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 doublecomplex c_b2 = {0.,0.};
516 static integer c__1 = 1;
518 /* > \brief \b ZHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded
519 Bunch-Kaufman ("rook") diagonal pivoting method. */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download ZHETRI_ROOK + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetri_
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetri_
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetri_
542 /* SUBROUTINE ZHETRI_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 /* > ZHETRI_ROOK computes the inverse of a complex Hermitian indefinite matrix */
556 /* > A using the factorization A = U*D*U**H or A = L*D*L**H computed by */
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**H; */
569 /* > = 'L': Lower triangular, form is A = L*D*L**H. */
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 ZHETRF_ROOK. */
584 /* > On exit, if INFO = 0, the (Hermitian) 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 ZHETRF_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 November 2013 */
629 /* > \ingroup complex16HEcomputational */
631 /* > \par Contributors: */
632 /* ================== */
636 /* > November 2013, 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 */
645 /* ===================================================================== */
646 /* Subroutine */ int zhetri_rook_(char *uplo, integer *n, doublecomplex *a,
647 integer *lda, integer *ipiv, doublecomplex *work, integer *info)
649 /* System generated locals */
650 integer a_dim1, a_offset, i__1, i__2, i__3;
652 doublecomplex z__1, z__2;
654 /* Local variables */
655 doublecomplex temp, akkp1;
659 extern logical lsame_(char *, char *);
660 extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
661 doublecomplex *, integer *, doublecomplex *, integer *);
663 extern /* Subroutine */ int zhemv_(char *, integer *, doublecomplex *,
664 doublecomplex *, integer *, doublecomplex *, integer *,
665 doublecomplex *, doublecomplex *, integer *);
667 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
668 doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
669 integer *, doublecomplex *, integer *);
672 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
676 /* -- LAPACK computational routine (version 3.5.0) -- */
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;
696 upper = lsame_(uplo, "U");
697 if (! upper && ! lsame_(uplo, "L")) {
701 } else if (*lda < f2cmax(1,*n)) {
706 xerbla_("ZHETRI_ROOK", &i__1, (ftnlen)11);
710 /* Quick return if possible */
716 /* Check that the diagonal matrix D is nonsingular. */
720 /* Upper triangular storage: examine D from bottom to top */
722 for (*info = *n; *info >= 1; --(*info)) {
723 i__1 = *info + *info * a_dim1;
724 if (ipiv[*info] > 0 && (a[i__1].r == 0. && a[i__1].i == 0.)) {
731 /* Lower triangular storage: examine D from top to bottom. */
734 for (*info = 1; *info <= i__1; ++(*info)) {
735 i__2 = *info + *info * a_dim1;
736 if (ipiv[*info] > 0 && (a[i__2].r == 0. && a[i__2].i == 0.)) {
746 /* Compute inv(A) from the factorization A = U*D*U**H. */
748 /* K is the main loop index, increasing from 1 to N in steps of */
749 /* 1 or 2, depending on the size of the diagonal blocks. */
754 /* If K > N, exit from loop. */
762 /* 1 x 1 diagonal block */
764 /* Invert the diagonal block. */
766 i__1 = k + k * a_dim1;
767 i__2 = k + k * a_dim1;
768 d__1 = 1. / a[i__2].r;
769 a[i__1].r = d__1, a[i__1].i = 0.;
771 /* Compute column K of the inverse. */
775 zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
777 z__1.r = -1., z__1.i = 0.;
778 zhemv_(uplo, &i__1, &z__1, &a[a_offset], lda, &work[1], &c__1,
779 &c_b2, &a[k * a_dim1 + 1], &c__1);
780 i__1 = k + k * a_dim1;
781 i__2 = k + k * a_dim1;
783 zdotc_(&z__2, &i__3, &work[1], &c__1, &a[k * a_dim1 + 1], &
786 z__1.r = a[i__2].r - d__1, z__1.i = a[i__2].i;
787 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
792 /* 2 x 2 diagonal block */
794 /* Invert the diagonal block. */
796 t = z_abs(&a[k + (k + 1) * a_dim1]);
797 i__1 = k + k * a_dim1;
799 i__1 = k + 1 + (k + 1) * a_dim1;
800 akp1 = a[i__1].r / t;
801 i__1 = k + (k + 1) * a_dim1;
802 z__1.r = a[i__1].r / t, z__1.i = a[i__1].i / t;
803 akkp1.r = z__1.r, akkp1.i = z__1.i;
804 d__ = t * (ak * akp1 - 1.);
805 i__1 = k + k * a_dim1;
807 a[i__1].r = d__1, a[i__1].i = 0.;
808 i__1 = k + 1 + (k + 1) * a_dim1;
810 a[i__1].r = d__1, a[i__1].i = 0.;
811 i__1 = k + (k + 1) * a_dim1;
812 z__2.r = -akkp1.r, z__2.i = -akkp1.i;
813 z__1.r = z__2.r / d__, z__1.i = z__2.i / d__;
814 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
816 /* Compute columns K and K+1 of the inverse. */
820 zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
822 z__1.r = -1., z__1.i = 0.;
823 zhemv_(uplo, &i__1, &z__1, &a[a_offset], lda, &work[1], &c__1,
824 &c_b2, &a[k * a_dim1 + 1], &c__1);
825 i__1 = k + k * a_dim1;
826 i__2 = k + k * a_dim1;
828 zdotc_(&z__2, &i__3, &work[1], &c__1, &a[k * a_dim1 + 1], &
831 z__1.r = a[i__2].r - d__1, z__1.i = a[i__2].i;
832 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
833 i__1 = k + (k + 1) * a_dim1;
834 i__2 = k + (k + 1) * a_dim1;
836 zdotc_(&z__2, &i__3, &a[k * a_dim1 + 1], &c__1, &a[(k + 1) *
838 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
839 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
841 zcopy_(&i__1, &a[(k + 1) * a_dim1 + 1], &c__1, &work[1], &
844 z__1.r = -1., z__1.i = 0.;
845 zhemv_(uplo, &i__1, &z__1, &a[a_offset], lda, &work[1], &c__1,
846 &c_b2, &a[(k + 1) * a_dim1 + 1], &c__1);
847 i__1 = k + 1 + (k + 1) * a_dim1;
848 i__2 = k + 1 + (k + 1) * a_dim1;
850 zdotc_(&z__2, &i__3, &work[1], &c__1, &a[(k + 1) * a_dim1 + 1]
853 z__1.r = a[i__2].r - d__1, z__1.i = a[i__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:k) */
869 zswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 +
874 for (j = kp + 1; j <= i__1; ++j) {
875 d_cnjg(&z__1, &a[j + k * a_dim1]);
876 temp.r = z__1.r, temp.i = z__1.i;
877 i__2 = j + k * a_dim1;
878 d_cnjg(&z__1, &a[kp + j * a_dim1]);
879 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
880 i__2 = kp + j * a_dim1;
881 a[i__2].r = temp.r, a[i__2].i = temp.i;
885 i__1 = kp + k * a_dim1;
886 d_cnjg(&z__1, &a[kp + k * a_dim1]);
887 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
889 i__1 = k + k * a_dim1;
890 temp.r = a[i__1].r, temp.i = a[i__1].i;
891 i__1 = k + k * a_dim1;
892 i__2 = kp + kp * a_dim1;
893 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
894 i__1 = kp + kp * a_dim1;
895 a[i__1].r = temp.r, a[i__1].i = temp.i;
899 /* Interchange rows and columns K and K+1 with -IPIV(K) and */
900 /* -IPIV(K+1) in the leading submatrix A(k+1:n,k+1:n) */
902 /* (1) Interchange rows and columns K and -IPIV(K) */
909 zswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 +
914 for (j = kp + 1; j <= i__1; ++j) {
915 d_cnjg(&z__1, &a[j + k * a_dim1]);
916 temp.r = z__1.r, temp.i = z__1.i;
917 i__2 = j + k * a_dim1;
918 d_cnjg(&z__1, &a[kp + j * a_dim1]);
919 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
920 i__2 = kp + j * a_dim1;
921 a[i__2].r = temp.r, a[i__2].i = temp.i;
925 i__1 = kp + k * a_dim1;
926 d_cnjg(&z__1, &a[kp + k * a_dim1]);
927 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
929 i__1 = k + k * a_dim1;
930 temp.r = a[i__1].r, temp.i = a[i__1].i;
931 i__1 = k + k * a_dim1;
932 i__2 = kp + kp * a_dim1;
933 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
934 i__1 = kp + kp * a_dim1;
935 a[i__1].r = temp.r, a[i__1].i = temp.i;
937 i__1 = k + (k + 1) * a_dim1;
938 temp.r = a[i__1].r, temp.i = a[i__1].i;
939 i__1 = k + (k + 1) * a_dim1;
940 i__2 = kp + (k + 1) * a_dim1;
941 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
942 i__1 = kp + (k + 1) * a_dim1;
943 a[i__1].r = temp.r, a[i__1].i = temp.i;
946 /* (2) Interchange rows and columns K+1 and -IPIV(K+1) */
954 zswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 +
959 for (j = kp + 1; j <= i__1; ++j) {
960 d_cnjg(&z__1, &a[j + k * a_dim1]);
961 temp.r = z__1.r, temp.i = z__1.i;
962 i__2 = j + k * a_dim1;
963 d_cnjg(&z__1, &a[kp + j * a_dim1]);
964 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
965 i__2 = kp + j * a_dim1;
966 a[i__2].r = temp.r, a[i__2].i = temp.i;
970 i__1 = kp + k * a_dim1;
971 d_cnjg(&z__1, &a[kp + k * a_dim1]);
972 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
974 i__1 = k + k * a_dim1;
975 temp.r = a[i__1].r, temp.i = a[i__1].i;
976 i__1 = k + k * a_dim1;
977 i__2 = kp + kp * a_dim1;
978 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
979 i__1 = kp + kp * a_dim1;
980 a[i__1].r = temp.r, a[i__1].i = temp.i;
991 /* Compute inv(A) from the factorization A = L*D*L**H. */
993 /* K is the main loop index, decreasing from N to 1 in steps of */
994 /* 1 or 2, depending on the size of the diagonal blocks. */
999 /* If K < 1, exit from loop. */
1007 /* 1 x 1 diagonal block */
1009 /* Invert the diagonal block. */
1011 i__1 = k + k * a_dim1;
1012 i__2 = k + k * a_dim1;
1013 d__1 = 1. / a[i__2].r;
1014 a[i__1].r = d__1, a[i__1].i = 0.;
1016 /* Compute column K of the inverse. */
1020 zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
1022 z__1.r = -1., z__1.i = 0.;
1023 zhemv_(uplo, &i__1, &z__1, &a[k + 1 + (k + 1) * a_dim1], lda,
1024 &work[1], &c__1, &c_b2, &a[k + 1 + k * a_dim1], &c__1);
1025 i__1 = k + k * a_dim1;
1026 i__2 = k + k * a_dim1;
1028 zdotc_(&z__2, &i__3, &work[1], &c__1, &a[k + 1 + k * a_dim1],
1031 z__1.r = a[i__2].r - d__1, z__1.i = a[i__2].i;
1032 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1037 /* 2 x 2 diagonal block */
1039 /* Invert the diagonal block. */
1041 t = z_abs(&a[k + (k - 1) * a_dim1]);
1042 i__1 = k - 1 + (k - 1) * a_dim1;
1044 i__1 = k + k * a_dim1;
1045 akp1 = a[i__1].r / t;
1046 i__1 = k + (k - 1) * a_dim1;
1047 z__1.r = a[i__1].r / t, z__1.i = a[i__1].i / t;
1048 akkp1.r = z__1.r, akkp1.i = z__1.i;
1049 d__ = t * (ak * akp1 - 1.);
1050 i__1 = k - 1 + (k - 1) * a_dim1;
1052 a[i__1].r = d__1, a[i__1].i = 0.;
1053 i__1 = k + k * a_dim1;
1055 a[i__1].r = d__1, a[i__1].i = 0.;
1056 i__1 = k + (k - 1) * a_dim1;
1057 z__2.r = -akkp1.r, z__2.i = -akkp1.i;
1058 z__1.r = z__2.r / d__, z__1.i = z__2.i / d__;
1059 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1061 /* Compute columns K-1 and K of the inverse. */
1065 zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
1067 z__1.r = -1., z__1.i = 0.;
1068 zhemv_(uplo, &i__1, &z__1, &a[k + 1 + (k + 1) * a_dim1], lda,
1069 &work[1], &c__1, &c_b2, &a[k + 1 + k * a_dim1], &c__1);
1070 i__1 = k + k * a_dim1;
1071 i__2 = k + k * a_dim1;
1073 zdotc_(&z__2, &i__3, &work[1], &c__1, &a[k + 1 + k * a_dim1],
1076 z__1.r = a[i__2].r - d__1, z__1.i = a[i__2].i;
1077 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1078 i__1 = k + (k - 1) * a_dim1;
1079 i__2 = k + (k - 1) * a_dim1;
1081 zdotc_(&z__2, &i__3, &a[k + 1 + k * a_dim1], &c__1, &a[k + 1
1082 + (k - 1) * a_dim1], &c__1);
1083 z__1.r = a[i__2].r - z__2.r, z__1.i = a[i__2].i - z__2.i;
1084 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1086 zcopy_(&i__1, &a[k + 1 + (k - 1) * a_dim1], &c__1, &work[1], &
1089 z__1.r = -1., z__1.i = 0.;
1090 zhemv_(uplo, &i__1, &z__1, &a[k + 1 + (k + 1) * a_dim1], lda,
1091 &work[1], &c__1, &c_b2, &a[k + 1 + (k - 1) * a_dim1],
1093 i__1 = k - 1 + (k - 1) * a_dim1;
1094 i__2 = k - 1 + (k - 1) * a_dim1;
1096 zdotc_(&z__2, &i__3, &work[1], &c__1, &a[k + 1 + (k - 1) *
1099 z__1.r = a[i__2].r - d__1, z__1.i = a[i__2].i;
1100 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1107 /* Interchange rows and columns K and IPIV(K) in the trailing */
1108 /* submatrix A(k:n,k:n) */
1115 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 +
1116 kp * a_dim1], &c__1);
1120 for (j = k + 1; j <= i__1; ++j) {
1121 d_cnjg(&z__1, &a[j + k * a_dim1]);
1122 temp.r = z__1.r, temp.i = z__1.i;
1123 i__2 = j + k * a_dim1;
1124 d_cnjg(&z__1, &a[kp + j * a_dim1]);
1125 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
1126 i__2 = kp + j * a_dim1;
1127 a[i__2].r = temp.r, a[i__2].i = temp.i;
1131 i__1 = kp + k * a_dim1;
1132 d_cnjg(&z__1, &a[kp + k * a_dim1]);
1133 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1135 i__1 = k + k * a_dim1;
1136 temp.r = a[i__1].r, temp.i = a[i__1].i;
1137 i__1 = k + k * a_dim1;
1138 i__2 = kp + kp * a_dim1;
1139 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1140 i__1 = kp + kp * a_dim1;
1141 a[i__1].r = temp.r, a[i__1].i = temp.i;
1145 /* Interchange rows and columns K and K-1 with -IPIV(K) and */
1146 /* -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n) */
1148 /* (1) Interchange rows and columns K and -IPIV(K) */
1155 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 +
1156 kp * a_dim1], &c__1);
1160 for (j = k + 1; j <= i__1; ++j) {
1161 d_cnjg(&z__1, &a[j + k * a_dim1]);
1162 temp.r = z__1.r, temp.i = z__1.i;
1163 i__2 = j + k * a_dim1;
1164 d_cnjg(&z__1, &a[kp + j * a_dim1]);
1165 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
1166 i__2 = kp + j * a_dim1;
1167 a[i__2].r = temp.r, a[i__2].i = temp.i;
1171 i__1 = kp + k * a_dim1;
1172 d_cnjg(&z__1, &a[kp + k * a_dim1]);
1173 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1175 i__1 = k + k * a_dim1;
1176 temp.r = a[i__1].r, temp.i = a[i__1].i;
1177 i__1 = k + k * a_dim1;
1178 i__2 = kp + kp * a_dim1;
1179 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1180 i__1 = kp + kp * a_dim1;
1181 a[i__1].r = temp.r, a[i__1].i = temp.i;
1183 i__1 = k + (k - 1) * a_dim1;
1184 temp.r = a[i__1].r, temp.i = a[i__1].i;
1185 i__1 = k + (k - 1) * a_dim1;
1186 i__2 = kp + (k - 1) * a_dim1;
1187 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1188 i__1 = kp + (k - 1) * a_dim1;
1189 a[i__1].r = temp.r, a[i__1].i = temp.i;
1192 /* (2) Interchange rows and columns K-1 and -IPIV(K-1) */
1200 zswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 +
1201 kp * a_dim1], &c__1);
1205 for (j = k + 1; j <= i__1; ++j) {
1206 d_cnjg(&z__1, &a[j + k * a_dim1]);
1207 temp.r = z__1.r, temp.i = z__1.i;
1208 i__2 = j + k * a_dim1;
1209 d_cnjg(&z__1, &a[kp + j * a_dim1]);
1210 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
1211 i__2 = kp + j * a_dim1;
1212 a[i__2].r = temp.r, a[i__2].i = temp.i;
1216 i__1 = kp + k * a_dim1;
1217 d_cnjg(&z__1, &a[kp + k * a_dim1]);
1218 a[i__1].r = z__1.r, a[i__1].i = z__1.i;
1220 i__1 = k + k * a_dim1;
1221 temp.r = a[i__1].r, temp.i = a[i__1].i;
1222 i__1 = k + k * a_dim1;
1223 i__2 = kp + kp * a_dim1;
1224 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
1225 i__1 = kp + kp * a_dim1;
1226 a[i__1].r = temp.r, a[i__1].i = temp.i;
1238 /* End of ZHETRI_ROOK */
1240 } /* zhetri_rook__ */