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 = {1.,0.};
516 static doublecomplex c_b2 = {0.,0.};
518 /* > \brief \b ZSYTRI2X */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download ZSYTRI2X + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytri2
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytri2
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytri2
541 /* SUBROUTINE ZSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO ) */
544 /* INTEGER INFO, LDA, N, NB */
545 /* INTEGER IPIV( * ) */
546 /* COMPLEX*16 A( LDA, * ), WORK( N+NB+1,* ) */
549 /* > \par Purpose: */
554 /* > ZSYTRI2X computes the inverse of a complex symmetric indefinite matrix */
555 /* > A using the factorization A = U*D*U**T or A = L*D*L**T computed by */
562 /* > \param[in] UPLO */
564 /* > UPLO is CHARACTER*1 */
565 /* > Specifies whether the details of the factorization are stored */
566 /* > as an upper or lower triangular matrix. */
567 /* > = 'U': Upper triangular, form is A = U*D*U**T; */
568 /* > = 'L': Lower triangular, form is A = L*D*L**T. */
574 /* > The order of the matrix A. N >= 0. */
577 /* > \param[in,out] A */
579 /* > A is COMPLEX*16 array, dimension (LDA,N) */
580 /* > On entry, the NNB diagonal matrix D and the multipliers */
581 /* > used to obtain the factor U or L as computed by ZSYTRF. */
583 /* > On exit, if INFO = 0, the (symmetric) inverse of the original */
584 /* > matrix. If UPLO = 'U', the upper triangular part of the */
585 /* > inverse is formed and the part of A below the diagonal is not */
586 /* > referenced; if UPLO = 'L' the lower triangular part of the */
587 /* > inverse is formed and the part of A above the diagonal is */
588 /* > not referenced. */
591 /* > \param[in] LDA */
593 /* > LDA is INTEGER */
594 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
597 /* > \param[in] IPIV */
599 /* > IPIV is INTEGER array, dimension (N) */
600 /* > Details of the interchanges and the NNB structure of D */
601 /* > as determined by ZSYTRF. */
604 /* > \param[out] WORK */
606 /* > WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3) */
609 /* > \param[in] NB */
611 /* > NB is INTEGER */
615 /* > \param[out] INFO */
617 /* > INFO is INTEGER */
618 /* > = 0: successful exit */
619 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
620 /* > > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
621 /* > inverse could not be computed. */
627 /* > \author Univ. of Tennessee */
628 /* > \author Univ. of California Berkeley */
629 /* > \author Univ. of Colorado Denver */
630 /* > \author NAG Ltd. */
632 /* > \date June 2017 */
634 /* > \ingroup complex16SYcomputational */
636 /* ===================================================================== */
637 /* Subroutine */ int zsytri2x_(char *uplo, integer *n, doublecomplex *a,
638 integer *lda, integer *ipiv, doublecomplex *work, integer *nb,
641 /* System generated locals */
642 integer a_dim1, a_offset, work_dim1, work_offset, i__1, i__2, i__3, i__4,
644 doublecomplex z__1, z__2, z__3;
646 /* Local variables */
648 doublecomplex akkp1, d__;
650 extern /* Subroutine */ int zsyswapr_(char *, integer *, doublecomplex *,
651 integer *, integer *, integer *);
653 extern logical lsame_(char *, char *);
655 extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
656 integer *, doublecomplex *, doublecomplex *, integer *,
657 doublecomplex *, integer *, doublecomplex *, doublecomplex *,
661 extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *,
662 integer *, integer *, doublecomplex *, doublecomplex *, integer *,
663 doublecomplex *, integer *);
664 doublecomplex ak, u01_i_j__;
666 doublecomplex u11_i_j__;
668 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), ztrtri_(
669 char *, char *, integer *, doublecomplex *, integer *, integer *);
671 doublecomplex akp1, u01_ip1_j__, u11_ip1_j__;
672 extern /* Subroutine */ int zsyconv_(char *, char *, integer *,
673 doublecomplex *, integer *, integer *, doublecomplex *, integer *);
676 /* -- LAPACK computational routine (version 3.7.1) -- */
677 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
678 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
682 /* ===================================================================== */
685 /* Test the input parameters. */
687 /* Parameter adjustments */
689 a_offset = 1 + a_dim1 * 1;
692 work_dim1 = *n + *nb + 1;
693 work_offset = 1 + work_dim1 * 1;
698 upper = lsame_(uplo, "U");
699 if (! upper && ! lsame_(uplo, "L")) {
703 } else if (*lda < f2cmax(1,*n)) {
707 /* Quick return if possible */
712 xerbla_("ZSYTRI2X", &i__1, (ftnlen)8);
720 /* Workspace got Non-diag elements of D */
722 zsyconv_(uplo, "C", n, &a[a_offset], lda, &ipiv[1], &work[work_offset], &
725 /* Check that the diagonal matrix D is nonsingular. */
729 /* Upper triangular storage: examine D from bottom to top */
731 for (*info = *n; *info >= 1; --(*info)) {
732 i__1 = *info + *info * a_dim1;
733 if (ipiv[*info] > 0 && (a[i__1].r == 0. && a[i__1].i == 0.)) {
739 /* Lower triangular storage: examine D from top to bottom. */
742 for (*info = 1; *info <= i__1; ++(*info)) {
743 i__2 = *info + *info * a_dim1;
744 if (ipiv[*info] > 0 && (a[i__2].r == 0. && a[i__2].i == 0.)) {
751 /* Splitting Workspace */
752 /* U01 is a block (N,NB+1) */
753 /* The first element of U01 is in WORK(1,1) */
754 /* U11 is a block (NB+1,NB+1) */
755 /* The first element of U11 is in WORK(N+1,1) */
757 /* INVD is a block (N,2) */
758 /* The first element of INVD is in WORK(1,INVD) */
762 /* invA = P * inv(U**T)*inv(D)*inv(U)*P**T. */
764 ztrtri_(uplo, "U", n, &a[a_offset], lda, info);
766 /* inv(D) and inv(D)*inv(U) */
771 /* 1 x 1 diagonal NNB */
772 i__1 = k + invd * work_dim1;
773 z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
774 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
775 i__1 = k + (invd + 1) * work_dim1;
776 work[i__1].r = 0., work[i__1].i = 0.;
779 /* 2 x 2 diagonal NNB */
780 i__1 = k + 1 + work_dim1;
781 t.r = work[i__1].r, t.i = work[i__1].i;
782 z_div(&z__1, &a[k + k * a_dim1], &t);
783 ak.r = z__1.r, ak.i = z__1.i;
784 z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &t);
785 akp1.r = z__1.r, akp1.i = z__1.i;
786 z_div(&z__1, &work[k + 1 + work_dim1], &t);
787 akkp1.r = z__1.r, akkp1.i = z__1.i;
788 z__3.r = ak.r * akp1.r - ak.i * akp1.i, z__3.i = ak.r *
789 akp1.i + ak.i * akp1.r;
790 z__2.r = z__3.r - 1., z__2.i = z__3.i + 0.;
791 z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r * z__2.i +
793 d__.r = z__1.r, d__.i = z__1.i;
794 i__1 = k + invd * work_dim1;
795 z_div(&z__1, &akp1, &d__);
796 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
797 i__1 = k + 1 + (invd + 1) * work_dim1;
798 z_div(&z__1, &ak, &d__);
799 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
800 i__1 = k + (invd + 1) * work_dim1;
801 z__2.r = -akkp1.r, z__2.i = -akkp1.i;
802 z_div(&z__1, &z__2, &d__);
803 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
804 i__1 = k + 1 + invd * work_dim1;
805 z__2.r = -akkp1.r, z__2.i = -akkp1.i;
806 z_div(&z__1, &z__2, &d__);
807 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
812 /* inv(U**T) = (inv(U))**T */
814 /* inv(U**T)*inv(D)*inv(U) */
823 /* count negative elements, */
825 for (i__ = cut + 1 - nnb; i__ <= i__1; ++i__) {
830 /* need a even number for a clear cut */
831 if (count % 2 == 1) {
840 for (i__ = 1; i__ <= i__1; ++i__) {
842 for (j = 1; j <= i__2; ++j) {
843 i__3 = i__ + j * work_dim1;
844 i__4 = i__ + (cut + j) * a_dim1;
845 work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
852 for (i__ = 1; i__ <= i__1; ++i__) {
853 i__2 = u11 + i__ + i__ * work_dim1;
854 work[i__2].r = 1., work[i__2].i = 0.;
856 for (j = 1; j <= i__2; ++j) {
857 i__3 = u11 + i__ + j * work_dim1;
858 work[i__3].r = 0., work[i__3].i = 0.;
861 for (j = i__ + 1; j <= i__2; ++j) {
862 i__3 = u11 + i__ + j * work_dim1;
863 i__4 = cut + i__ + (cut + j) * a_dim1;
864 work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
874 for (j = 1; j <= i__1; ++j) {
875 i__2 = i__ + j * work_dim1;
876 i__3 = i__ + invd * work_dim1;
877 i__4 = i__ + j * work_dim1;
878 z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
879 work[i__4].i, z__1.i = work[i__3].r * work[
880 i__4].i + work[i__3].i * work[i__4].r;
881 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
886 for (j = 1; j <= i__1; ++j) {
887 i__2 = i__ + j * work_dim1;
888 u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
890 i__2 = i__ + 1 + j * work_dim1;
891 u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
893 i__2 = i__ + j * work_dim1;
894 i__3 = i__ + invd * work_dim1;
895 z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
896 u01_i_j__.i, z__2.i = work[i__3].r *
897 u01_i_j__.i + work[i__3].i * u01_i_j__.r;
898 i__4 = i__ + (invd + 1) * work_dim1;
899 z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
900 u01_ip1_j__.i, z__3.i = work[i__4].r *
901 u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
902 z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
903 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
904 i__2 = i__ + 1 + j * work_dim1;
905 i__3 = i__ + 1 + invd * work_dim1;
906 z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
907 u01_i_j__.i, z__2.i = work[i__3].r *
908 u01_i_j__.i + work[i__3].i * u01_i_j__.r;
909 i__4 = i__ + 1 + (invd + 1) * work_dim1;
910 z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
911 u01_ip1_j__.i, z__3.i = work[i__4].r *
912 u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
913 z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
914 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
924 if (ipiv[cut + i__] > 0) {
926 for (j = i__; j <= i__1; ++j) {
927 i__2 = u11 + i__ + j * work_dim1;
928 i__3 = cut + i__ + invd * work_dim1;
929 i__4 = u11 + i__ + j * work_dim1;
930 z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
931 work[i__4].i, z__1.i = work[i__3].r * work[
932 i__4].i + work[i__3].i * work[i__4].r;
933 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
938 for (j = i__; j <= i__1; ++j) {
939 i__2 = u11 + i__ + j * work_dim1;
940 u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
942 i__2 = u11 + i__ + 1 + j * work_dim1;
943 u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
945 i__2 = u11 + i__ + j * work_dim1;
946 i__3 = cut + i__ + invd * work_dim1;
947 i__4 = u11 + i__ + j * work_dim1;
948 z__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
949 work[i__4].i, z__2.i = work[i__3].r * work[
950 i__4].i + work[i__3].i * work[i__4].r;
951 i__5 = cut + i__ + (invd + 1) * work_dim1;
952 i__6 = u11 + i__ + 1 + j * work_dim1;
953 z__3.r = work[i__5].r * work[i__6].r - work[i__5].i *
954 work[i__6].i, z__3.i = work[i__5].r * work[
955 i__6].i + work[i__5].i * work[i__6].r;
956 z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
957 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
958 i__2 = u11 + i__ + 1 + j * work_dim1;
959 i__3 = cut + i__ + 1 + invd * work_dim1;
960 z__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
961 u11_i_j__.i, z__2.i = work[i__3].r *
962 u11_i_j__.i + work[i__3].i * u11_i_j__.r;
963 i__4 = cut + i__ + 1 + (invd + 1) * work_dim1;
964 z__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
965 u11_ip1_j__.i, z__3.i = work[i__4].r *
966 u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
967 z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
968 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
974 /* U11**T*invD1*U11->U11 */
977 ztrmm_("L", "U", "T", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut +
978 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
981 for (i__ = 1; i__ <= i__1; ++i__) {
983 for (j = i__; j <= i__2; ++j) {
984 i__3 = cut + i__ + (cut + j) * a_dim1;
985 i__4 = u11 + i__ + j * work_dim1;
986 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
990 /* U01**T*invD*U01->A(CUT+I,CUT+J) */
994 zgemm_("T", "N", &nnb, &nnb, &cut, &c_b1, &a[(cut + 1) * a_dim1 +
995 1], lda, &work[work_offset], &i__1, &c_b2, &work[u11 + 1
996 + work_dim1], &i__2);
998 /* U11 = U11**T*invD1*U11 + U01**T*invD*U01 */
1001 for (i__ = 1; i__ <= i__1; ++i__) {
1003 for (j = i__; j <= i__2; ++j) {
1004 i__3 = cut + i__ + (cut + j) * a_dim1;
1005 i__4 = cut + i__ + (cut + j) * a_dim1;
1006 i__5 = u11 + i__ + j * work_dim1;
1007 z__1.r = a[i__4].r + work[i__5].r, z__1.i = a[i__4].i +
1009 a[i__3].r = z__1.r, a[i__3].i = z__1.i;
1013 /* U01 = U00**T*invD0*U01 */
1015 i__1 = *n + *nb + 1;
1016 ztrmm_("L", uplo, "T", "U", &cut, &nnb, &c_b1, &a[a_offset], lda,
1017 &work[work_offset], &i__1);
1022 for (i__ = 1; i__ <= i__1; ++i__) {
1024 for (j = 1; j <= i__2; ++j) {
1025 i__3 = i__ + (cut + j) * a_dim1;
1026 i__4 = i__ + j * work_dim1;
1027 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
1035 /* Apply PERMUTATIONS P and P**T: P * inv(U**T)*inv(D)*inv(U) *P**T */
1039 if (ipiv[i__] > 0) {
1042 zsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
1045 zsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
1052 zsyswapr_(uplo, n, &a[a_offset], lda, &i__1, &ip);
1056 zsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__1);
1065 /* invA = P * inv(U**T)*inv(D)*inv(U)*P**T. */
1067 ztrtri_(uplo, "U", n, &a[a_offset], lda, info);
1069 /* inv(D) and inv(D)*inv(U) */
1074 /* 1 x 1 diagonal NNB */
1075 i__1 = k + invd * work_dim1;
1076 z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
1077 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
1078 i__1 = k + (invd + 1) * work_dim1;
1079 work[i__1].r = 0., work[i__1].i = 0.;
1082 /* 2 x 2 diagonal NNB */
1083 i__1 = k - 1 + work_dim1;
1084 t.r = work[i__1].r, t.i = work[i__1].i;
1085 z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &t);
1086 ak.r = z__1.r, ak.i = z__1.i;
1087 z_div(&z__1, &a[k + k * a_dim1], &t);
1088 akp1.r = z__1.r, akp1.i = z__1.i;
1089 z_div(&z__1, &work[k - 1 + work_dim1], &t);
1090 akkp1.r = z__1.r, akkp1.i = z__1.i;
1091 z__3.r = ak.r * akp1.r - ak.i * akp1.i, z__3.i = ak.r *
1092 akp1.i + ak.i * akp1.r;
1093 z__2.r = z__3.r - 1., z__2.i = z__3.i + 0.;
1094 z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r * z__2.i +
1096 d__.r = z__1.r, d__.i = z__1.i;
1097 i__1 = k - 1 + invd * work_dim1;
1098 z_div(&z__1, &akp1, &d__);
1099 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
1100 i__1 = k + invd * work_dim1;
1101 z_div(&z__1, &ak, &d__);
1102 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
1103 i__1 = k + (invd + 1) * work_dim1;
1104 z__2.r = -akkp1.r, z__2.i = -akkp1.i;
1105 z_div(&z__1, &z__2, &d__);
1106 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
1107 i__1 = k - 1 + (invd + 1) * work_dim1;
1108 z__2.r = -akkp1.r, z__2.i = -akkp1.i;
1109 z_div(&z__1, &z__2, &d__);
1110 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
1115 /* inv(U**T) = (inv(U))**T */
1117 /* inv(U**T)*inv(D)*inv(U) */
1122 if (cut + nnb >= *n) {
1126 /* count negative elements, */
1128 for (i__ = cut + 1; i__ <= i__1; ++i__) {
1129 if (ipiv[i__] < 0) {
1133 /* need a even number for a clear cut */
1134 if (count % 2 == 1) {
1139 i__1 = *n - cut - nnb;
1140 for (i__ = 1; i__ <= i__1; ++i__) {
1142 for (j = 1; j <= i__2; ++j) {
1143 i__3 = i__ + j * work_dim1;
1144 i__4 = cut + nnb + i__ + (cut + j) * a_dim1;
1145 work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
1150 for (i__ = 1; i__ <= i__1; ++i__) {
1151 i__2 = u11 + i__ + i__ * work_dim1;
1152 work[i__2].r = 1., work[i__2].i = 0.;
1154 for (j = i__ + 1; j <= i__2; ++j) {
1155 i__3 = u11 + i__ + j * work_dim1;
1156 work[i__3].r = 0., work[i__3].i = 0.;
1159 for (j = 1; j <= i__2; ++j) {
1160 i__3 = u11 + i__ + j * work_dim1;
1161 i__4 = cut + i__ + (cut + j) * a_dim1;
1162 work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
1168 i__ = *n - cut - nnb;
1170 if (ipiv[cut + nnb + i__] > 0) {
1172 for (j = 1; j <= i__1; ++j) {
1173 i__2 = i__ + j * work_dim1;
1174 i__3 = cut + nnb + i__ + invd * work_dim1;
1175 i__4 = i__ + j * work_dim1;
1176 z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
1177 work[i__4].i, z__1.i = work[i__3].r * work[
1178 i__4].i + work[i__3].i * work[i__4].r;
1179 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
1184 for (j = 1; j <= i__1; ++j) {
1185 i__2 = i__ + j * work_dim1;
1186 u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
1188 i__2 = i__ - 1 + j * work_dim1;
1189 u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
1191 i__2 = i__ + j * work_dim1;
1192 i__3 = cut + nnb + i__ + invd * work_dim1;
1193 z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
1194 u01_i_j__.i, z__2.i = work[i__3].r *
1195 u01_i_j__.i + work[i__3].i * u01_i_j__.r;
1196 i__4 = cut + nnb + i__ + (invd + 1) * work_dim1;
1197 z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
1198 u01_ip1_j__.i, z__3.i = work[i__4].r *
1199 u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
1200 z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
1201 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
1202 i__2 = i__ - 1 + j * work_dim1;
1203 i__3 = cut + nnb + i__ - 1 + (invd + 1) * work_dim1;
1204 z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
1205 u01_i_j__.i, z__2.i = work[i__3].r *
1206 u01_i_j__.i + work[i__3].i * u01_i_j__.r;
1207 i__4 = cut + nnb + i__ - 1 + invd * work_dim1;
1208 z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
1209 u01_ip1_j__.i, z__3.i = work[i__4].r *
1210 u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
1211 z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
1212 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
1222 if (ipiv[cut + i__] > 0) {
1224 for (j = 1; j <= i__1; ++j) {
1225 i__2 = u11 + i__ + j * work_dim1;
1226 i__3 = cut + i__ + invd * work_dim1;
1227 i__4 = u11 + i__ + j * work_dim1;
1228 z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
1229 work[i__4].i, z__1.i = work[i__3].r * work[
1230 i__4].i + work[i__3].i * work[i__4].r;
1231 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
1236 for (j = 1; j <= i__1; ++j) {
1237 i__2 = u11 + i__ + j * work_dim1;
1238 u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
1240 i__2 = u11 + i__ - 1 + j * work_dim1;
1241 u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
1243 i__2 = u11 + i__ + j * work_dim1;
1244 i__3 = cut + i__ + invd * work_dim1;
1245 i__4 = u11 + i__ + j * work_dim1;
1246 z__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
1247 work[i__4].i, z__2.i = work[i__3].r * work[
1248 i__4].i + work[i__3].i * work[i__4].r;
1249 i__5 = cut + i__ + (invd + 1) * work_dim1;
1250 z__3.r = work[i__5].r * u11_ip1_j__.r - work[i__5].i *
1251 u11_ip1_j__.i, z__3.i = work[i__5].r *
1252 u11_ip1_j__.i + work[i__5].i * u11_ip1_j__.r;
1253 z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
1254 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
1255 i__2 = u11 + i__ - 1 + j * work_dim1;
1256 i__3 = cut + i__ - 1 + (invd + 1) * work_dim1;
1257 z__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
1258 u11_i_j__.i, z__2.i = work[i__3].r *
1259 u11_i_j__.i + work[i__3].i * u11_i_j__.r;
1260 i__4 = cut + i__ - 1 + invd * work_dim1;
1261 z__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
1262 u11_ip1_j__.i, z__3.i = work[i__4].r *
1263 u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
1264 z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
1265 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
1271 /* L11**T*invD1*L11->L11 */
1273 i__1 = *n + *nb + 1;
1274 ztrmm_("L", uplo, "T", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut
1275 + 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
1278 for (i__ = 1; i__ <= i__1; ++i__) {
1280 for (j = 1; j <= i__2; ++j) {
1281 i__3 = cut + i__ + (cut + j) * a_dim1;
1282 i__4 = u11 + i__ + j * work_dim1;
1283 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
1287 if (cut + nnb < *n) {
1289 /* L21**T*invD2*L21->A(CUT+I,CUT+J) */
1291 i__1 = *n - nnb - cut;
1292 i__2 = *n + *nb + 1;
1293 i__3 = *n + *nb + 1;
1294 zgemm_("T", "N", &nnb, &nnb, &i__1, &c_b1, &a[cut + nnb + 1 +
1295 (cut + 1) * a_dim1], lda, &work[work_offset], &i__2, &
1296 c_b2, &work[u11 + 1 + work_dim1], &i__3);
1298 /* L11 = L11**T*invD1*L11 + U01**T*invD*U01 */
1301 for (i__ = 1; i__ <= i__1; ++i__) {
1303 for (j = 1; j <= i__2; ++j) {
1304 i__3 = cut + i__ + (cut + j) * a_dim1;
1305 i__4 = cut + i__ + (cut + j) * a_dim1;
1306 i__5 = u11 + i__ + j * work_dim1;
1307 z__1.r = a[i__4].r + work[i__5].r, z__1.i = a[i__4].i
1309 a[i__3].r = z__1.r, a[i__3].i = z__1.i;
1313 /* U01 = L22**T*invD2*L21 */
1315 i__1 = *n - nnb - cut;
1316 i__2 = *n + *nb + 1;
1317 ztrmm_("L", uplo, "T", "U", &i__1, &nnb, &c_b1, &a[cut + nnb
1318 + 1 + (cut + nnb + 1) * a_dim1], lda, &work[
1319 work_offset], &i__2);
1321 i__1 = *n - cut - nnb;
1322 for (i__ = 1; i__ <= i__1; ++i__) {
1324 for (j = 1; j <= i__2; ++j) {
1325 i__3 = cut + nnb + i__ + (cut + j) * a_dim1;
1326 i__4 = i__ + j * work_dim1;
1327 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
1332 /* L11 = L11**T*invD1*L11 */
1335 for (i__ = 1; i__ <= i__1; ++i__) {
1337 for (j = 1; j <= i__2; ++j) {
1338 i__3 = cut + i__ + (cut + j) * a_dim1;
1339 i__4 = u11 + i__ + j * work_dim1;
1340 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
1350 /* Apply PERMUTATIONS P and P**T: P * inv(U**T)*inv(D)*inv(U) *P**T */
1354 if (ipiv[i__] > 0) {
1357 zsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
1360 zsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
1365 zsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
1368 zsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
1378 /* End of ZSYTRI2X */