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 ZSYTRS_ROOK */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download ZSYTRS_ROOK + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytrs_
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytrs_
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrs_
541 /* SUBROUTINE ZSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) */
544 /* INTEGER INFO, LDA, LDB, N, NRHS */
545 /* INTEGER IPIV( * ) */
546 /* COMPLEX*16 A( LDA, * ), B( LDB, * ) */
549 /* > \par Purpose: */
554 /* > ZSYTRS_ROOK solves a system of linear equations A*X = B with */
555 /* > a complex symmetric matrix A using the factorization A = U*D*U**T or */
556 /* > A = L*D*L**T computed by ZSYTRF_ROOK. */
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. */
586 /* > A is COMPLEX*16 array, dimension (LDA,N) */
587 /* > The block diagonal matrix D and the multipliers used to */
588 /* > obtain the factor U or L as computed by ZSYTRF_ROOK. */
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 block structure of D */
601 /* > as determined by ZSYTRF_ROOK. */
604 /* > \param[in,out] B */
606 /* > B is COMPLEX*16 array, dimension (LDB,NRHS) */
607 /* > On entry, the right hand side matrix B. */
608 /* > On exit, the solution matrix X. */
611 /* > \param[in] LDB */
613 /* > LDB is INTEGER */
614 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
617 /* > \param[out] INFO */
619 /* > INFO is INTEGER */
620 /* > = 0: successful exit */
621 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
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 complex16SYcomputational */
636 /* > \par Contributors: */
637 /* ================== */
641 /* > December 2016, Igor Kozachenko, */
642 /* > Computer Science Division, */
643 /* > University of California, Berkeley */
645 /* > September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, */
646 /* > School of Mathematics, */
647 /* > University of Manchester */
651 /* ===================================================================== */
652 /* Subroutine */ int zsytrs_rook_(char *uplo, integer *n, integer *nrhs,
653 doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b,
654 integer *ldb, integer *info)
656 /* System generated locals */
657 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
658 doublecomplex z__1, z__2, z__3;
660 /* Local variables */
663 extern logical lsame_(char *, char *);
665 extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
666 doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
667 doublecomplex *, doublecomplex *, integer *, doublecomplex *,
668 integer *, doublecomplex *, doublecomplex *, integer *);
670 extern /* Subroutine */ int zgeru_(integer *, integer *, doublecomplex *,
671 doublecomplex *, integer *, doublecomplex *, integer *,
672 doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
673 integer *, doublecomplex *, integer *);
674 doublecomplex ak, bk;
676 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
677 doublecomplex akm1, bkm1;
680 /* -- LAPACK computational routine (version 3.7.0) -- */
681 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
682 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
686 /* ===================================================================== */
689 /* Parameter adjustments */
691 a_offset = 1 + a_dim1 * 1;
695 b_offset = 1 + b_dim1 * 1;
700 upper = lsame_(uplo, "U");
701 if (! upper && ! lsame_(uplo, "L")) {
705 } else if (*nrhs < 0) {
707 } else if (*lda < f2cmax(1,*n)) {
709 } else if (*ldb < f2cmax(1,*n)) {
714 xerbla_("ZSYTRS_ROOK", &i__1, (ftnlen)11);
718 /* Quick return if possible */
720 if (*n == 0 || *nrhs == 0) {
726 /* Solve A*X = B, where A = U*D*U**T. */
728 /* First solve U*D*X = B, overwriting B with X. */
730 /* K is the main loop index, decreasing from N to 1 in steps of */
731 /* 1 or 2, depending on the size of the diagonal blocks. */
736 /* If K < 1, exit from loop. */
744 /* 1 x 1 diagonal block */
746 /* Interchange rows K and IPIV(K). */
750 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
753 /* Multiply by inv(U(K)), where U(K) is the transformation */
754 /* stored in column K of A. */
757 z__1.r = -1., z__1.i = 0.;
758 zgeru_(&i__1, nrhs, &z__1, &a[k * a_dim1 + 1], &c__1, &b[k +
759 b_dim1], ldb, &b[b_dim1 + 1], ldb);
761 /* Multiply by the inverse of the diagonal block. */
763 z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
764 zscal_(nrhs, &z__1, &b[k + b_dim1], ldb);
768 /* 2 x 2 diagonal block */
770 /* Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1) */
774 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
779 zswap_(nrhs, &b[k - 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
782 /* Multiply by inv(U(K)), where U(K) is the transformation */
783 /* stored in columns K-1 and K of A. */
787 z__1.r = -1., z__1.i = 0.;
788 zgeru_(&i__1, nrhs, &z__1, &a[k * a_dim1 + 1], &c__1, &b[k +
789 b_dim1], ldb, &b[b_dim1 + 1], ldb);
791 z__1.r = -1., z__1.i = 0.;
792 zgeru_(&i__1, nrhs, &z__1, &a[(k - 1) * a_dim1 + 1], &c__1, &
793 b[k - 1 + b_dim1], ldb, &b[b_dim1 + 1], ldb);
796 /* Multiply by the inverse of the diagonal block. */
798 i__1 = k - 1 + k * a_dim1;
799 akm1k.r = a[i__1].r, akm1k.i = a[i__1].i;
800 z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &akm1k);
801 akm1.r = z__1.r, akm1.i = z__1.i;
802 z_div(&z__1, &a[k + k * a_dim1], &akm1k);
803 ak.r = z__1.r, ak.i = z__1.i;
804 z__2.r = akm1.r * ak.r - akm1.i * ak.i, z__2.i = akm1.r * ak.i +
806 z__1.r = z__2.r - 1., z__1.i = z__2.i + 0.;
807 denom.r = z__1.r, denom.i = z__1.i;
809 for (j = 1; j <= i__1; ++j) {
810 z_div(&z__1, &b[k - 1 + j * b_dim1], &akm1k);
811 bkm1.r = z__1.r, bkm1.i = z__1.i;
812 z_div(&z__1, &b[k + j * b_dim1], &akm1k);
813 bk.r = z__1.r, bk.i = z__1.i;
814 i__2 = k - 1 + j * b_dim1;
815 z__3.r = ak.r * bkm1.r - ak.i * bkm1.i, z__3.i = ak.r *
816 bkm1.i + ak.i * bkm1.r;
817 z__2.r = z__3.r - bk.r, z__2.i = z__3.i - bk.i;
818 z_div(&z__1, &z__2, &denom);
819 b[i__2].r = z__1.r, b[i__2].i = z__1.i;
820 i__2 = k + j * b_dim1;
821 z__3.r = akm1.r * bk.r - akm1.i * bk.i, z__3.i = akm1.r *
822 bk.i + akm1.i * bk.r;
823 z__2.r = z__3.r - bkm1.r, z__2.i = z__3.i - bkm1.i;
824 z_div(&z__1, &z__2, &denom);
825 b[i__2].r = z__1.r, b[i__2].i = z__1.i;
834 /* Next solve U**T *X = B, overwriting B with X. */
836 /* K is the main loop index, increasing from 1 to N in steps of */
837 /* 1 or 2, depending on the size of the diagonal blocks. */
842 /* If K > N, exit from loop. */
850 /* 1 x 1 diagonal block */
852 /* Multiply by inv(U**T(K)), where U(K) is the transformation */
853 /* stored in column K of A. */
857 z__1.r = -1., z__1.i = 0.;
858 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &a[
859 k * a_dim1 + 1], &c__1, &c_b1, &b[k + b_dim1], ldb);
862 /* Interchange rows K and IPIV(K). */
866 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
871 /* 2 x 2 diagonal block */
873 /* Multiply by inv(U**T(K+1)), where U(K+1) is the transformation */
874 /* stored in columns K and K+1 of A. */
878 z__1.r = -1., z__1.i = 0.;
879 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &a[
880 k * a_dim1 + 1], &c__1, &c_b1, &b[k + b_dim1], ldb);
882 z__1.r = -1., z__1.i = 0.;
883 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &a[
884 (k + 1) * a_dim1 + 1], &c__1, &c_b1, &b[k + 1 +
888 /* Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1). */
892 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
897 zswap_(nrhs, &b[k + 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
909 /* Solve A*X = B, where A = L*D*L**T. */
911 /* First solve L*D*X = B, overwriting B with X. */
913 /* K is the main loop index, increasing from 1 to N in steps of */
914 /* 1 or 2, depending on the size of the diagonal blocks. */
919 /* If K > N, exit from loop. */
927 /* 1 x 1 diagonal block */
929 /* Interchange rows K and IPIV(K). */
933 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
936 /* Multiply by inv(L(K)), where L(K) is the transformation */
937 /* stored in column K of A. */
941 z__1.r = -1., z__1.i = 0.;
942 zgeru_(&i__1, nrhs, &z__1, &a[k + 1 + k * a_dim1], &c__1, &b[
943 k + b_dim1], ldb, &b[k + 1 + b_dim1], ldb);
946 /* Multiply by the inverse of the diagonal block. */
948 z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
949 zscal_(nrhs, &z__1, &b[k + b_dim1], ldb);
953 /* 2 x 2 diagonal block */
955 /* Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1) */
959 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
964 zswap_(nrhs, &b[k + 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
967 /* Multiply by inv(L(K)), where L(K) is the transformation */
968 /* stored in columns K and K+1 of A. */
972 z__1.r = -1., z__1.i = 0.;
973 zgeru_(&i__1, nrhs, &z__1, &a[k + 2 + k * a_dim1], &c__1, &b[
974 k + b_dim1], ldb, &b[k + 2 + b_dim1], ldb);
976 z__1.r = -1., z__1.i = 0.;
977 zgeru_(&i__1, nrhs, &z__1, &a[k + 2 + (k + 1) * a_dim1], &
978 c__1, &b[k + 1 + b_dim1], ldb, &b[k + 2 + b_dim1],
982 /* Multiply by the inverse of the diagonal block. */
984 i__1 = k + 1 + k * a_dim1;
985 akm1k.r = a[i__1].r, akm1k.i = a[i__1].i;
986 z_div(&z__1, &a[k + k * a_dim1], &akm1k);
987 akm1.r = z__1.r, akm1.i = z__1.i;
988 z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &akm1k);
989 ak.r = z__1.r, ak.i = z__1.i;
990 z__2.r = akm1.r * ak.r - akm1.i * ak.i, z__2.i = akm1.r * ak.i +
992 z__1.r = z__2.r - 1., z__1.i = z__2.i + 0.;
993 denom.r = z__1.r, denom.i = z__1.i;
995 for (j = 1; j <= i__1; ++j) {
996 z_div(&z__1, &b[k + j * b_dim1], &akm1k);
997 bkm1.r = z__1.r, bkm1.i = z__1.i;
998 z_div(&z__1, &b[k + 1 + j * b_dim1], &akm1k);
999 bk.r = z__1.r, bk.i = z__1.i;
1000 i__2 = k + j * b_dim1;
1001 z__3.r = ak.r * bkm1.r - ak.i * bkm1.i, z__3.i = ak.r *
1002 bkm1.i + ak.i * bkm1.r;
1003 z__2.r = z__3.r - bk.r, z__2.i = z__3.i - bk.i;
1004 z_div(&z__1, &z__2, &denom);
1005 b[i__2].r = z__1.r, b[i__2].i = z__1.i;
1006 i__2 = k + 1 + j * b_dim1;
1007 z__3.r = akm1.r * bk.r - akm1.i * bk.i, z__3.i = akm1.r *
1008 bk.i + akm1.i * bk.r;
1009 z__2.r = z__3.r - bkm1.r, z__2.i = z__3.i - bkm1.i;
1010 z_div(&z__1, &z__2, &denom);
1011 b[i__2].r = z__1.r, b[i__2].i = z__1.i;
1020 /* Next solve L**T *X = B, overwriting B with X. */
1022 /* K is the main loop index, decreasing from N to 1 in steps of */
1023 /* 1 or 2, depending on the size of the diagonal blocks. */
1028 /* If K < 1, exit from loop. */
1036 /* 1 x 1 diagonal block */
1038 /* Multiply by inv(L**T(K)), where L(K) is the transformation */
1039 /* stored in column K of A. */
1043 z__1.r = -1., z__1.i = 0.;
1044 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1],
1045 ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b1, &b[k +
1049 /* Interchange rows K and IPIV(K). */
1053 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
1058 /* 2 x 2 diagonal block */
1060 /* Multiply by inv(L**T(K-1)), where L(K-1) is the transformation */
1061 /* stored in columns K-1 and K of A. */
1065 z__1.r = -1., z__1.i = 0.;
1066 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1],
1067 ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b1, &b[k +
1070 z__1.r = -1., z__1.i = 0.;
1071 zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1],
1072 ldb, &a[k + 1 + (k - 1) * a_dim1], &c__1, &c_b1, &b[k
1073 - 1 + b_dim1], ldb);
1076 /* Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1) */
1080 zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
1085 zswap_(nrhs, &b[k - 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
1098 /* End of ZSYTRS_ROOK */
1100 } /* zsytrs_rook__ */