &a[(j - 1) * nb + 1 + (j * nb + 1) * a_dim1],
891 /* Expand T(J,J) into full format */
894 for (i__ = 1; i__ <= i__2; ++i__) {
895 i__3 = td + 1 + (j * nb + i__ - 1) * ldtb;
896 i__4 = td + 1 + (j * nb + i__ - 1) * ldtb;
898 tb[i__3].r = d__1, tb[i__3].i = 0.;
900 for (k = i__ + 1; k <= i__3; ++k) {
901 i__4 = td + (k - i__) + 1 + (j * nb + i__ - 1) * ldtb;
902 d_cnjg(&z__1, &tb[td - (k - (i__ + 1)) + (j * nb + k - 1)
904 tb[i__4].r = z__1.r, tb[i__4].i = z__1.i;
915 zgemm_("NoTranspose", "NoTranspose", &kb, &kb, &kb, &
916 c_b14, &tb[td + 1 + j * nb * ldtb], &i__2, &a[
917 (j - 1) * nb + 1 + (j * nb + 1) * a_dim1],
918 lda, &c_b15, &work[j * nb + 1], n);
922 zgemm_("NoTranspose", "NoTranspose", &kb, &kb, &i__2,
923 &c_b14, &tb[td + nb + 1 + (j - 1) * nb * ldtb]
924 , &i__3, &a[(j - 2) * nb + 1 + (j * nb + 1) *
925 a_dim1], lda, &c_b15, &work[j * nb + 1], n);
928 /* Update with the previous column */
930 i__2 = *n - (j + 1) * nb;
932 zgemm_("Conjugate transpose", "NoTranspose", &nb, &i__2, &
933 i__3, &c_b23, &work[nb + 1], n, &a[((j + 1) * nb
934 + 1) * a_dim1 + 1], lda, &c_b14, &a[j * nb + 1 + (
935 (j + 1) * nb + 1) * a_dim1], lda);
938 /* Copy panel to workspace to call ZGETRF */
941 for (k = 1; k <= i__2; ++k) {
942 i__3 = *n - (j + 1) * nb;
943 zcopy_(&i__3, &a[j * nb + k + ((j + 1) * nb + 1) * a_dim1]
944 , lda, &work[(k - 1) * *n + 1], &c__1);
947 /* Factorize panel */
949 i__2 = *n - (j + 1) * nb;
950 zgetrf_(&i__2, &nb, &work[1], n, &ipiv[(j + 1) * nb + 1], &
952 /* IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN */
953 /* INFO = IINFO+(J+1)*NB */
956 /* Copy panel back */
959 for (k = 1; k <= i__2; ++k) {
961 /* Copy only L-factor */
963 i__3 = *n - k - (j + 1) * nb;
964 zcopy_(&i__3, &work[k + 1 + (k - 1) * *n], &c__1, &a[j *
965 nb + k + ((j + 1) * nb + k + 1) * a_dim1], lda);
967 /* Transpose U-factor to be copied back into T(J+1, J) */
969 zlacgv_(&k, &work[(k - 1) * *n + 1], &c__1);
972 /* Compute T(J+1, J), zero out for GEMM update */
975 i__2 = nb, i__3 = *n - (j + 1) * nb;
976 kb = f2cmin(i__2,i__3);
978 zlaset_("Full", &kb, &nb, &c_b15, &c_b15, &tb[td + nb + 1 + j
979 * nb * ldtb], &i__2);
981 zlacpy_("Upper", &kb, &nb, &work[1], n, &tb[td + nb + 1 + j *
985 ztrsm_("R", "U", "N", "U", &kb, &nb, &c_b14, &a[(j - 1) *
986 nb + 1 + (j * nb + 1) * a_dim1], lda, &tb[td + nb
987 + 1 + j * nb * ldtb], &i__2);
990 /* Copy T(J,J+1) into T(J+1, J), both upper/lower for GEMM */
994 for (k = 1; k <= i__2; ++k) {
996 for (i__ = 1; i__ <= i__3; ++i__) {
997 i__4 = td - nb + k - i__ + 1 + (j * nb + nb + i__ - 1)
999 d_cnjg(&z__1, &tb[td + nb + i__ - k + 1 + (j * nb + k
1001 tb[i__4].r = z__1.r, tb[i__4].i = z__1.i;
1004 zlaset_("Lower", &kb, &nb, &c_b15, &c_b14, &a[j * nb + 1 + ((
1005 j + 1) * nb + 1) * a_dim1], lda);
1007 /* Apply pivots to trailing submatrix of A */
1010 for (k = 1; k <= i__2; ++k) {
1012 ipiv[(j + 1) * nb + k] += (j + 1) * nb;
1014 i1 = (j + 1) * nb + k;
1015 i2 = ipiv[(j + 1) * nb + k];
1017 /* > Apply pivots to previous columns of L */
1019 zswap_(&i__3, &a[(j + 1) * nb + 1 + i1 * a_dim1], &
1020 c__1, &a[(j + 1) * nb + 1 + i2 * a_dim1], &
1022 /* > Swap A(I1+1:M, I1) with A(I2, I1+1:M) */
1025 zswap_(&i__3, &a[i1 + (i1 + 1) * a_dim1], lda, &a[
1026 i1 + 1 + i2 * a_dim1], &c__1);
1028 zlacgv_(&i__3, &a[i1 + 1 + i2 * a_dim1], &c__1);
1031 zlacgv_(&i__3, &a[i1 + (i1 + 1) * a_dim1], lda);
1032 /* > Swap A(I2+1:M, I1) with A(I2+1:M, I2) */
1035 zswap_(&i__3, &a[i1 + (i2 + 1) * a_dim1], lda, &a[
1036 i2 + (i2 + 1) * a_dim1], lda);
1038 /* > Swap A(I1, I1) with A(I2, I2) */
1039 i__3 = i1 + i1 * a_dim1;
1040 piv.r = a[i__3].r, piv.i = a[i__3].i;
1041 i__3 = i1 + i1 * a_dim1;
1042 i__4 = i2 + i2 * a_dim1;
1043 a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
1044 i__3 = i2 + i2 * a_dim1;
1045 a[i__3].r = piv.r, a[i__3].i = piv.i;
1046 /* > Apply pivots to previous columns of L */
1049 zswap_(&i__3, &a[i1 * a_dim1 + 1], &c__1, &a[i2 *
1050 a_dim1 + 1], &c__1);
1058 /* ..................................................... */
1059 /* Factorize A as L*D*L**H using the lower triangle of A */
1060 /* ..................................................... */
1063 for (j = 0; j <= i__1; ++j) {
1065 /* Generate Jth column of W and H */
1068 i__2 = nb, i__3 = *n - j * nb;
1069 kb = f2cmin(i__2,i__3);
1071 for (i__ = 1; i__ <= i__2; ++i__) {
1073 /* H(I,J) = T(I,I)*L(J,I)' + T(I+1,I)'*L(J,I+1)' */
1080 zgemm_("NoTranspose", "Conjugate transpose", &nb, &kb, &
1081 jb, &c_b14, &tb[td + 1 + i__ * nb * ldtb], &i__3,
1082 &a[j * nb + 1 + ((i__ - 1) * nb + 1) * a_dim1],
1083 lda, &c_b15, &work[i__ * nb + 1], n);
1085 /* H(I,J) = T(I,I-1)*L(J,I-1)' + T(I,I)*L(J,I)' + T(I,I+1)*L(J,I+1)' */
1087 jb = (nb << 1) + kb;
1092 zgemm_("NoTranspose", "Conjugate transpose", &nb, &kb, &
1093 jb, &c_b14, &tb[td + nb + 1 + (i__ - 1) * nb *
1094 ldtb], &i__3, &a[j * nb + 1 + ((i__ - 2) * nb + 1)
1095 * a_dim1], lda, &c_b15, &work[i__ * nb + 1], n);
1099 /* Compute T(J,J) */
1102 zlacpy_("Lower", &kb, &kb, &a[j * nb + 1 + (j * nb + 1) * a_dim1],
1103 lda, &tb[td + 1 + j * nb * ldtb], &i__2);
1105 /* T(J,J) = L(J,1:J)*H(1:J) */
1106 i__2 = (j - 1) * nb;
1108 zgemm_("NoTranspose", "NoTranspose", &kb, &kb, &i__2, &c_b23,
1109 &a[j * nb + 1 + a_dim1], lda, &work[nb + 1], n, &
1110 c_b14, &tb[td + 1 + j * nb * ldtb], &i__3);
1111 /* T(J,J) += L(J,J)*T(J,J-1)*L(J,J-1)' */
1113 zgemm_("NoTranspose", "NoTranspose", &kb, &nb, &kb, &c_b14, &
1114 a[j * nb + 1 + ((j - 1) * nb + 1) * a_dim1], lda, &tb[
1115 td + nb + 1 + (j - 1) * nb * ldtb], &i__2, &c_b15, &
1118 zgemm_("NoTranspose", "Conjugate transpose", &kb, &kb, &nb, &
1119 c_b23, &work[1], n, &a[j * nb + 1 + ((j - 2) * nb + 1)
1120 * a_dim1], lda, &c_b14, &tb[td + 1 + j * nb * ldtb],
1125 zhegst_(&c__1, "Lower", &kb, &tb[td + 1 + j * nb * ldtb], &
1126 i__2, &a[j * nb + 1 + ((j - 1) * nb + 1) * a_dim1],
1130 /* Expand T(J,J) into full format */
1133 for (i__ = 1; i__ <= i__2; ++i__) {
1134 i__3 = td + 1 + (j * nb + i__ - 1) * ldtb;
1135 i__4 = td + 1 + (j * nb + i__ - 1) * ldtb;
1137 tb[i__3].r = d__1, tb[i__3].i = 0.;
1139 for (k = i__ + 1; k <= i__3; ++k) {
1140 i__4 = td - (k - (i__ + 1)) + (j * nb + k - 1) * ldtb;
1141 d_cnjg(&z__1, &tb[td + (k - i__) + 1 + (j * nb + i__ - 1)
1143 tb[i__4].r = z__1.r, tb[i__4].i = z__1.i;
1150 /* Compute H(J,J) */
1154 zgemm_("NoTranspose", "Conjugate transpose", &kb, &kb,
1155 &kb, &c_b14, &tb[td + 1 + j * nb * ldtb], &
1156 i__2, &a[j * nb + 1 + ((j - 1) * nb + 1) *
1157 a_dim1], lda, &c_b15, &work[j * nb + 1], n);
1161 zgemm_("NoTranspose", "Conjugate transpose", &kb, &kb,
1162 &i__2, &c_b14, &tb[td + nb + 1 + (j - 1) *
1163 nb * ldtb], &i__3, &a[j * nb + 1 + ((j - 2) *
1164 nb + 1) * a_dim1], lda, &c_b15, &work[j * nb
1168 /* Update with the previous column */
1170 i__2 = *n - (j + 1) * nb;
1172 zgemm_("NoTranspose", "NoTranspose", &i__2, &nb, &i__3, &
1173 c_b23, &a[(j + 1) * nb + 1 + a_dim1], lda, &work[
1174 nb + 1], n, &c_b14, &a[(j + 1) * nb + 1 + (j * nb
1175 + 1) * a_dim1], lda);
1178 /* Factorize panel */
1180 i__2 = *n - (j + 1) * nb;
1181 zgetrf_(&i__2, &nb, &a[(j + 1) * nb + 1 + (j * nb + 1) *
1182 a_dim1], lda, &ipiv[(j + 1) * nb + 1], &iinfo);
1183 /* IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN */
1184 /* INFO = IINFO+(J+1)*NB */
1187 /* Compute T(J+1, J), zero out for GEMM update */
1190 i__2 = nb, i__3 = *n - (j + 1) * nb;
1191 kb = f2cmin(i__2,i__3);
1193 zlaset_("Full", &kb, &nb, &c_b15, &c_b15, &tb[td + nb + 1 + j
1194 * nb * ldtb], &i__2);
1196 zlacpy_("Upper", &kb, &nb, &a[(j + 1) * nb + 1 + (j * nb + 1)
1197 * a_dim1], lda, &tb[td + nb + 1 + j * nb * ldtb], &
1201 ztrsm_("R", "L", "C", "U", &kb, &nb, &c_b14, &a[j * nb +
1202 1 + ((j - 1) * nb + 1) * a_dim1], lda, &tb[td +
1203 nb + 1 + j * nb * ldtb], &i__2);
1206 /* Copy T(J+1,J) into T(J, J+1), both upper/lower for GEMM */
1210 for (k = 1; k <= i__2; ++k) {
1212 for (i__ = 1; i__ <= i__3; ++i__) {
1213 i__4 = td - nb + k - i__ + 1 + (j * nb + nb + i__ - 1)
1215 d_cnjg(&z__1, &tb[td + nb + i__ - k + 1 + (j * nb + k
1217 tb[i__4].r = z__1.r, tb[i__4].i = z__1.i;
1220 zlaset_("Upper", &kb, &nb, &c_b15, &c_b14, &a[(j + 1) * nb +
1221 1 + (j * nb + 1) * a_dim1], lda);
1223 /* Apply pivots to trailing submatrix of A */
1226 for (k = 1; k <= i__2; ++k) {
1228 ipiv[(j + 1) * nb + k] += (j + 1) * nb;
1230 i1 = (j + 1) * nb + k;
1231 i2 = ipiv[(j + 1) * nb + k];
1233 /* > Apply pivots to previous columns of L */
1235 zswap_(&i__3, &a[i1 + ((j + 1) * nb + 1) * a_dim1],
1236 lda, &a[i2 + ((j + 1) * nb + 1) * a_dim1],
1238 /* > Swap A(I1+1:M, I1) with A(I2, I1+1:M) */
1241 zswap_(&i__3, &a[i1 + 1 + i1 * a_dim1], &c__1, &a[
1242 i2 + (i1 + 1) * a_dim1], lda);
1244 zlacgv_(&i__3, &a[i2 + (i1 + 1) * a_dim1], lda);
1247 zlacgv_(&i__3, &a[i1 + 1 + i1 * a_dim1], &c__1);
1248 /* > Swap A(I2+1:M, I1) with A(I2+1:M, I2) */
1251 zswap_(&i__3, &a[i2 + 1 + i1 * a_dim1], &c__1, &a[
1252 i2 + 1 + i2 * a_dim1], &c__1);
1254 /* > Swap A(I1, I1) with A(I2, I2) */
1255 i__3 = i1 + i1 * a_dim1;
1256 piv.r = a[i__3].r, piv.i = a[i__3].i;
1257 i__3 = i1 + i1 * a_dim1;
1258 i__4 = i2 + i2 * a_dim1;
1259 a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
1260 i__3 = i2 + i2 * a_dim1;
1261 a[i__3].r = piv.r, a[i__3].i = piv.i;
1262 /* > Apply pivots to previous columns of L */
1265 zswap_(&i__3, &a[i1 + a_dim1], lda, &a[i2 +
1271 /* Apply pivots to previous columns of L */
1273 /* CALL ZLASWP( J*NB, A( 1, 1 ), LDA, */
1274 /* $ (J+1)*NB+1, (J+1)*NB+KB, IPIV, 1 ) */
1279 /* Factor the band matrix */
1280 zgbtrf_(n, n, &nb, &nb, &tb[1], &ldtb, &ipiv2[1], info);
1284 /* End of ZHETRF_AA_2STAGE */
1286 } /* zhetrf_aa_2stage__ */