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 complex c_b1 = {1.f,0.f};
516 static complex c_b2 = {0.f,0.f};
518 /* > \brief \b CHETRI2X */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download CHETRI2X + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetri2
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetri2
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetri2
541 /* SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO ) */
544 /* INTEGER INFO, LDA, N, NB */
545 /* INTEGER IPIV( * ) */
546 /* COMPLEX A( LDA, * ), WORK( N+NB+1,* ) */
549 /* > \par Purpose: */
554 /* > CHETRI2X computes the inverse of a complex Hermitian indefinite matrix */
555 /* > A using the factorization A = U*D*U**H or A = L*D*L**H 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**H; */
568 /* > = 'L': Lower triangular, form is A = L*D*L**H. */
574 /* > The order of the matrix A. N >= 0. */
577 /* > \param[in,out] A */
579 /* > A is COMPLEX 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 CHETRF. */
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 CHETRF. */
604 /* > \param[out] WORK */
606 /* > WORK is COMPLEX 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 December 2016 */
634 /* > \ingroup complexHEcomputational */
636 /* ===================================================================== */
637 /* Subroutine */ int chetri2x_(char *uplo, integer *n, complex *a, integer *
638 lda, integer *ipiv, complex *work, integer *nb, integer *info)
640 /* System generated locals */
641 integer a_dim1, a_offset, work_dim1, work_offset, i__1, i__2, i__3, i__4,
644 complex q__1, q__2, q__3;
646 /* Local variables */
648 extern /* Subroutine */ int cheswapr_(char *, integer *, complex *,
649 integer *, integer *, integer *);
653 extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
654 integer *, complex *, complex *, integer *, complex *, integer *,
655 complex *, complex *, integer *);
656 extern logical lsame_(char *, char *);
658 extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *,
659 integer *, integer *, complex *, complex *, integer *, complex *,
663 complex ak, u01_i_j__;
667 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), ctrtri_(
668 char *, char *, integer *, complex *, integer *, integer *);
671 extern /* Subroutine */ int csyconv_(char *, char *, integer *, complex *,
672 integer *, integer *, complex *, integer *);
673 complex u01_ip1_j__, u11_ip1_j__;
676 /* -- LAPACK computational routine (version 3.7.0) -- */
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_("CHETRI2X", &i__1, (ftnlen)8);
720 /* Workspace got Non-diag elements of D */
722 csyconv_(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.f && a[i__1].i == 0.f)) {
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.f && a[i__2].i == 0.f)) {
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**H)*inv(D)*inv(U)*P**H. */
764 ctrtri_(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 i__2 = k + k * a_dim1;
774 r__1 = 1.f / a[i__2].r;
775 work[i__1].r = r__1, work[i__1].i = 0.f;
776 i__1 = k + (invd + 1) * work_dim1;
777 work[i__1].r = 0.f, work[i__1].i = 0.f;
780 /* 2 x 2 diagonal NNB */
781 r__1 = c_abs(&work[k + 1 + work_dim1]);
782 t.r = r__1, t.i = 0.f;
783 i__1 = k + k * a_dim1;
785 q__2.r = r__1, q__2.i = 0.f;
786 c_div(&q__1, &q__2, &t);
787 ak.r = q__1.r, ak.i = q__1.i;
788 i__1 = k + 1 + (k + 1) * a_dim1;
790 q__2.r = r__1, q__2.i = 0.f;
791 c_div(&q__1, &q__2, &t);
792 akp1.r = q__1.r, akp1.i = q__1.i;
793 c_div(&q__1, &work[k + 1 + work_dim1], &t);
794 akkp1.r = q__1.r, akkp1.i = q__1.i;
795 q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r *
796 akp1.i + ak.i * akp1.r;
797 q__2.r = q__3.r - 1.f, q__2.i = q__3.i;
798 q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i +
800 d__.r = q__1.r, d__.i = q__1.i;
801 i__1 = k + invd * work_dim1;
802 c_div(&q__1, &akp1, &d__);
803 work[i__1].r = q__1.r, work[i__1].i = q__1.i;
804 i__1 = k + 1 + (invd + 1) * work_dim1;
805 c_div(&q__1, &ak, &d__);
806 work[i__1].r = q__1.r, work[i__1].i = q__1.i;
807 i__1 = k + (invd + 1) * work_dim1;
808 q__2.r = -akkp1.r, q__2.i = -akkp1.i;
809 c_div(&q__1, &q__2, &d__);
810 work[i__1].r = q__1.r, work[i__1].i = q__1.i;
811 i__1 = k + 1 + invd * work_dim1;
812 r_cnjg(&q__1, &work[k + (invd + 1) * work_dim1]);
813 work[i__1].r = q__1.r, work[i__1].i = q__1.i;
818 /* inv(U**H) = (inv(U))**H */
820 /* inv(U**H)*inv(D)*inv(U) */
829 /* count negative elements, */
831 for (i__ = cut + 1 - nnb; i__ <= i__1; ++i__) {
836 /* need a even number for a clear cut */
837 if (count % 2 == 1) {
846 for (i__ = 1; i__ <= i__1; ++i__) {
848 for (j = 1; j <= i__2; ++j) {
849 i__3 = i__ + j * work_dim1;
850 i__4 = i__ + (cut + j) * a_dim1;
851 work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
858 for (i__ = 1; i__ <= i__1; ++i__) {
859 i__2 = u11 + i__ + i__ * work_dim1;
860 work[i__2].r = 1.f, work[i__2].i = 0.f;
862 for (j = 1; j <= i__2; ++j) {
863 i__3 = u11 + i__ + j * work_dim1;
864 work[i__3].r = 0.f, work[i__3].i = 0.f;
867 for (j = i__ + 1; j <= i__2; ++j) {
868 i__3 = u11 + i__ + j * work_dim1;
869 i__4 = cut + i__ + (cut + j) * a_dim1;
870 work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
880 for (j = 1; j <= i__1; ++j) {
881 i__2 = i__ + j * work_dim1;
882 i__3 = i__ + invd * work_dim1;
883 i__4 = i__ + j * work_dim1;
884 q__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
885 work[i__4].i, q__1.i = work[i__3].r * work[
886 i__4].i + work[i__3].i * work[i__4].r;
887 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
892 for (j = 1; j <= i__1; ++j) {
893 i__2 = i__ + j * work_dim1;
894 u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
896 i__2 = i__ + 1 + j * work_dim1;
897 u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
899 i__2 = i__ + j * work_dim1;
900 i__3 = i__ + invd * work_dim1;
901 q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
902 u01_i_j__.i, q__2.i = work[i__3].r *
903 u01_i_j__.i + work[i__3].i * u01_i_j__.r;
904 i__4 = i__ + (invd + 1) * work_dim1;
905 q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
906 u01_ip1_j__.i, q__3.i = work[i__4].r *
907 u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
908 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
909 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
910 i__2 = i__ + 1 + j * work_dim1;
911 i__3 = i__ + 1 + invd * work_dim1;
912 q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
913 u01_i_j__.i, q__2.i = work[i__3].r *
914 u01_i_j__.i + work[i__3].i * u01_i_j__.r;
915 i__4 = i__ + 1 + (invd + 1) * work_dim1;
916 q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
917 u01_ip1_j__.i, q__3.i = work[i__4].r *
918 u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
919 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
920 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
930 if (ipiv[cut + i__] > 0) {
932 for (j = i__; j <= i__1; ++j) {
933 i__2 = u11 + i__ + j * work_dim1;
934 i__3 = cut + i__ + invd * work_dim1;
935 i__4 = u11 + i__ + j * work_dim1;
936 q__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
937 work[i__4].i, q__1.i = work[i__3].r * work[
938 i__4].i + work[i__3].i * work[i__4].r;
939 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
944 for (j = i__; j <= i__1; ++j) {
945 i__2 = u11 + i__ + j * work_dim1;
946 u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
948 i__2 = u11 + i__ + 1 + j * work_dim1;
949 u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
951 i__2 = u11 + i__ + j * work_dim1;
952 i__3 = cut + i__ + invd * work_dim1;
953 i__4 = u11 + i__ + j * work_dim1;
954 q__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
955 work[i__4].i, q__2.i = work[i__3].r * work[
956 i__4].i + work[i__3].i * work[i__4].r;
957 i__5 = cut + i__ + (invd + 1) * work_dim1;
958 i__6 = u11 + i__ + 1 + j * work_dim1;
959 q__3.r = work[i__5].r * work[i__6].r - work[i__5].i *
960 work[i__6].i, q__3.i = work[i__5].r * work[
961 i__6].i + work[i__5].i * work[i__6].r;
962 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
963 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
964 i__2 = u11 + i__ + 1 + j * work_dim1;
965 i__3 = cut + i__ + 1 + invd * work_dim1;
966 q__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
967 u11_i_j__.i, q__2.i = work[i__3].r *
968 u11_i_j__.i + work[i__3].i * u11_i_j__.r;
969 i__4 = cut + i__ + 1 + (invd + 1) * work_dim1;
970 q__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
971 u11_ip1_j__.i, q__3.i = work[i__4].r *
972 u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
973 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
974 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
980 /* U11**H*invD1*U11->U11 */
983 ctrmm_("L", "U", "C", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut +
984 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
987 for (i__ = 1; i__ <= i__1; ++i__) {
989 for (j = i__; j <= i__2; ++j) {
990 i__3 = cut + i__ + (cut + j) * a_dim1;
991 i__4 = u11 + i__ + j * work_dim1;
992 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
996 /* U01**H*invD*U01->A(CUT+I,CUT+J) */
1000 cgemm_("C", "N", &nnb, &nnb, &cut, &c_b1, &a[(cut + 1) * a_dim1 +
1001 1], lda, &work[work_offset], &i__1, &c_b2, &work[u11 + 1
1002 + work_dim1], &i__2);
1004 /* U11 = U11**H*invD1*U11 + U01**H*invD*U01 */
1007 for (i__ = 1; i__ <= i__1; ++i__) {
1009 for (j = i__; j <= i__2; ++j) {
1010 i__3 = cut + i__ + (cut + j) * a_dim1;
1011 i__4 = cut + i__ + (cut + j) * a_dim1;
1012 i__5 = u11 + i__ + j * work_dim1;
1013 q__1.r = a[i__4].r + work[i__5].r, q__1.i = a[i__4].i +
1015 a[i__3].r = q__1.r, a[i__3].i = q__1.i;
1019 /* U01 = U00**H*invD0*U01 */
1021 i__1 = *n + *nb + 1;
1022 ctrmm_("L", uplo, "C", "U", &cut, &nnb, &c_b1, &a[a_offset], lda,
1023 &work[work_offset], &i__1);
1028 for (i__ = 1; i__ <= i__1; ++i__) {
1030 for (j = 1; j <= i__2; ++j) {
1031 i__3 = i__ + (cut + j) * a_dim1;
1032 i__4 = i__ + j * work_dim1;
1033 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
1041 /* Apply PERMUTATIONS P and P**H: P * inv(U**H)*inv(D)*inv(U) *P**H */
1045 if (ipiv[i__] > 0) {
1048 cheswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
1051 cheswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
1058 cheswapr_(uplo, n, &a[a_offset], lda, &i__1, &ip);
1062 cheswapr_(uplo, n, &a[a_offset], lda, &ip, &i__1);
1071 /* invA = P * inv(U**H)*inv(D)*inv(U)*P**H. */
1073 ctrtri_(uplo, "U", n, &a[a_offset], lda, info);
1075 /* inv(D) and inv(D)*inv(U) */
1080 /* 1 x 1 diagonal NNB */
1081 i__1 = k + invd * work_dim1;
1082 i__2 = k + k * a_dim1;
1083 r__1 = 1.f / a[i__2].r;
1084 work[i__1].r = r__1, work[i__1].i = 0.f;
1085 i__1 = k + (invd + 1) * work_dim1;
1086 work[i__1].r = 0.f, work[i__1].i = 0.f;
1089 /* 2 x 2 diagonal NNB */
1090 r__1 = c_abs(&work[k - 1 + work_dim1]);
1091 t.r = r__1, t.i = 0.f;
1092 i__1 = k - 1 + (k - 1) * a_dim1;
1094 q__2.r = r__1, q__2.i = 0.f;
1095 c_div(&q__1, &q__2, &t);
1096 ak.r = q__1.r, ak.i = q__1.i;
1097 i__1 = k + k * a_dim1;
1099 q__2.r = r__1, q__2.i = 0.f;
1100 c_div(&q__1, &q__2, &t);
1101 akp1.r = q__1.r, akp1.i = q__1.i;
1102 c_div(&q__1, &work[k - 1 + work_dim1], &t);
1103 akkp1.r = q__1.r, akkp1.i = q__1.i;
1104 q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r *
1105 akp1.i + ak.i * akp1.r;
1106 q__2.r = q__3.r - 1.f, q__2.i = q__3.i;
1107 q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i +
1109 d__.r = q__1.r, d__.i = q__1.i;
1110 i__1 = k - 1 + invd * work_dim1;
1111 c_div(&q__1, &akp1, &d__);
1112 work[i__1].r = q__1.r, work[i__1].i = q__1.i;
1113 i__1 = k + invd * work_dim1;
1114 c_div(&q__1, &ak, &d__);
1115 work[i__1].r = q__1.r, work[i__1].i = q__1.i;
1116 i__1 = k + (invd + 1) * work_dim1;
1117 q__2.r = -akkp1.r, q__2.i = -akkp1.i;
1118 c_div(&q__1, &q__2, &d__);
1119 work[i__1].r = q__1.r, work[i__1].i = q__1.i;
1120 i__1 = k - 1 + (invd + 1) * work_dim1;
1121 r_cnjg(&q__1, &work[k + (invd + 1) * work_dim1]);
1122 work[i__1].r = q__1.r, work[i__1].i = q__1.i;
1127 /* inv(U**H) = (inv(U))**H */
1129 /* inv(U**H)*inv(D)*inv(U) */
1134 if (cut + nnb >= *n) {
1138 /* count negative elements, */
1140 for (i__ = cut + 1; i__ <= i__1; ++i__) {
1141 if (ipiv[i__] < 0) {
1145 /* need a even number for a clear cut */
1146 if (count % 2 == 1) {
1151 i__1 = *n - cut - nnb;
1152 for (i__ = 1; i__ <= i__1; ++i__) {
1154 for (j = 1; j <= i__2; ++j) {
1155 i__3 = i__ + j * work_dim1;
1156 i__4 = cut + nnb + i__ + (cut + j) * a_dim1;
1157 work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
1162 for (i__ = 1; i__ <= i__1; ++i__) {
1163 i__2 = u11 + i__ + i__ * work_dim1;
1164 work[i__2].r = 1.f, work[i__2].i = 0.f;
1166 for (j = i__ + 1; j <= i__2; ++j) {
1167 i__3 = u11 + i__ + j * work_dim1;
1168 work[i__3].r = 0.f, work[i__3].i = 0.f;
1171 for (j = 1; j <= i__2; ++j) {
1172 i__3 = u11 + i__ + j * work_dim1;
1173 i__4 = cut + i__ + (cut + j) * a_dim1;
1174 work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
1180 i__ = *n - cut - nnb;
1182 if (ipiv[cut + nnb + i__] > 0) {
1184 for (j = 1; j <= i__1; ++j) {
1185 i__2 = i__ + j * work_dim1;
1186 i__3 = cut + nnb + i__ + invd * work_dim1;
1187 i__4 = i__ + j * work_dim1;
1188 q__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
1189 work[i__4].i, q__1.i = work[i__3].r * work[
1190 i__4].i + work[i__3].i * work[i__4].r;
1191 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
1196 for (j = 1; j <= i__1; ++j) {
1197 i__2 = i__ + j * work_dim1;
1198 u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
1200 i__2 = i__ - 1 + j * work_dim1;
1201 u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
1203 i__2 = i__ + j * work_dim1;
1204 i__3 = cut + nnb + i__ + invd * work_dim1;
1205 q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
1206 u01_i_j__.i, q__2.i = work[i__3].r *
1207 u01_i_j__.i + work[i__3].i * u01_i_j__.r;
1208 i__4 = cut + nnb + i__ + (invd + 1) * work_dim1;
1209 q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
1210 u01_ip1_j__.i, q__3.i = work[i__4].r *
1211 u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
1212 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
1213 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
1214 i__2 = i__ - 1 + j * work_dim1;
1215 i__3 = cut + nnb + i__ - 1 + (invd + 1) * work_dim1;
1216 q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
1217 u01_i_j__.i, q__2.i = work[i__3].r *
1218 u01_i_j__.i + work[i__3].i * u01_i_j__.r;
1219 i__4 = cut + nnb + i__ - 1 + invd * work_dim1;
1220 q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
1221 u01_ip1_j__.i, q__3.i = work[i__4].r *
1222 u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
1223 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
1224 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
1234 if (ipiv[cut + i__] > 0) {
1236 for (j = 1; j <= i__1; ++j) {
1237 i__2 = u11 + i__ + j * work_dim1;
1238 i__3 = cut + i__ + invd * work_dim1;
1239 i__4 = u11 + i__ + j * work_dim1;
1240 q__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
1241 work[i__4].i, q__1.i = work[i__3].r * work[
1242 i__4].i + work[i__3].i * work[i__4].r;
1243 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
1248 for (j = 1; j <= i__1; ++j) {
1249 i__2 = u11 + i__ + j * work_dim1;
1250 u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
1252 i__2 = u11 + i__ - 1 + j * work_dim1;
1253 u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
1255 i__2 = u11 + i__ + j * work_dim1;
1256 i__3 = cut + i__ + invd * work_dim1;
1257 i__4 = u11 + i__ + j * work_dim1;
1258 q__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
1259 work[i__4].i, q__2.i = work[i__3].r * work[
1260 i__4].i + work[i__3].i * work[i__4].r;
1261 i__5 = cut + i__ + (invd + 1) * work_dim1;
1262 q__3.r = work[i__5].r * u11_ip1_j__.r - work[i__5].i *
1263 u11_ip1_j__.i, q__3.i = work[i__5].r *
1264 u11_ip1_j__.i + work[i__5].i * u11_ip1_j__.r;
1265 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
1266 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
1267 i__2 = u11 + i__ - 1 + j * work_dim1;
1268 i__3 = cut + i__ - 1 + (invd + 1) * work_dim1;
1269 q__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
1270 u11_i_j__.i, q__2.i = work[i__3].r *
1271 u11_i_j__.i + work[i__3].i * u11_i_j__.r;
1272 i__4 = cut + i__ - 1 + invd * work_dim1;
1273 q__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
1274 u11_ip1_j__.i, q__3.i = work[i__4].r *
1275 u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
1276 q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
1277 work[i__2].r = q__1.r, work[i__2].i = q__1.i;
1283 /* L11**H*invD1*L11->L11 */
1285 i__1 = *n + *nb + 1;
1286 ctrmm_("L", uplo, "C", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut
1287 + 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
1290 for (i__ = 1; i__ <= i__1; ++i__) {
1292 for (j = 1; j <= i__2; ++j) {
1293 i__3 = cut + i__ + (cut + j) * a_dim1;
1294 i__4 = u11 + i__ + j * work_dim1;
1295 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
1299 if (cut + nnb < *n) {
1301 /* L21**H*invD2*L21->A(CUT+I,CUT+J) */
1303 i__1 = *n - nnb - cut;
1304 i__2 = *n + *nb + 1;
1305 i__3 = *n + *nb + 1;
1306 cgemm_("C", "N", &nnb, &nnb, &i__1, &c_b1, &a[cut + nnb + 1 +
1307 (cut + 1) * a_dim1], lda, &work[work_offset], &i__2, &
1308 c_b2, &work[u11 + 1 + work_dim1], &i__3);
1310 /* L11 = L11**H*invD1*L11 + U01**H*invD*U01 */
1313 for (i__ = 1; i__ <= i__1; ++i__) {
1315 for (j = 1; j <= i__2; ++j) {
1316 i__3 = cut + i__ + (cut + j) * a_dim1;
1317 i__4 = cut + i__ + (cut + j) * a_dim1;
1318 i__5 = u11 + i__ + j * work_dim1;
1319 q__1.r = a[i__4].r + work[i__5].r, q__1.i = a[i__4].i
1321 a[i__3].r = q__1.r, a[i__3].i = q__1.i;
1325 /* L01 = L22**H*invD2*L21 */
1327 i__1 = *n - nnb - cut;
1328 i__2 = *n + *nb + 1;
1329 ctrmm_("L", uplo, "C", "U", &i__1, &nnb, &c_b1, &a[cut + nnb
1330 + 1 + (cut + nnb + 1) * a_dim1], lda, &work[
1331 work_offset], &i__2);
1333 i__1 = *n - cut - nnb;
1334 for (i__ = 1; i__ <= i__1; ++i__) {
1336 for (j = 1; j <= i__2; ++j) {
1337 i__3 = cut + nnb + i__ + (cut + j) * a_dim1;
1338 i__4 = i__ + j * work_dim1;
1339 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
1344 /* L11 = L11**H*invD1*L11 */
1347 for (i__ = 1; i__ <= i__1; ++i__) {
1349 for (j = 1; j <= i__2; ++j) {
1350 i__3 = cut + i__ + (cut + j) * a_dim1;
1351 i__4 = u11 + i__ + j * work_dim1;
1352 a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
1362 /* Apply PERMUTATIONS P and P**H: P * inv(U**H)*inv(D)*inv(U) *P**H */
1366 if (ipiv[i__] > 0) {
1369 cheswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
1372 cheswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
1377 cheswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
1380 cheswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
1390 /* End of CHETRI2X */