14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static complex c_b1 = {0.f,0.f};
516 static complex c_b2 = {1.f,0.f};
517 static integer c__3 = 3;
518 static integer c__1 = 1;
520 /* > \brief \b CLAGSY */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
530 /* SUBROUTINE CLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) */
532 /* INTEGER INFO, K, LDA, N */
533 /* INTEGER ISEED( 4 ) */
535 /* COMPLEX A( LDA, * ), WORK( * ) */
538 /* > \par Purpose: */
543 /* > CLAGSY generates a complex symmetric matrix A, by pre- and post- */
544 /* > multiplying a real diagonal matrix D with a random unitary matrix: */
545 /* > A = U*D*U**T. The semi-bandwidth may then be reduced to k by */
546 /* > additional unitary transformations. */
555 /* > The order of the matrix A. N >= 0. */
561 /* > The number of nonzero subdiagonals within the band of A. */
562 /* > 0 <= K <= N-1. */
567 /* > D is REAL array, dimension (N) */
568 /* > The diagonal elements of the diagonal matrix D. */
571 /* > \param[out] A */
573 /* > A is COMPLEX array, dimension (LDA,N) */
574 /* > The generated n by n symmetric matrix A (the full matrix is */
578 /* > \param[in] LDA */
580 /* > LDA is INTEGER */
581 /* > The leading dimension of the array A. LDA >= N. */
584 /* > \param[in,out] ISEED */
586 /* > ISEED is INTEGER array, dimension (4) */
587 /* > On entry, the seed of the random number generator; the array */
588 /* > elements must be between 0 and 4095, and ISEED(4) must be */
590 /* > On exit, the seed is updated. */
593 /* > \param[out] WORK */
595 /* > WORK is COMPLEX array, dimension (2*N) */
598 /* > \param[out] INFO */
600 /* > INFO is INTEGER */
601 /* > = 0: successful exit */
602 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
608 /* > \author Univ. of Tennessee */
609 /* > \author Univ. of California Berkeley */
610 /* > \author Univ. of Colorado Denver */
611 /* > \author NAG Ltd. */
613 /* > \date December 2016 */
615 /* > \ingroup complex_matgen */
617 /* ===================================================================== */
618 /* Subroutine */ int clagsy_(integer *n, integer *k, real *d__, complex *a,
619 integer *lda, integer *iseed, complex *work, integer *info)
621 /* System generated locals */
622 integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8,
625 complex q__1, q__2, q__3, q__4;
627 /* Local variables */
629 extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
630 complex *, integer *, complex *, integer *, complex *, integer *);
632 extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
634 extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
635 *, complex *, integer *);
636 extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
637 , complex *, integer *, complex *, integer *, complex *, complex *
638 , integer *), caxpy_(integer *, complex *, complex *,
639 integer *, complex *, integer *), csymv_(char *, integer *,
640 complex *, complex *, integer *, complex *, integer *, complex *,
641 complex *, integer *);
642 extern real scnrm2_(integer *, complex *, integer *);
645 extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
647 extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_(
648 integer *, integer *, integer *, complex *);
652 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
653 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
654 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
658 /* ===================================================================== */
661 /* Test the input arguments */
663 /* Parameter adjustments */
666 a_offset = 1 + a_dim1 * 1;
675 } else if (*k < 0 || *k > *n - 1) {
677 } else if (*lda < f2cmax(1,*n)) {
682 xerbla_("CLAGSY", &i__1);
686 /* initialize lower triangle of A to diagonal matrix */
689 for (j = 1; j <= i__1; ++j) {
691 for (i__ = j + 1; i__ <= i__2; ++i__) {
692 i__3 = i__ + j * a_dim1;
693 a[i__3].r = 0.f, a[i__3].i = 0.f;
699 for (i__ = 1; i__ <= i__1; ++i__) {
700 i__2 = i__ + i__ * a_dim1;
702 a[i__2].r = d__[i__3], a[i__2].i = 0.f;
706 /* Generate lower triangle of symmetric matrix */
708 for (i__ = *n - 1; i__ >= 1; --i__) {
710 /* generate random reflection */
713 clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
715 wn = scnrm2_(&i__1, &work[1], &c__1);
716 r__1 = wn / c_abs(&work[1]);
717 q__1.r = r__1 * work[1].r, q__1.i = r__1 * work[1].i;
718 wa.r = q__1.r, wa.i = q__1.i;
720 tau.r = 0.f, tau.i = 0.f;
722 q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
723 wb.r = q__1.r, wb.i = q__1.i;
725 c_div(&q__1, &c_b2, &wb);
726 cscal_(&i__1, &q__1, &work[2], &c__1);
727 work[1].r = 1.f, work[1].i = 0.f;
728 c_div(&q__1, &wb, &wa);
730 tau.r = r__1, tau.i = 0.f;
733 /* apply random reflection to A(i:n,i:n) from the left */
736 /* compute y := tau * A * conjg(u) */
739 clacgv_(&i__1, &work[1], &c__1);
741 csymv_("Lower", &i__1, &tau, &a[i__ + i__ * a_dim1], lda, &work[1], &
742 c__1, &c_b1, &work[*n + 1], &c__1);
744 clacgv_(&i__1, &work[1], &c__1);
746 /* compute v := y - 1/2 * tau * ( u, y ) * u */
748 q__3.r = -.5f, q__3.i = 0.f;
749 q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
752 cdotc_(&q__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1);
753 q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
755 alpha.r = q__1.r, alpha.i = q__1.i;
757 caxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);
759 /* apply the transformation as a rank-2 update to A(i:n,i:n) */
761 /* CALL CSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1, */
762 /* $ A( I, I ), LDA ) */
765 for (jj = i__; jj <= i__1; ++jj) {
767 for (ii = jj; ii <= i__2; ++ii) {
768 i__3 = ii + jj * a_dim1;
769 i__4 = ii + jj * a_dim1;
771 i__6 = *n + jj - i__ + 1;
772 q__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[
773 i__6].i, q__3.i = work[i__5].r * work[i__6].i + work[
774 i__5].i * work[i__6].r;
775 q__2.r = a[i__4].r - q__3.r, q__2.i = a[i__4].i - q__3.i;
776 i__7 = *n + ii - i__ + 1;
778 q__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[
779 i__8].i, q__4.i = work[i__7].r * work[i__8].i + work[
780 i__7].i * work[i__8].r;
781 q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
782 a[i__3].r = q__1.r, a[i__3].i = q__1.i;
790 /* Reduce number of subdiagonals to K */
793 for (i__ = 1; i__ <= i__1; ++i__) {
795 /* generate reflection to annihilate A(k+i+1:n,i) */
797 i__2 = *n - *k - i__ + 1;
798 wn = scnrm2_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
799 r__1 = wn / c_abs(&a[*k + i__ + i__ * a_dim1]);
800 i__2 = *k + i__ + i__ * a_dim1;
801 q__1.r = r__1 * a[i__2].r, q__1.i = r__1 * a[i__2].i;
802 wa.r = q__1.r, wa.i = q__1.i;
804 tau.r = 0.f, tau.i = 0.f;
806 i__2 = *k + i__ + i__ * a_dim1;
807 q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
808 wb.r = q__1.r, wb.i = q__1.i;
809 i__2 = *n - *k - i__;
810 c_div(&q__1, &c_b2, &wb);
811 cscal_(&i__2, &q__1, &a[*k + i__ + 1 + i__ * a_dim1], &c__1);
812 i__2 = *k + i__ + i__ * a_dim1;
813 a[i__2].r = 1.f, a[i__2].i = 0.f;
814 c_div(&q__1, &wb, &wa);
816 tau.r = r__1, tau.i = 0.f;
819 /* apply reflection to A(k+i:n,i+1:k+i-1) from the left */
821 i__2 = *n - *k - i__ + 1;
823 cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i__ + (i__
824 + 1) * a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &
825 c_b1, &work[1], &c__1);
826 i__2 = *n - *k - i__ + 1;
828 q__1.r = -tau.r, q__1.i = -tau.i;
829 cgerc_(&i__2, &i__3, &q__1, &a[*k + i__ + i__ * a_dim1], &c__1, &work[
830 1], &c__1, &a[*k + i__ + (i__ + 1) * a_dim1], lda);
832 /* apply reflection to A(k+i:n,k+i:n) from the left and the right */
834 /* compute y := tau * A * conjg(u) */
836 i__2 = *n - *k - i__ + 1;
837 clacgv_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
838 i__2 = *n - *k - i__ + 1;
839 csymv_("Lower", &i__2, &tau, &a[*k + i__ + (*k + i__) * a_dim1], lda,
840 &a[*k + i__ + i__ * a_dim1], &c__1, &c_b1, &work[1], &c__1);
841 i__2 = *n - *k - i__ + 1;
842 clacgv_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
844 /* compute v := y - 1/2 * tau * ( u, y ) * u */
846 q__3.r = -.5f, q__3.i = 0.f;
847 q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
849 i__2 = *n - *k - i__ + 1;
850 cdotc_(&q__4, &i__2, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
852 q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
854 alpha.r = q__1.r, alpha.i = q__1.i;
855 i__2 = *n - *k - i__ + 1;
856 caxpy_(&i__2, &alpha, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
859 /* apply symmetric rank-2 update to A(k+i:n,k+i:n) */
861 /* CALL CSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1, */
862 /* $ A( K+I, K+I ), LDA ) */
865 for (jj = *k + i__; jj <= i__2; ++jj) {
867 for (ii = jj; ii <= i__3; ++ii) {
868 i__4 = ii + jj * a_dim1;
869 i__5 = ii + jj * a_dim1;
870 i__6 = ii + i__ * a_dim1;
871 i__7 = jj - *k - i__ + 1;
872 q__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i,
873 q__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[
875 q__2.r = a[i__5].r - q__3.r, q__2.i = a[i__5].i - q__3.i;
876 i__8 = ii - *k - i__ + 1;
877 i__9 = jj + i__ * a_dim1;
878 q__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i,
879 q__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[
881 q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
882 a[i__4].r = q__1.r, a[i__4].i = q__1.i;
888 i__2 = *k + i__ + i__ * a_dim1;
889 q__1.r = -wa.r, q__1.i = -wa.i;
890 a[i__2].r = q__1.r, a[i__2].i = q__1.i;
892 for (j = *k + i__ + 1; j <= i__2; ++j) {
893 i__3 = j + i__ * a_dim1;
894 a[i__3].r = 0.f, a[i__3].i = 0.f;
900 /* Store full symmetric matrix */
903 for (j = 1; j <= i__1; ++j) {
905 for (i__ = j + 1; i__ <= i__2; ++i__) {
906 i__3 = j + i__ * a_dim1;
907 i__4 = i__ + j * a_dim1;
908 a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;