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_b2 = {0.f,0.f};
516 static integer c__1 = 1;
518 /* > \brief \b CHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity t
519 ransformation (unblocked algorithm). */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download CHETD2 + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetd2.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetd2.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetd2.
542 /* SUBROUTINE CHETD2( UPLO, N, A, LDA, D, E, TAU, INFO ) */
545 /* INTEGER INFO, LDA, N */
546 /* REAL D( * ), E( * ) */
547 /* COMPLEX A( LDA, * ), TAU( * ) */
550 /* > \par Purpose: */
555 /* > CHETD2 reduces a complex Hermitian matrix A to real symmetric */
556 /* > tridiagonal form T by a unitary similarity transformation: */
557 /* > Q**H * A * Q = T. */
563 /* > \param[in] UPLO */
565 /* > UPLO is CHARACTER*1 */
566 /* > Specifies whether the upper or lower triangular part of the */
567 /* > Hermitian matrix A is stored: */
568 /* > = 'U': Upper triangular */
569 /* > = 'L': Lower triangular */
575 /* > The order of the matrix A. N >= 0. */
578 /* > \param[in,out] A */
580 /* > A is COMPLEX array, dimension (LDA,N) */
581 /* > On entry, the Hermitian matrix A. If UPLO = 'U', the leading */
582 /* > n-by-n upper triangular part of A contains the upper */
583 /* > triangular part of the matrix A, and the strictly lower */
584 /* > triangular part of A is not referenced. If UPLO = 'L', the */
585 /* > leading n-by-n lower triangular part of A contains the lower */
586 /* > triangular part of the matrix A, and the strictly upper */
587 /* > triangular part of A is not referenced. */
588 /* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */
589 /* > of A are overwritten by the corresponding elements of the */
590 /* > tridiagonal matrix T, and the elements above the first */
591 /* > superdiagonal, with the array TAU, represent the unitary */
592 /* > matrix Q as a product of elementary reflectors; if UPLO */
593 /* > = 'L', the diagonal and first subdiagonal of A are over- */
594 /* > written by the corresponding elements of the tridiagonal */
595 /* > matrix T, and the elements below the first subdiagonal, with */
596 /* > the array TAU, represent the unitary matrix Q as a product */
597 /* > of elementary reflectors. See Further Details. */
600 /* > \param[in] LDA */
602 /* > LDA is INTEGER */
603 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
606 /* > \param[out] D */
608 /* > D is REAL array, dimension (N) */
609 /* > The diagonal elements of the tridiagonal matrix T: */
610 /* > D(i) = A(i,i). */
613 /* > \param[out] E */
615 /* > E is REAL array, dimension (N-1) */
616 /* > The off-diagonal elements of the tridiagonal matrix T: */
617 /* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */
620 /* > \param[out] TAU */
622 /* > TAU is COMPLEX array, dimension (N-1) */
623 /* > The scalar factors of the elementary reflectors (see Further */
627 /* > \param[out] INFO */
629 /* > INFO is INTEGER */
630 /* > = 0: successful exit */
631 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
637 /* > \author Univ. of Tennessee */
638 /* > \author Univ. of California Berkeley */
639 /* > \author Univ. of Colorado Denver */
640 /* > \author NAG Ltd. */
642 /* > \date December 2016 */
644 /* > \ingroup complexHEcomputational */
646 /* > \par Further Details: */
647 /* ===================== */
651 /* > If UPLO = 'U', the matrix Q is represented as a product of elementary */
654 /* > Q = H(n-1) . . . H(2) H(1). */
656 /* > Each H(i) has the form */
658 /* > H(i) = I - tau * v * v**H */
660 /* > where tau is a complex scalar, and v is a complex vector with */
661 /* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */
662 /* > A(1:i-1,i+1), and tau in TAU(i). */
664 /* > If UPLO = 'L', the matrix Q is represented as a product of elementary */
667 /* > Q = H(1) H(2) . . . H(n-1). */
669 /* > Each H(i) has the form */
671 /* > H(i) = I - tau * v * v**H */
673 /* > where tau is a complex scalar, and v is a complex vector with */
674 /* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */
675 /* > and tau in TAU(i). */
677 /* > The contents of A on exit are illustrated by the following examples */
680 /* > if UPLO = 'U': if UPLO = 'L': */
682 /* > ( d e v2 v3 v4 ) ( d ) */
683 /* > ( d e v3 v4 ) ( e d ) */
684 /* > ( d e v4 ) ( v1 e d ) */
685 /* > ( d e ) ( v1 v2 e d ) */
686 /* > ( d ) ( v1 v2 v3 e d ) */
688 /* > where d and e denote diagonal and off-diagonal elements of T, and vi */
689 /* > denotes an element of the vector defining H(i). */
692 /* ===================================================================== */
693 /* Subroutine */ int chetd2_(char *uplo, integer *n, complex *a, integer *lda,
694 real *d__, real *e, complex *tau, integer *info)
696 /* System generated locals */
697 integer a_dim1, a_offset, i__1, i__2, i__3;
699 complex q__1, q__2, q__3, q__4;
701 /* Local variables */
703 extern /* Subroutine */ int cher2_(char *, integer *, complex *, complex *
704 , integer *, complex *, integer *, complex *, integer *);
707 extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
708 *, complex *, integer *);
709 extern logical lsame_(char *, char *);
710 extern /* Subroutine */ int chemv_(char *, integer *, complex *, complex *
711 , integer *, complex *, integer *, complex *, complex *, integer *
712 ), caxpy_(integer *, complex *, complex *, integer *,
713 complex *, integer *);
715 extern /* Subroutine */ int clarfg_(integer *, complex *, complex *,
716 integer *, complex *), xerbla_(char *, integer *, ftnlen);
719 /* -- LAPACK computational routine (version 3.7.0) -- */
720 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
721 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
725 /* ===================================================================== */
728 /* Test the input parameters */
730 /* Parameter adjustments */
732 a_offset = 1 + a_dim1 * 1;
740 upper = lsame_(uplo, "U");
741 if (! upper && ! lsame_(uplo, "L")) {
745 } else if (*lda < f2cmax(1,*n)) {
750 xerbla_("CHETD2", &i__1, (ftnlen)6);
754 /* Quick return if possible */
762 /* Reduce the upper triangle of A */
764 i__1 = *n + *n * a_dim1;
765 i__2 = *n + *n * a_dim1;
767 a[i__1].r = r__1, a[i__1].i = 0.f;
768 for (i__ = *n - 1; i__ >= 1; --i__) {
770 /* Generate elementary reflector H(i) = I - tau * v * v**H */
771 /* to annihilate A(1:i-1,i+1) */
773 i__1 = i__ + (i__ + 1) * a_dim1;
774 alpha.r = a[i__1].r, alpha.i = a[i__1].i;
775 clarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui);
779 if (taui.r != 0.f || taui.i != 0.f) {
781 /* Apply H(i) from both sides to A(1:i,1:i) */
783 i__1 = i__ + (i__ + 1) * a_dim1;
784 a[i__1].r = 1.f, a[i__1].i = 0.f;
786 /* Compute x := tau * A * v storing x in TAU(1:i) */
788 chemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) *
789 a_dim1 + 1], &c__1, &c_b2, &tau[1], &c__1);
791 /* Compute w := x - 1/2 * tau * (x**H * v) * v */
793 q__3.r = -.5f, q__3.i = 0.f;
794 q__2.r = q__3.r * taui.r - q__3.i * taui.i, q__2.i = q__3.r *
795 taui.i + q__3.i * taui.r;
796 cdotc_(&q__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1]
798 q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r *
799 q__4.i + q__2.i * q__4.r;
800 alpha.r = q__1.r, alpha.i = q__1.i;
801 caxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[
804 /* Apply the transformation as a rank-2 update: */
805 /* A := A - v * w**H - w * v**H */
807 q__1.r = -1.f, q__1.i = 0.f;
808 cher2_(uplo, &i__, &q__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, &
809 tau[1], &c__1, &a[a_offset], lda);
812 i__1 = i__ + i__ * a_dim1;
813 i__2 = i__ + i__ * a_dim1;
815 a[i__1].r = r__1, a[i__1].i = 0.f;
817 i__1 = i__ + (i__ + 1) * a_dim1;
819 a[i__1].r = e[i__2], a[i__1].i = 0.f;
821 i__2 = i__ + 1 + (i__ + 1) * a_dim1;
822 d__[i__1] = a[i__2].r;
824 tau[i__1].r = taui.r, tau[i__1].i = taui.i;
831 /* Reduce the lower triangle of A */
836 a[i__1].r = r__1, a[i__1].i = 0.f;
838 for (i__ = 1; i__ <= i__1; ++i__) {
840 /* Generate elementary reflector H(i) = I - tau * v * v**H */
841 /* to annihilate A(i+2:n,i) */
843 i__2 = i__ + 1 + i__ * a_dim1;
844 alpha.r = a[i__2].r, alpha.i = a[i__2].i;
848 clarfg_(&i__2, &alpha, &a[f2cmin(i__3,*n) + i__ * a_dim1], &c__1, &
853 if (taui.r != 0.f || taui.i != 0.f) {
855 /* Apply H(i) from both sides to A(i+1:n,i+1:n) */
857 i__2 = i__ + 1 + i__ * a_dim1;
858 a[i__2].r = 1.f, a[i__2].i = 0.f;
860 /* Compute x := tau * A * v storing y in TAU(i:n-1) */
863 chemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1],
864 lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b2, &tau[
867 /* Compute w := x - 1/2 * tau * (x**H * v) * v */
869 q__3.r = -.5f, q__3.i = 0.f;
870 q__2.r = q__3.r * taui.r - q__3.i * taui.i, q__2.i = q__3.r *
871 taui.i + q__3.i * taui.r;
873 cdotc_(&q__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ *
875 q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r *
876 q__4.i + q__2.i * q__4.r;
877 alpha.r = q__1.r, alpha.i = q__1.i;
879 caxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
882 /* Apply the transformation as a rank-2 update: */
883 /* A := A - v * w**H - w * v**H */
886 q__1.r = -1.f, q__1.i = 0.f;
887 cher2_(uplo, &i__2, &q__1, &a[i__ + 1 + i__ * a_dim1], &c__1,
888 &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1],
892 i__2 = i__ + 1 + (i__ + 1) * a_dim1;
893 i__3 = i__ + 1 + (i__ + 1) * a_dim1;
895 a[i__2].r = r__1, a[i__2].i = 0.f;
897 i__2 = i__ + 1 + i__ * a_dim1;
899 a[i__2].r = e[i__3], a[i__2].i = 0.f;
901 i__3 = i__ + i__ * a_dim1;
902 d__[i__2] = a[i__3].r;
904 tau[i__2].r = taui.r, tau[i__2].i = taui.i;
908 i__2 = *n + *n * a_dim1;
909 d__[i__1] = a[i__2].r;