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.};
517 static integer c__1 = 1;
519 /* > \brief \b ZSYTRI_ROOK */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download ZSYTRI_ROOK + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytri_
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytri_
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytri_
542 /* SUBROUTINE ZSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO ) */
545 /* INTEGER INFO, LDA, N */
546 /* INTEGER IPIV( * ) */
547 /* COMPLEX*16 A( LDA, * ), WORK( * ) */
550 /* > \par Purpose: */
555 /* > ZSYTRI_ROOK computes the inverse of a complex symmetric */
556 /* > matrix A using the factorization A = U*D*U**T or A = L*D*L**T */
557 /* > computed by ZSYTRF_ROOK. */
563 /* > \param[in] UPLO */
565 /* > UPLO is CHARACTER*1 */
566 /* > Specifies whether the details of the factorization are stored */
567 /* > as an upper or lower triangular matrix. */
568 /* > = 'U': Upper triangular, form is A = U*D*U**T; */
569 /* > = 'L': Lower triangular, form is A = L*D*L**T. */
575 /* > The order of the matrix A. N >= 0. */
578 /* > \param[in,out] A */
580 /* > A is COMPLEX*16 array, dimension (LDA,N) */
581 /* > On entry, the block diagonal matrix D and the multipliers */
582 /* > used to obtain the factor U or L as computed by ZSYTRF_ROOK. */
584 /* > On exit, if INFO = 0, the (symmetric) inverse of the original */
585 /* > matrix. If UPLO = 'U', the upper triangular part of the */
586 /* > inverse is formed and the part of A below the diagonal is not */
587 /* > referenced; if UPLO = 'L' the lower triangular part of the */
588 /* > inverse is formed and the part of A above the diagonal is */
589 /* > not referenced. */
592 /* > \param[in] LDA */
594 /* > LDA is INTEGER */
595 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
598 /* > \param[in] IPIV */
600 /* > IPIV is INTEGER array, dimension (N) */
601 /* > Details of the interchanges and the block structure of D */
602 /* > as determined by ZSYTRF_ROOK. */
605 /* > \param[out] WORK */
607 /* > WORK is COMPLEX*16 array, dimension (N) */
610 /* > \param[out] INFO */
612 /* > INFO is INTEGER */
613 /* > = 0: successful exit */
614 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
615 /* > > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
616 /* > inverse could not be computed. */
622 /* > \author Univ. of Tennessee */
623 /* > \author Univ. of California Berkeley */
624 /* > \author Univ. of Colorado Denver */
625 /* > \author NAG Ltd. */
627 /* > \date December 2016 */
629 /* > \ingroup complex16SYcomputational */
631 /* > \par Contributors: */
632 /* ================== */
636 /* > December 2016, Igor Kozachenko, */
637 /* > Computer Science Division, */
638 /* > University of California, Berkeley */
640 /* > September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, */
641 /* > School of Mathematics, */
642 /* > University of Manchester */
646 /* ===================================================================== */
647 /* Subroutine */ int zsytri_rook_(char *uplo, integer *n, doublecomplex *a,
648 integer *lda, integer *ipiv, doublecomplex *work, integer *info)
650 /* System generated locals */
651 integer a_dim1, a_offset, i__1, i__2, i__3;
652 doublecomplex z__1, z__2, z__3;
654 /* Local variables */
655 doublecomplex temp, akkp1, d__;
658 extern logical lsame_(char *, char *);
661 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
662 doublecomplex *, integer *);
663 extern /* Double Complex */ VOID zdotu_(doublecomplex *, integer *,
664 doublecomplex *, integer *, doublecomplex *, integer *);
665 extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *,
666 doublecomplex *, integer *), zsymv_(char *, integer *,
667 doublecomplex *, doublecomplex *, integer *, doublecomplex *,
668 integer *, doublecomplex *, doublecomplex *, integer *);
671 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
675 /* -- LAPACK computational routine (version 3.7.0) -- */
676 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
677 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
681 /* ===================================================================== */
684 /* Test the input parameters. */
686 /* Parameter adjustments */
688 a_offset = 1 + a_dim1 * 1;
695 upper = lsame_(uplo, "U");
696 if (! upper && ! lsame_(uplo, "L")) {
700 } else if (*lda < f2cmax(1,*n)) {
705 xerbla_("ZSYTRI_ROOK", &i__1, (ftnlen)11);
709 /* Quick return if possible */
715 /* Check that the diagonal matrix D is nonsingular. */
719 /* Upper triangular storage: examine D from bottom to top */
721 for (*info = *n; *info >= 1; --(*info)) {
722 i__1 = *info + *info * a_dim1;
723 if (ipiv[*info] > 0 && (a[i__1].r == 0. && a[i__1].i == 0.)) {
730 /* Lower triangular storage: examine D from top to bottom. */
733 for (*info = 1; *info <= i__1; ++(*info)) {
734 i__2 = *info + *info * a_dim1;
735 if (ipiv[*info] > 0 && (a[i__2].r == 0. && a[i__2].i == 0.)) {
745 /* Compute inv(A) from the factorization A = U*D*U**T. */
747 /* K is the main loop index, increasing from 1 to N in steps of */
748 /* 1 or 2, depending on the size of the diagonal blocks. */
753 /* If K > N, exit from loop. */
761 /* 1 x 1 diagonal block */
763 /* Invert the diagonal block. */
765 i__1 = k + k * a_dim1;
766 z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
767 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
769 /* Compute column K of the inverse. */
773 zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
775 z__1.r = -1., z__1.i = 0.;
776 zsymv_(uplo, &i__1, &z__1, &a[a_offset], lda, &work[1], &c__1,
777 &c_b2, &a[k * a_dim1 + 1], &c__1);
778 i__1 = k + k * a_dim1;
779 i__2 = k + k * a_dim1;
781 zdotu_(&z__2, &i__3, &work[1], &c__1, &a[k * a_dim1 + 1], &
783 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
784 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
789 /* 2 x 2 diagonal block */
791 /* Invert the diagonal block. */
793 i__1 = k + (k + 1) * a_dim1;
794 t.r = a[i__1].r, t.i = a[i__1].i;
795 z_div(&z__1, &a[k + k * a_dim1], &t);
796 ak.r = z__1.r, ak.i = z__1.i;
797 z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &t);
798 akp1.r = z__1.r, akp1.i = z__1.i;
799 z_div(&z__1, &a[k + (k + 1) * a_dim1], &t);
800 akkp1.r = z__1.r, akkp1.i = z__1.i;
801 z__3.r = ak.r * akp1.r - ak.i * akp1.i, z__3.i = ak.r * akp1.i +
803 z__2.r = z__3.r - 1., z__2.i = z__3.i + 0.;
804 z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r * z__2.i + t.i
806 d__.r = z__1.r, d__.i = z__1.i;
807 i__1 = k + k * a_dim1;
808 z_div(&z__1, &akp1, &d__);
809 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
810 i__1 = k + 1 + (k + 1) * a_dim1;
811 z_div(&z__1, &ak, &d__);
812 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
813 i__1 = k + (k + 1) * a_dim1;
814 z__2.r = -akkp1.r, z__2.i = -akkp1.i;
815 z_div(&z__1, &z__2, &d__);
816 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
818 /* Compute columns K and K+1 of the inverse. */
822 zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
824 z__1.r = -1., z__1.i = 0.;
825 zsymv_(uplo, &i__1, &z__1, &a[a_offset], lda, &work[1], &c__1,
826 &c_b2, &a[k * a_dim1 + 1], &c__1);
827 i__1 = k + k * a_dim1;
828 i__2 = k + k * a_dim1;
830 zdotu_(&z__2, &i__3, &work[1], &c__1, &a[k * a_dim1 + 1], &
832 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
833 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
834 i__1 = k + (k + 1) * a_dim1;
835 i__2 = k + (k + 1) * a_dim1;
837 zdotu_(&z__2, &i__3, &a[k * a_dim1 + 1], &c__1, &a[(k + 1) *
839 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
840 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
842 zcopy_(&i__1, &a[(k + 1) * a_dim1 + 1], &c__1, &work[1], &
845 z__1.r = -1., z__1.i = 0.;
846 zsymv_(uplo, &i__1, &z__1, &a[a_offset], lda, &work[1], &c__1,
847 &c_b2, &a[(k + 1) * a_dim1 + 1], &c__1);
848 i__1 = k + 1 + (k + 1) * a_dim1;
849 i__2 = k + 1 + (k + 1) * a_dim1;
851 zdotu_(&z__2, &i__3, &work[1], &c__1, &a[(k + 1) * a_dim1 + 1]
853 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
854 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
861 /* Interchange rows and columns K and IPIV(K) in the leading */
862 /* submatrix A(1:k+1,1:k+1) */
868 zswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 +
872 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + (kp + 1)
874 i__1 = k + k * a_dim1;
875 temp.r = a[i__1].r, temp.i = a[i__1].i;
876 i__1 = k + k * a_dim1;
877 i__2 = kp + kp * a_dim1;
878 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
879 i__1 = kp + kp * a_dim1;
880 a[i__1].r = temp.r, a[i__1].i = temp.i;
884 /* Interchange rows and columns K and K+1 with -IPIV(K) and */
885 /* -IPIV(K+1)in the leading submatrix A(1:k+1,1:k+1) */
891 zswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 +
895 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + (kp + 1)
898 i__1 = k + k * a_dim1;
899 temp.r = a[i__1].r, temp.i = a[i__1].i;
900 i__1 = k + k * a_dim1;
901 i__2 = kp + kp * a_dim1;
902 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
903 i__1 = kp + kp * a_dim1;
904 a[i__1].r = temp.r, a[i__1].i = temp.i;
905 i__1 = k + (k + 1) * a_dim1;
906 temp.r = a[i__1].r, temp.i = a[i__1].i;
907 i__1 = k + (k + 1) * a_dim1;
908 i__2 = kp + (k + 1) * a_dim1;
909 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
910 i__1 = kp + (k + 1) * a_dim1;
911 a[i__1].r = temp.r, a[i__1].i = temp.i;
919 zswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 +
923 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + (kp + 1)
925 i__1 = k + k * a_dim1;
926 temp.r = a[i__1].r, temp.i = a[i__1].i;
927 i__1 = k + k * a_dim1;
928 i__2 = kp + kp * a_dim1;
929 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
930 i__1 = kp + kp * a_dim1;
931 a[i__1].r = temp.r, a[i__1].i = temp.i;
942 /* Compute inv(A) from the factorization A = L*D*L**T. */
944 /* K is the main loop index, increasing from 1 to N in steps of */
945 /* 1 or 2, depending on the size of the diagonal blocks. */
950 /* If K < 1, exit from loop. */
958 /* 1 x 1 diagonal block */
960 /* Invert the diagonal block. */
962 i__1 = k + k * a_dim1;
963 z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
964 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
966 /* Compute column K of the inverse. */
970 zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
972 z__1.r = -1., z__1.i = 0.;
973 zsymv_(uplo, &i__1, &z__1, &a[k + 1 + (k + 1) * a_dim1], lda,
974 &work[1], &c__1, &c_b2, &a[k + 1 + k * a_dim1], &c__1);
975 i__1 = k + k * a_dim1;
976 i__2 = k + k * a_dim1;
978 zdotu_(&z__2, &i__3, &work[1], &c__1, &a[k + 1 + k * a_dim1],
980 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
981 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
986 /* 2 x 2 diagonal block */
988 /* Invert the diagonal block. */
990 i__1 = k + (k - 1) * a_dim1;
991 t.r = a[i__1].r, t.i = a[i__1].i;
992 z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &t);
993 ak.r = z__1.r, ak.i = z__1.i;
994 z_div(&z__1, &a[k + k * a_dim1], &t);
995 akp1.r = z__1.r, akp1.i = z__1.i;
996 z_div(&z__1, &a[k + (k - 1) * a_dim1], &t);
997 akkp1.r = z__1.r, akkp1.i = z__1.i;
998 z__3.r = ak.r * akp1.r - ak.i * akp1.i, z__3.i = ak.r * akp1.i +
1000 z__2.r = z__3.r - 1., z__2.i = z__3.i + 0.;
1001 z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r * z__2.i + t.i
1003 d__.r = z__1.r, d__.i = z__1.i;
1004 i__1 = k - 1 + (k - 1) * a_dim1;
1005 z_div(&z__1, &akp1, &d__);
1006 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1007 i__1 = k + k * a_dim1;
1008 z_div(&z__1, &ak, &d__);
1009 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1010 i__1 = k + (k - 1) * a_dim1;
1011 z__2.r = -akkp1.r, z__2.i = -akkp1.i;
1012 z_div(&z__1, &z__2, &d__);
1013 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1015 /* Compute columns K-1 and K of the inverse. */
1019 zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
1021 z__1.r = -1., z__1.i = 0.;
1022 zsymv_(uplo, &i__1, &z__1, &a[k + 1 + (k + 1) * a_dim1], lda,
1023 &work[1], &c__1, &c_b2, &a[k + 1 + k * a_dim1], &c__1);
1024 i__1 = k + k * a_dim1;
1025 i__2 = k + k * a_dim1;
1027 zdotu_(&z__2, &i__3, &work[1], &c__1, &a[k + 1 + k * a_dim1],
1029 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
1030 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1031 i__1 = k + (k - 1) * a_dim1;
1032 i__2 = k + (k - 1) * a_dim1;
1034 zdotu_(&z__2, &i__3, &a[k + 1 + k * a_dim1], &c__1, &a[k + 1
1035 + (k - 1) * a_dim1], &c__1);
1036 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
1037 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1039 zcopy_(&i__1, &a[k + 1 + (k - 1) * a_dim1], &c__1, &work[1], &
1042 z__1.r = -1., z__1.i = 0.;
1043 zsymv_(uplo, &i__1, &z__1, &a[k + 1 + (k + 1) * a_dim1], lda,
1044 &work[1], &c__1, &c_b2, &a[k + 1 + (k - 1) * a_dim1],
1046 i__1 = k - 1 + (k - 1) * a_dim1;
1047 i__2 = k - 1 + (k - 1) * a_dim1;
1049 zdotu_(&z__2, &i__3, &work[1], &c__1, &a[k + 1 + (k - 1) *
1051 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
1052 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1059 /* Interchange rows and columns K and IPIV(K) in the trailing */
1060 /* submatrix A(k-1:n,k-1:n) */
1066 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 +
1067 kp * a_dim1], &c__1);
1070 zswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[kp + (k + 1) *
1072 i__1 = k + k * a_dim1;
1073 temp.r = a[i__1].r, temp.i = a[i__1].i;
1074 i__1 = k + k * a_dim1;
1075 i__2 = kp + kp * a_dim1;
1076 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1077 i__1 = kp + kp * a_dim1;
1078 a[i__1].r = temp.r, a[i__1].i = temp.i;
1082 /* Interchange rows and columns K and K-1 with -IPIV(K) and */
1083 /* -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n) */
1089 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 +
1090 kp * a_dim1], &c__1);
1093 zswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[kp + (k + 1) *
1096 i__1 = k + k * a_dim1;
1097 temp.r = a[i__1].r, temp.i = a[i__1].i;
1098 i__1 = k + k * a_dim1;
1099 i__2 = kp + kp * a_dim1;
1100 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1101 i__1 = kp + kp * a_dim1;
1102 a[i__1].r = temp.r, a[i__1].i = temp.i;
1103 i__1 = k + (k - 1) * a_dim1;
1104 temp.r = a[i__1].r, temp.i = a[i__1].i;
1105 i__1 = k + (k - 1) * a_dim1;
1106 i__2 = kp + (k - 1) * a_dim1;
1107 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1108 i__1 = kp + (k - 1) * a_dim1;
1109 a[i__1].r = temp.r, a[i__1].i = temp.i;
1117 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 +
1118 kp * a_dim1], &c__1);
1121 zswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[kp + (k + 1) *
1123 i__1 = k + k * a_dim1;
1124 temp.r = a[i__1].r, temp.i = a[i__1].i;
1125 i__1 = k + k * a_dim1;
1126 i__2 = kp + kp * a_dim1;
1127 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1128 i__1 = kp + kp * a_dim1;
1129 a[i__1].r = temp.r, a[i__1].i = temp.i;
1141 /* End of ZSYTRI_ROOK */
1143 } /* zsytri_rook__ */