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]/Cd(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 doublecomplex c_b1 = {0.,0.};
516 static doublecomplex c_b2 = {1.,0.};
517 static integer c__1 = 1;
519 /* > \brief \b ZLAHEF_AA */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download ZLAHEF_AA + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahef_
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahef_
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahef_
542 /* SUBROUTINE ZLAHEF_AA( UPLO, J1, M, NB, A, LDA, IPIV, */
546 /* INTEGER J1, M, NB, LDA, LDH */
547 /* INTEGER IPIV( * ) */
548 /* COMPLEX*16 A( LDA, * ), H( LDH, * ), WORK( * ) */
551 /* > \par Purpose: */
556 /* > DLAHEF_AA factorizes a panel of a complex hermitian matrix A using */
557 /* > the Aasen's algorithm. The panel consists of a set of NB rows of A */
558 /* > when UPLO is U, or a set of NB columns when UPLO is L. */
560 /* > In order to factorize the panel, the Aasen's algorithm requires the */
561 /* > last row, or column, of the previous panel. The first row, or column, */
562 /* > of A is set to be the first row, or column, of an identity matrix, */
563 /* > which is used to factorize the first panel. */
565 /* > The resulting J-th row of U, or J-th column of L, is stored in the */
566 /* > (J-1)-th row, or column, of A (without the unit diagonals), while */
567 /* > the diagonal and subdiagonal of A are overwritten by those of T. */
574 /* > \param[in] UPLO */
576 /* > UPLO is CHARACTER*1 */
577 /* > = 'U': Upper triangle of A is stored; */
578 /* > = 'L': Lower triangle of A is stored. */
581 /* > \param[in] J1 */
583 /* > J1 is INTEGER */
584 /* > The location of the first row, or column, of the panel */
585 /* > within the submatrix of A, passed to this routine, e.g., */
586 /* > when called by ZHETRF_AA, for the first panel, J1 is 1, */
587 /* > while for the remaining panels, J1 is 2. */
593 /* > The dimension of the submatrix. M >= 0. */
596 /* > \param[in] NB */
598 /* > NB is INTEGER */
599 /* > The dimension of the panel to be facotorized. */
602 /* > \param[in,out] A */
604 /* > A is COMPLEX*16 array, dimension (LDA,M) for */
605 /* > the first panel, while dimension (LDA,M+1) for the */
606 /* > remaining panels. */
608 /* > On entry, A contains the last row, or column, of */
609 /* > the previous panel, and the trailing submatrix of A */
610 /* > to be factorized, except for the first panel, only */
611 /* > the panel is passed. */
613 /* > On exit, the leading panel is factorized. */
616 /* > \param[in] LDA */
618 /* > LDA is INTEGER */
619 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
622 /* > \param[out] IPIV */
624 /* > IPIV is INTEGER array, dimension (N) */
625 /* > Details of the row and column interchanges, */
626 /* > the row and column k were interchanged with the row and */
627 /* > column IPIV(k). */
630 /* > \param[in,out] H */
632 /* > H is COMPLEX*16 workspace, dimension (LDH,NB). */
636 /* > \param[in] LDH */
638 /* > LDH is INTEGER */
639 /* > The leading dimension of the workspace H. LDH >= f2cmax(1,M). */
642 /* > \param[out] WORK */
644 /* > WORK is COMPLEX*16 workspace, dimension (M). */
651 /* > \author Univ. of Tennessee */
652 /* > \author Univ. of California Berkeley */
653 /* > \author Univ. of Colorado Denver */
654 /* > \author NAG Ltd. */
656 /* > \date November 2017 */
658 /* > \ingroup complex16HEcomputational */
660 /* ===================================================================== */
661 /* Subroutine */ int zlahef_aa_(char *uplo, integer *j1, integer *m, integer
662 *nb, doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *
663 h__, integer *ldh, doublecomplex *work)
665 /* System generated locals */
666 integer a_dim1, a_offset, h_dim1, h_offset, i__1, i__2;
668 doublecomplex z__1, z__2;
670 /* Local variables */
673 extern logical lsame_(char *, char *);
674 extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
675 doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
676 doublecomplex *, doublecomplex *, integer *, doublecomplex *,
677 integer *, doublecomplex *, doublecomplex *, integer *);
679 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
680 doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
681 integer *, doublecomplex *, integer *), zaxpy_(integer *,
682 doublecomplex *, doublecomplex *, integer *, doublecomplex *,
685 extern /* Subroutine */ int zlacgv_(integer *, doublecomplex *, integer *)
687 extern integer izamax_(integer *, doublecomplex *, integer *);
688 extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
689 doublecomplex *, doublecomplex *, doublecomplex *, integer *);
693 /* -- LAPACK computational routine (version 3.8.0) -- */
694 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
695 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
700 /* ===================================================================== */
703 /* Parameter adjustments */
705 a_offset = 1 + a_dim1 * 1;
709 h_offset = 1 + h_dim1 * 1;
716 /* K1 is the first column of the panel to be factorized */
717 /* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks */
721 if (lsame_(uplo, "U")) {
723 /* ..................................................... */
724 /* Factorize A as U**T*D*U using the upper triangle of A */
725 /* ..................................................... */
728 if (j > f2cmin(*m,*nb)) {
732 /* K is the column to be factorized */
733 /* when being called from ZHETRF_AA, */
734 /* > for the first block column, J1 is 1, hence J1+J-1 is J, */
735 /* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, */
740 /* Only need to compute T(J, J) */
747 /* H(J:N, J) := A(J, J:N) - H(J:N, 1:(J-1)) * L(J1:(J-1), J), */
748 /* where H(J:N, J) has been initialized to be A(J, J:N) */
752 /* K is the column to be factorized */
753 /* > for the first block column, K is J, skipping the first two */
755 /* > for the rest of the columns, K is J+1, skipping only the */
759 zlacgv_(&i__1, &a[j * a_dim1 + 1], &c__1);
761 z__1.r = -1., z__1.i = 0.;
762 zgemv_("No transpose", &mj, &i__1, &z__1, &h__[j + k1 * h_dim1],
763 ldh, &a[j * a_dim1 + 1], &c__1, &c_b2, &h__[j + j *
766 zlacgv_(&i__1, &a[j * a_dim1 + 1], &c__1);
769 /* Copy H(i:n, i) into WORK */
771 zcopy_(&mj, &h__[j + j * h_dim1], &c__1, &work[1], &c__1);
775 /* Compute WORK := WORK - L(J-1, J:N) * T(J-1,J), */
776 /* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N) */
778 d_cnjg(&z__2, &a[k - 1 + j * a_dim1]);
779 z__1.r = -z__2.r, z__1.i = -z__2.i;
780 alpha.r = z__1.r, alpha.i = z__1.i;
781 zaxpy_(&mj, &alpha, &a[k - 2 + j * a_dim1], lda, &work[1], &c__1);
784 /* Set A(J, J) = T(J, J) */
786 i__1 = k + j * a_dim1;
788 a[i__1].r = d__1, a[i__1].i = 0.;
792 /* Compute WORK(2:N) = T(J, J) L(J, (J+1):N) */
793 /* where A(J, J) stores T(J, J) and A(J-1, (J+1):N) stores U(J, (J+1):N) */
796 i__1 = k + j * a_dim1;
797 z__1.r = -a[i__1].r, z__1.i = -a[i__1].i;
798 alpha.r = z__1.r, alpha.i = z__1.i;
800 zaxpy_(&i__1, &alpha, &a[k - 1 + (j + 1) * a_dim1], lda, &
804 /* Find f2cmax(|WORK(2:n)|) */
807 i2 = izamax_(&i__1, &work[2], &c__1) + 1;
809 piv.r = work[i__1].r, piv.i = work[i__1].i;
811 /* Apply hermitian pivot */
813 if (i2 != 2 && (piv.r != 0. || piv.i != 0.)) {
815 /* Swap WORK(I1) and WORK(I2) */
820 work[i__1].r = work[i__2].r, work[i__1].i = work[i__2].i;
822 work[i__1].r = piv.r, work[i__1].i = piv.i;
824 /* Swap A(I1, I1+1:N) with A(I1+1:N, I2) */
829 zswap_(&i__1, &a[*j1 + i1 - 1 + (i1 + 1) * a_dim1], lda, &a[*
830 j1 + i1 + i2 * a_dim1], &c__1);
832 zlacgv_(&i__1, &a[*j1 + i1 - 1 + (i1 + 1) * a_dim1], lda);
834 zlacgv_(&i__1, &a[*j1 + i1 + i2 * a_dim1], &c__1);
836 /* Swap A(I1, I2+1:N) with A(I2, I2+1:N) */
840 zswap_(&i__1, &a[*j1 + i1 - 1 + (i2 + 1) * a_dim1], lda, &
841 a[*j1 + i2 - 1 + (i2 + 1) * a_dim1], lda);
844 /* Swap A(I1, I1) with A(I2,I2) */
846 i__1 = i1 + *j1 - 1 + i1 * a_dim1;
847 piv.r = a[i__1].r, piv.i = a[i__1].i;
848 i__1 = *j1 + i1 - 1 + i1 * a_dim1;
849 i__2 = *j1 + i2 - 1 + i2 * a_dim1;
850 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
851 i__1 = *j1 + i2 - 1 + i2 * a_dim1;
852 a[i__1].r = piv.r, a[i__1].i = piv.i;
854 /* Swap H(I1, 1:J1) with H(I2, 1:J1) */
857 zswap_(&i__1, &h__[i1 + h_dim1], ldh, &h__[i2 + h_dim1], ldh);
862 /* Swap L(1:I1-1, I1) with L(1:I1-1, I2), */
863 /* skipping the first column */
866 zswap_(&i__1, &a[i1 * a_dim1 + 1], &c__1, &a[i2 * a_dim1
873 /* Set A(J, J+1) = T(J, J+1) */
875 i__1 = k + (j + 1) * a_dim1;
876 a[i__1].r = work[2].r, a[i__1].i = work[2].i;
880 /* Copy A(J+1:N, J+1) into H(J:N, J), */
883 zcopy_(&i__1, &a[k + 1 + (j + 1) * a_dim1], lda, &h__[j + 1 +
884 (j + 1) * h_dim1], &c__1);
887 /* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1), */
888 /* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1) */
891 i__1 = k + (j + 1) * a_dim1;
892 if (a[i__1].r != 0. || a[i__1].i != 0.) {
893 z_div(&z__1, &c_b2, &a[k + (j + 1) * a_dim1]);
894 alpha.r = z__1.r, alpha.i = z__1.i;
896 zcopy_(&i__1, &work[3], &c__1, &a[k + (j + 2) * a_dim1],
899 zscal_(&i__1, &alpha, &a[k + (j + 2) * a_dim1], lda);
902 zlaset_("Full", &c__1, &i__1, &c_b1, &c_b1, &a[k + (j + 2)
914 /* ..................................................... */
915 /* Factorize A as L*D*L**T using the lower triangle of A */
916 /* ..................................................... */
919 if (j > f2cmin(*m,*nb)) {
923 /* K is the column to be factorized */
924 /* when being called from ZHETRF_AA, */
925 /* > for the first block column, J1 is 1, hence J1+J-1 is J, */
926 /* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, */
931 /* Only need to compute T(J, J) */
938 /* H(J:N, J) := A(J:N, J) - H(J:N, 1:(J-1)) * L(J, J1:(J-1))^T, */
939 /* where H(J:N, J) has been initialized to be A(J:N, J) */
943 /* K is the column to be factorized */
944 /* > for the first block column, K is J, skipping the first two */
946 /* > for the rest of the columns, K is J+1, skipping only the */
950 zlacgv_(&i__1, &a[j + a_dim1], lda);
952 z__1.r = -1., z__1.i = 0.;
953 zgemv_("No transpose", &mj, &i__1, &z__1, &h__[j + k1 * h_dim1],
954 ldh, &a[j + a_dim1], lda, &c_b2, &h__[j + j * h_dim1], &
957 zlacgv_(&i__1, &a[j + a_dim1], lda);
960 /* Copy H(J:N, J) into WORK */
962 zcopy_(&mj, &h__[j + j * h_dim1], &c__1, &work[1], &c__1);
966 /* Compute WORK := WORK - L(J:N, J-1) * T(J-1,J), */
967 /* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1) */
969 d_cnjg(&z__2, &a[j + (k - 1) * a_dim1]);
970 z__1.r = -z__2.r, z__1.i = -z__2.i;
971 alpha.r = z__1.r, alpha.i = z__1.i;
972 zaxpy_(&mj, &alpha, &a[j + (k - 2) * a_dim1], &c__1, &work[1], &
976 /* Set A(J, J) = T(J, J) */
978 i__1 = j + k * a_dim1;
980 a[i__1].r = d__1, a[i__1].i = 0.;
984 /* Compute WORK(2:N) = T(J, J) L((J+1):N, J) */
985 /* where A(J, J) = T(J, J) and A((J+1):N, J-1) = L((J+1):N, J) */
988 i__1 = j + k * a_dim1;
989 z__1.r = -a[i__1].r, z__1.i = -a[i__1].i;
990 alpha.r = z__1.r, alpha.i = z__1.i;
992 zaxpy_(&i__1, &alpha, &a[j + 1 + (k - 1) * a_dim1], &c__1, &
996 /* Find f2cmax(|WORK(2:n)|) */
999 i2 = izamax_(&i__1, &work[2], &c__1) + 1;
1001 piv.r = work[i__1].r, piv.i = work[i__1].i;
1003 /* Apply hermitian pivot */
1005 if (i2 != 2 && (piv.r != 0. || piv.i != 0.)) {
1007 /* Swap WORK(I1) and WORK(I2) */
1012 work[i__1].r = work[i__2].r, work[i__1].i = work[i__2].i;
1014 work[i__1].r = piv.r, work[i__1].i = piv.i;
1016 /* Swap A(I1+1:N, I1) with A(I2, I1+1:N) */
1021 zswap_(&i__1, &a[i1 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1, &a[
1022 i2 + (*j1 + i1) * a_dim1], lda);
1024 zlacgv_(&i__1, &a[i1 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1);
1026 zlacgv_(&i__1, &a[i2 + (*j1 + i1) * a_dim1], lda);
1028 /* Swap A(I2+1:N, I1) with A(I2+1:N, I2) */
1032 zswap_(&i__1, &a[i2 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1,
1033 &a[i2 + 1 + (*j1 + i2 - 1) * a_dim1], &c__1);
1036 /* Swap A(I1, I1) with A(I2, I2) */
1038 i__1 = i1 + (*j1 + i1 - 1) * a_dim1;
1039 piv.r = a[i__1].r, piv.i = a[i__1].i;
1040 i__1 = i1 + (*j1 + i1 - 1) * a_dim1;
1041 i__2 = i2 + (*j1 + i2 - 1) * a_dim1;
1042 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1043 i__1 = i2 + (*j1 + i2 - 1) * a_dim1;
1044 a[i__1].r = piv.r, a[i__1].i = piv.i;
1046 /* Swap H(I1, I1:J1) with H(I2, I2:J1) */
1049 zswap_(&i__1, &h__[i1 + h_dim1], ldh, &h__[i2 + h_dim1], ldh);
1054 /* Swap L(1:I1-1, I1) with L(1:I1-1, I2), */
1055 /* skipping the first column */
1058 zswap_(&i__1, &a[i1 + a_dim1], lda, &a[i2 + a_dim1], lda);
1061 ipiv[j + 1] = j + 1;
1064 /* Set A(J+1, J) = T(J+1, J) */
1066 i__1 = j + 1 + k * a_dim1;
1067 a[i__1].r = work[2].r, a[i__1].i = work[2].i;
1071 /* Copy A(J+1:N, J+1) into H(J+1:N, J), */
1074 zcopy_(&i__1, &a[j + 1 + (k + 1) * a_dim1], &c__1, &h__[j + 1
1075 + (j + 1) * h_dim1], &c__1);
1078 /* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1), */
1079 /* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1) */
1082 i__1 = j + 1 + k * a_dim1;
1083 if (a[i__1].r != 0. || a[i__1].i != 0.) {
1084 z_div(&z__1, &c_b2, &a[j + 1 + k * a_dim1]);
1085 alpha.r = z__1.r, alpha.i = z__1.i;
1087 zcopy_(&i__1, &work[3], &c__1, &a[j + 2 + k * a_dim1], &
1090 zscal_(&i__1, &alpha, &a[j + 2 + k * a_dim1], &c__1);
1093 zlaset_("Full", &i__1, &c__1, &c_b1, &c_b1, &a[j + 2 + k *
1105 /* End of ZLAHEF_AA */