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 integer c__1 = 1;
518 /* > \brief \b ZSPTRS */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download ZSPTRS + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsptrs.
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsptrs.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsptrs.
541 /* SUBROUTINE ZSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) */
544 /* INTEGER INFO, LDB, N, NRHS */
545 /* INTEGER IPIV( * ) */
546 /* COMPLEX*16 AP( * ), B( LDB, * ) */
549 /* > \par Purpose: */
554 /* > ZSPTRS solves a system of linear equations A*X = B with a complex */
555 /* > symmetric matrix A stored in packed format using the factorization */
556 /* > A = U*D*U**T or A = L*D*L**T computed by ZSPTRF. */
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] NRHS */
579 /* > NRHS is INTEGER */
580 /* > The number of right hand sides, i.e., the number of columns */
581 /* > of the matrix B. NRHS >= 0. */
584 /* > \param[in] AP */
586 /* > AP is COMPLEX*16 array, dimension (N*(N+1)/2) */
587 /* > The block diagonal matrix D and the multipliers used to */
588 /* > obtain the factor U or L as computed by ZSPTRF, stored as a */
589 /* > packed triangular matrix. */
592 /* > \param[in] IPIV */
594 /* > IPIV is INTEGER array, dimension (N) */
595 /* > Details of the interchanges and the block structure of D */
596 /* > as determined by ZSPTRF. */
599 /* > \param[in,out] B */
601 /* > B is COMPLEX*16 array, dimension (LDB,NRHS) */
602 /* > On entry, the right hand side matrix B. */
603 /* > On exit, the solution matrix X. */
606 /* > \param[in] LDB */
608 /* > LDB is INTEGER */
609 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
612 /* > \param[out] INFO */
614 /* > INFO is INTEGER */
615 /* > = 0: successful exit */
616 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
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 complex16OTHERcomputational */
631 /* ===================================================================== */
632 /* Subroutine */ int zsptrs_(char *uplo, integer *n, integer *nrhs,
633 doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb,
636 /* System generated locals */
637 integer b_dim1, b_offset, i__1, i__2;
638 doublecomplex z__1, z__2, z__3;
640 /* Local variables */
643 extern logical lsame_(char *, char *);
645 extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
646 doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
647 doublecomplex *, doublecomplex *, integer *, doublecomplex *,
648 integer *, doublecomplex *, doublecomplex *, integer *);
650 extern /* Subroutine */ int zgeru_(integer *, integer *, doublecomplex *,
651 doublecomplex *, integer *, doublecomplex *, integer *,
652 doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
653 integer *, doublecomplex *, integer *);
654 doublecomplex ak, bk;
656 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
657 doublecomplex akm1, bkm1;
660 /* -- LAPACK computational routine (version 3.7.0) -- */
661 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
662 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
666 /* ===================================================================== */
669 /* Parameter adjustments */
673 b_offset = 1 + b_dim1 * 1;
678 upper = lsame_(uplo, "U");
679 if (! upper && ! lsame_(uplo, "L")) {
683 } else if (*nrhs < 0) {
685 } else if (*ldb < f2cmax(1,*n)) {
690 xerbla_("ZSPTRS", &i__1, (ftnlen)6);
694 /* Quick return if possible */
696 if (*n == 0 || *nrhs == 0) {
702 /* Solve A*X = B, where A = U*D*U**T. */
704 /* First solve U*D*X = B, overwriting B with X. */
706 /* K is the main loop index, decreasing from N to 1 in steps of */
707 /* 1 or 2, depending on the size of the diagonal blocks. */
710 kc = *n * (*n + 1) / 2 + 1;
713 /* If K < 1, exit from loop. */
722 /* 1 x 1 diagonal block */
724 /* Interchange rows K and IPIV(K). */
728 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
731 /* Multiply by inv(U(K)), where U(K) is the transformation */
732 /* stored in column K of A. */
735 z__1.r = -1., z__1.i = 0.;
736 zgeru_(&i__1, nrhs, &z__1, &ap[kc], &c__1, &b[k + b_dim1], ldb, &
739 /* Multiply by the inverse of the diagonal block. */
741 z_div(&z__1, &c_b1, &ap[kc + k - 1]);
742 zscal_(nrhs, &z__1, &b[k + b_dim1], ldb);
746 /* 2 x 2 diagonal block */
748 /* Interchange rows K-1 and -IPIV(K). */
752 zswap_(nrhs, &b[k - 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
755 /* Multiply by inv(U(K)), where U(K) is the transformation */
756 /* stored in columns K-1 and K of A. */
759 z__1.r = -1., z__1.i = 0.;
760 zgeru_(&i__1, nrhs, &z__1, &ap[kc], &c__1, &b[k + b_dim1], ldb, &
763 z__1.r = -1., z__1.i = 0.;
764 zgeru_(&i__1, nrhs, &z__1, &ap[kc - (k - 1)], &c__1, &b[k - 1 +
765 b_dim1], ldb, &b[b_dim1 + 1], ldb);
767 /* Multiply by the inverse of the diagonal block. */
770 akm1k.r = ap[i__1].r, akm1k.i = ap[i__1].i;
771 z_div(&z__1, &ap[kc - 1], &akm1k);
772 akm1.r = z__1.r, akm1.i = z__1.i;
773 z_div(&z__1, &ap[kc + k - 1], &akm1k);
774 ak.r = z__1.r, ak.i = z__1.i;
775 z__2.r = akm1.r * ak.r - akm1.i * ak.i, z__2.i = akm1.r * ak.i +
777 z__1.r = z__2.r - 1., z__1.i = z__2.i + 0.;
778 denom.r = z__1.r, denom.i = z__1.i;
780 for (j = 1; j <= i__1; ++j) {
781 z_div(&z__1, &b[k - 1 + j * b_dim1], &akm1k);
782 bkm1.r = z__1.r, bkm1.i = z__1.i;
783 z_div(&z__1, &b[k + j * b_dim1], &akm1k);
784 bk.r = z__1.r, bk.i = z__1.i;
785 i__2 = k - 1 + j * b_dim1;
786 z__3.r = ak.r * bkm1.r - ak.i * bkm1.i, z__3.i = ak.r *
787 bkm1.i + ak.i * bkm1.r;
788 z__2.r = z__3.r - bk.r, z__2.i = z__3.i - bk.i;
789 z_div(&z__1, &z__2, &denom);
790 b[i__2].r = z__1.r, b[i__2].i = z__1.i;
791 i__2 = k + j * b_dim1;
792 z__3.r = akm1.r * bk.r - akm1.i * bk.i, z__3.i = akm1.r *
793 bk.i + akm1.i * bk.r;
794 z__2.r = z__3.r - bkm1.r, z__2.i = z__3.i - bkm1.i;
795 z_div(&z__1, &z__2, &denom);
796 b[i__2].r = z__1.r, b[i__2].i = z__1.i;
806 /* Next solve U**T*X = B, overwriting B with X. */
808 /* K is the main loop index, increasing from 1 to N in steps of */
809 /* 1 or 2, depending on the size of the diagonal blocks. */
815 /* If K > N, exit from loop. */
823 /* 1 x 1 diagonal block */
825 /* Multiply by inv(U**T(K)), where U(K) is the transformation */
826 /* stored in column K of A. */
829 z__1.r = -1., z__1.i = 0.;
830 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &ap[kc]
831 , &c__1, &c_b1, &b[k + b_dim1], ldb);
833 /* Interchange rows K and IPIV(K). */
837 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
843 /* 2 x 2 diagonal block */
845 /* Multiply by inv(U**T(K+1)), where U(K+1) is the transformation */
846 /* stored in columns K and K+1 of A. */
849 z__1.r = -1., z__1.i = 0.;
850 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &ap[kc]
851 , &c__1, &c_b1, &b[k + b_dim1], ldb);
853 z__1.r = -1., z__1.i = 0.;
854 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &ap[kc
855 + k], &c__1, &c_b1, &b[k + 1 + b_dim1], ldb);
857 /* Interchange rows K and -IPIV(K). */
861 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
863 kc = kc + (k << 1) + 1;
873 /* Solve A*X = B, where A = L*D*L**T. */
875 /* First solve L*D*X = B, overwriting B with X. */
877 /* K is the main loop index, increasing from 1 to N in steps of */
878 /* 1 or 2, depending on the size of the diagonal blocks. */
884 /* If K > N, exit from loop. */
892 /* 1 x 1 diagonal block */
894 /* Interchange rows K and IPIV(K). */
898 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
901 /* Multiply by inv(L(K)), where L(K) is the transformation */
902 /* stored in column K of A. */
906 z__1.r = -1., z__1.i = 0.;
907 zgeru_(&i__1, nrhs, &z__1, &ap[kc + 1], &c__1, &b[k + b_dim1],
908 ldb, &b[k + 1 + b_dim1], ldb);
911 /* Multiply by the inverse of the diagonal block. */
913 z_div(&z__1, &c_b1, &ap[kc]);
914 zscal_(nrhs, &z__1, &b[k + b_dim1], ldb);
915 kc = kc + *n - k + 1;
919 /* 2 x 2 diagonal block */
921 /* Interchange rows K+1 and -IPIV(K). */
925 zswap_(nrhs, &b[k + 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
928 /* Multiply by inv(L(K)), where L(K) is the transformation */
929 /* stored in columns K and K+1 of A. */
933 z__1.r = -1., z__1.i = 0.;
934 zgeru_(&i__1, nrhs, &z__1, &ap[kc + 2], &c__1, &b[k + b_dim1],
935 ldb, &b[k + 2 + b_dim1], ldb);
937 z__1.r = -1., z__1.i = 0.;
938 zgeru_(&i__1, nrhs, &z__1, &ap[kc + *n - k + 2], &c__1, &b[k
939 + 1 + b_dim1], ldb, &b[k + 2 + b_dim1], ldb);
942 /* Multiply by the inverse of the diagonal block. */
945 akm1k.r = ap[i__1].r, akm1k.i = ap[i__1].i;
946 z_div(&z__1, &ap[kc], &akm1k);
947 akm1.r = z__1.r, akm1.i = z__1.i;
948 z_div(&z__1, &ap[kc + *n - k + 1], &akm1k);
949 ak.r = z__1.r, ak.i = z__1.i;
950 z__2.r = akm1.r * ak.r - akm1.i * ak.i, z__2.i = akm1.r * ak.i +
952 z__1.r = z__2.r - 1., z__1.i = z__2.i + 0.;
953 denom.r = z__1.r, denom.i = z__1.i;
955 for (j = 1; j <= i__1; ++j) {
956 z_div(&z__1, &b[k + j * b_dim1], &akm1k);
957 bkm1.r = z__1.r, bkm1.i = z__1.i;
958 z_div(&z__1, &b[k + 1 + j * b_dim1], &akm1k);
959 bk.r = z__1.r, bk.i = z__1.i;
960 i__2 = k + j * b_dim1;
961 z__3.r = ak.r * bkm1.r - ak.i * bkm1.i, z__3.i = ak.r *
962 bkm1.i + ak.i * bkm1.r;
963 z__2.r = z__3.r - bk.r, z__2.i = z__3.i - bk.i;
964 z_div(&z__1, &z__2, &denom);
965 b[i__2].r = z__1.r, b[i__2].i = z__1.i;
966 i__2 = k + 1 + j * b_dim1;
967 z__3.r = akm1.r * bk.r - akm1.i * bk.i, z__3.i = akm1.r *
968 bk.i + akm1.i * bk.r;
969 z__2.r = z__3.r - bkm1.r, z__2.i = z__3.i - bkm1.i;
970 z_div(&z__1, &z__2, &denom);
971 b[i__2].r = z__1.r, b[i__2].i = z__1.i;
974 kc = kc + (*n - k << 1) + 1;
981 /* Next solve L**T*X = B, overwriting B with X. */
983 /* K is the main loop index, decreasing from N to 1 in steps of */
984 /* 1 or 2, depending on the size of the diagonal blocks. */
987 kc = *n * (*n + 1) / 2 + 1;
990 /* If K < 1, exit from loop. */
999 /* 1 x 1 diagonal block */
1001 /* Multiply by inv(L**T(K)), where L(K) is the transformation */
1002 /* stored in column K of A. */
1006 z__1.r = -1., z__1.i = 0.;
1007 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1],
1008 ldb, &ap[kc + 1], &c__1, &c_b1, &b[k + b_dim1], ldb);
1011 /* Interchange rows K and IPIV(K). */
1015 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
1020 /* 2 x 2 diagonal block */
1022 /* Multiply by inv(L**T(K-1)), where L(K-1) is the transformation */
1023 /* stored in columns K-1 and K of A. */
1027 z__1.r = -1., z__1.i = 0.;
1028 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1],
1029 ldb, &ap[kc + 1], &c__1, &c_b1, &b[k + b_dim1], ldb);
1031 z__1.r = -1., z__1.i = 0.;
1032 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1],
1033 ldb, &ap[kc - (*n - k)], &c__1, &c_b1, &b[k - 1 +
1037 /* Interchange rows K and -IPIV(K). */
1041 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);