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__1 = 1;
519 /* > \brief \b CLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download CLABRD + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clabrd.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clabrd.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clabrd.
542 /* SUBROUTINE CLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, */
545 /* INTEGER LDA, LDX, LDY, M, N, NB */
546 /* REAL D( * ), E( * ) */
547 /* COMPLEX A( LDA, * ), TAUP( * ), TAUQ( * ), X( LDX, * ), */
551 /* > \par Purpose: */
556 /* > CLABRD reduces the first NB rows and columns of a complex general */
557 /* > m by n matrix A to upper or lower real bidiagonal form by a unitary */
558 /* > transformation Q**H * A * P, and returns the matrices X and Y which */
559 /* > are needed to apply the transformation to the unreduced part of A. */
561 /* > If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */
562 /* > bidiagonal form. */
564 /* > This is an auxiliary routine called by CGEBRD */
573 /* > The number of rows in the matrix A. */
579 /* > The number of columns in the matrix A. */
582 /* > \param[in] NB */
584 /* > NB is INTEGER */
585 /* > The number of leading rows and columns of A to be reduced. */
588 /* > \param[in,out] A */
590 /* > A is COMPLEX array, dimension (LDA,N) */
591 /* > On entry, the m by n general matrix to be reduced. */
592 /* > On exit, the first NB rows and columns of the matrix are */
593 /* > overwritten; the rest of the array is unchanged. */
594 /* > If m >= n, elements on and below the diagonal in the first NB */
595 /* > columns, with the array TAUQ, represent the unitary */
596 /* > matrix Q as a product of elementary reflectors; and */
597 /* > elements above the diagonal in the first NB rows, with the */
598 /* > array TAUP, represent the unitary matrix P as a product */
599 /* > of elementary reflectors. */
600 /* > If m < n, elements below the diagonal in the first NB */
601 /* > columns, with the array TAUQ, represent the unitary */
602 /* > matrix Q as a product of elementary reflectors, and */
603 /* > elements on and above the diagonal in the first NB rows, */
604 /* > with the array TAUP, represent the unitary matrix P as */
605 /* > a product of elementary reflectors. */
606 /* > See Further Details. */
609 /* > \param[in] LDA */
611 /* > LDA is INTEGER */
612 /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
615 /* > \param[out] D */
617 /* > D is REAL array, dimension (NB) */
618 /* > The diagonal elements of the first NB rows and columns of */
619 /* > the reduced matrix. D(i) = A(i,i). */
622 /* > \param[out] E */
624 /* > E is REAL array, dimension (NB) */
625 /* > The off-diagonal elements of the first NB rows and columns of */
626 /* > the reduced matrix. */
629 /* > \param[out] TAUQ */
631 /* > TAUQ is COMPLEX array, dimension (NB) */
632 /* > The scalar factors of the elementary reflectors which */
633 /* > represent the unitary matrix Q. See Further Details. */
636 /* > \param[out] TAUP */
638 /* > TAUP is COMPLEX array, dimension (NB) */
639 /* > The scalar factors of the elementary reflectors which */
640 /* > represent the unitary matrix P. See Further Details. */
643 /* > \param[out] X */
645 /* > X is COMPLEX array, dimension (LDX,NB) */
646 /* > The m-by-nb matrix X required to update the unreduced part */
650 /* > \param[in] LDX */
652 /* > LDX is INTEGER */
653 /* > The leading dimension of the array X. LDX >= f2cmax(1,M). */
656 /* > \param[out] Y */
658 /* > Y is COMPLEX array, dimension (LDY,NB) */
659 /* > The n-by-nb matrix Y required to update the unreduced part */
663 /* > \param[in] LDY */
665 /* > LDY is INTEGER */
666 /* > The leading dimension of the array Y. LDY >= f2cmax(1,N). */
672 /* > \author Univ. of Tennessee */
673 /* > \author Univ. of California Berkeley */
674 /* > \author Univ. of Colorado Denver */
675 /* > \author NAG Ltd. */
677 /* > \date June 2017 */
679 /* > \ingroup complexOTHERauxiliary */
681 /* > \par Further Details: */
682 /* ===================== */
686 /* > The matrices Q and P are represented as products of elementary */
689 /* > Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) */
691 /* > Each H(i) and G(i) has the form: */
693 /* > H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H */
695 /* > where tauq and taup are complex scalars, and v and u are complex */
698 /* > If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */
699 /* > A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */
700 /* > A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
702 /* > If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */
703 /* > A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */
704 /* > A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
706 /* > The elements of the vectors v and u together form the m-by-nb matrix */
707 /* > V and the nb-by-n matrix U**H which are needed, with X and Y, to apply */
708 /* > the transformation to the unreduced part of the matrix, using a block */
709 /* > update of the form: A := A - V*Y**H - X*U**H. */
711 /* > The contents of A on exit are illustrated by the following examples */
714 /* > m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */
716 /* > ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) */
717 /* > ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) */
718 /* > ( v1 v2 a a a ) ( v1 1 a a a a ) */
719 /* > ( v1 v2 a a a ) ( v1 v2 a a a a ) */
720 /* > ( v1 v2 a a a ) ( v1 v2 a a a a ) */
721 /* > ( v1 v2 a a a ) */
723 /* > where a denotes an element of the original matrix which is unchanged, */
724 /* > vi denotes an element of the vector defining H(i), and ui an element */
725 /* > of the vector defining G(i). */
728 /* ===================================================================== */
729 /* Subroutine */ int clabrd_(integer *m, integer *n, integer *nb, complex *a,
730 integer *lda, real *d__, real *e, complex *tauq, complex *taup,
731 complex *x, integer *ldx, complex *y, integer *ldy)
733 /* System generated locals */
734 integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2,
738 /* Local variables */
741 extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
742 integer *), cgemv_(char *, integer *, integer *, complex *,
743 complex *, integer *, complex *, integer *, complex *, complex *,
744 integer *), clarfg_(integer *, complex *, complex *,
745 integer *, complex *), clacgv_(integer *, complex *, integer *);
748 /* -- LAPACK auxiliary routine (version 3.7.1) -- */
749 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
750 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
754 /* ===================================================================== */
757 /* Quick return if possible */
759 /* Parameter adjustments */
761 a_offset = 1 + a_dim1 * 1;
768 x_offset = 1 + x_dim1 * 1;
771 y_offset = 1 + y_dim1 * 1;
775 if (*m <= 0 || *n <= 0) {
781 /* Reduce to upper bidiagonal form */
784 for (i__ = 1; i__ <= i__1; ++i__) {
786 /* Update A(i:m,i) */
789 clacgv_(&i__2, &y[i__ + y_dim1], ldy);
792 q__1.r = -1.f, q__1.i = 0.f;
793 cgemv_("No transpose", &i__2, &i__3, &q__1, &a[i__ + a_dim1], lda,
794 &y[i__ + y_dim1], ldy, &c_b2, &a[i__ + i__ * a_dim1], &
797 clacgv_(&i__2, &y[i__ + y_dim1], ldy);
800 q__1.r = -1.f, q__1.i = 0.f;
801 cgemv_("No transpose", &i__2, &i__3, &q__1, &x[i__ + x_dim1], ldx,
802 &a[i__ * a_dim1 + 1], &c__1, &c_b2, &a[i__ + i__ *
805 /* Generate reflection Q(i) to annihilate A(i+1:m,i) */
807 i__2 = i__ + i__ * a_dim1;
808 alpha.r = a[i__2].r, alpha.i = a[i__2].i;
812 clarfg_(&i__2, &alpha, &a[f2cmin(i__3,*m) + i__ * a_dim1], &c__1, &
817 i__2 = i__ + i__ * a_dim1;
818 a[i__2].r = 1.f, a[i__2].i = 0.f;
820 /* Compute Y(i+1:n,i) */
824 cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + (
825 i__ + 1) * a_dim1], lda, &a[i__ + i__ * a_dim1], &
826 c__1, &c_b1, &y[i__ + 1 + i__ * y_dim1], &c__1);
829 cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ +
830 a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b1, &
831 y[i__ * y_dim1 + 1], &c__1);
834 q__1.r = -1.f, q__1.i = 0.f;
835 cgemv_("No transpose", &i__2, &i__3, &q__1, &y[i__ + 1 +
836 y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b2, &y[
837 i__ + 1 + i__ * y_dim1], &c__1);
840 cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &x[i__ +
841 x_dim1], ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b1, &
842 y[i__ * y_dim1 + 1], &c__1);
845 q__1.r = -1.f, q__1.i = 0.f;
846 cgemv_("Conjugate transpose", &i__2, &i__3, &q__1, &a[(i__ +
847 1) * a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &
848 c_b2, &y[i__ + 1 + i__ * y_dim1], &c__1);
850 cscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
852 /* Update A(i,i+1:n) */
855 clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
856 clacgv_(&i__, &a[i__ + a_dim1], lda);
858 q__1.r = -1.f, q__1.i = 0.f;
859 cgemv_("No transpose", &i__2, &i__, &q__1, &y[i__ + 1 +
860 y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b2, &a[i__ + (
861 i__ + 1) * a_dim1], lda);
862 clacgv_(&i__, &a[i__ + a_dim1], lda);
864 clacgv_(&i__2, &x[i__ + x_dim1], ldx);
867 q__1.r = -1.f, q__1.i = 0.f;
868 cgemv_("Conjugate transpose", &i__2, &i__3, &q__1, &a[(i__ +
869 1) * a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b2, &
870 a[i__ + (i__ + 1) * a_dim1], lda);
872 clacgv_(&i__2, &x[i__ + x_dim1], ldx);
874 /* Generate reflection P(i) to annihilate A(i,i+2:n) */
876 i__2 = i__ + (i__ + 1) * a_dim1;
877 alpha.r = a[i__2].r, alpha.i = a[i__2].i;
881 clarfg_(&i__2, &alpha, &a[i__ + f2cmin(i__3,*n) * a_dim1], lda, &
885 i__2 = i__ + (i__ + 1) * a_dim1;
886 a[i__2].r = 1.f, a[i__2].i = 0.f;
888 /* Compute X(i+1:m,i) */
892 cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + (i__
893 + 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1],
894 lda, &c_b1, &x[i__ + 1 + i__ * x_dim1], &c__1);
896 cgemv_("Conjugate transpose", &i__2, &i__, &c_b2, &y[i__ + 1
897 + y_dim1], ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &
898 c_b1, &x[i__ * x_dim1 + 1], &c__1);
900 q__1.r = -1.f, q__1.i = 0.f;
901 cgemv_("No transpose", &i__2, &i__, &q__1, &a[i__ + 1 +
902 a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b2, &x[
903 i__ + 1 + i__ * x_dim1], &c__1);
906 cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[(i__ + 1) *
907 a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, &
908 c_b1, &x[i__ * x_dim1 + 1], &c__1);
911 q__1.r = -1.f, q__1.i = 0.f;
912 cgemv_("No transpose", &i__2, &i__3, &q__1, &x[i__ + 1 +
913 x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b2, &x[
914 i__ + 1 + i__ * x_dim1], &c__1);
916 cscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
918 clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
924 /* Reduce to lower bidiagonal form */
927 for (i__ = 1; i__ <= i__1; ++i__) {
929 /* Update A(i,i:n) */
932 clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
934 clacgv_(&i__2, &a[i__ + a_dim1], lda);
937 q__1.r = -1.f, q__1.i = 0.f;
938 cgemv_("No transpose", &i__2, &i__3, &q__1, &y[i__ + y_dim1], ldy,
939 &a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1],
942 clacgv_(&i__2, &a[i__ + a_dim1], lda);
944 clacgv_(&i__2, &x[i__ + x_dim1], ldx);
947 q__1.r = -1.f, q__1.i = 0.f;
948 cgemv_("Conjugate transpose", &i__2, &i__3, &q__1, &a[i__ *
949 a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b2, &a[i__ +
952 clacgv_(&i__2, &x[i__ + x_dim1], ldx);
954 /* Generate reflection P(i) to annihilate A(i,i+1:n) */
956 i__2 = i__ + i__ * a_dim1;
957 alpha.r = a[i__2].r, alpha.i = a[i__2].i;
961 clarfg_(&i__2, &alpha, &a[i__ + f2cmin(i__3,*n) * a_dim1], lda, &
966 i__2 = i__ + i__ * a_dim1;
967 a[i__2].r = 1.f, a[i__2].i = 0.f;
969 /* Compute X(i+1:m,i) */
973 cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + i__ *
974 a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b1, &x[
975 i__ + 1 + i__ * x_dim1], &c__1);
978 cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &y[i__ +
979 y_dim1], ldy, &a[i__ + i__ * a_dim1], lda, &c_b1, &x[
980 i__ * x_dim1 + 1], &c__1);
983 q__1.r = -1.f, q__1.i = 0.f;
984 cgemv_("No transpose", &i__2, &i__3, &q__1, &a[i__ + 1 +
985 a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b2, &x[
986 i__ + 1 + i__ * x_dim1], &c__1);
989 cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i__ * a_dim1 +
990 1], lda, &a[i__ + i__ * a_dim1], lda, &c_b1, &x[i__ *
994 q__1.r = -1.f, q__1.i = 0.f;
995 cgemv_("No transpose", &i__2, &i__3, &q__1, &x[i__ + 1 +
996 x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b2, &x[
997 i__ + 1 + i__ * x_dim1], &c__1);
999 cscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
1000 i__2 = *n - i__ + 1;
1001 clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
1003 /* Update A(i+1:m,i) */
1006 clacgv_(&i__2, &y[i__ + y_dim1], ldy);
1009 q__1.r = -1.f, q__1.i = 0.f;
1010 cgemv_("No transpose", &i__2, &i__3, &q__1, &a[i__ + 1 +
1011 a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b2, &a[i__ +
1012 1 + i__ * a_dim1], &c__1);
1014 clacgv_(&i__2, &y[i__ + y_dim1], ldy);
1016 q__1.r = -1.f, q__1.i = 0.f;
1017 cgemv_("No transpose", &i__2, &i__, &q__1, &x[i__ + 1 +
1018 x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b2, &a[
1019 i__ + 1 + i__ * a_dim1], &c__1);
1021 /* Generate reflection Q(i) to annihilate A(i+2:m,i) */
1023 i__2 = i__ + 1 + i__ * a_dim1;
1024 alpha.r = a[i__2].r, alpha.i = a[i__2].i;
1028 clarfg_(&i__2, &alpha, &a[f2cmin(i__3,*m) + i__ * a_dim1], &c__1,
1032 i__2 = i__ + 1 + i__ * a_dim1;
1033 a[i__2].r = 1.f, a[i__2].i = 0.f;
1035 /* Compute Y(i+1:n,i) */
1039 cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1
1040 + (i__ + 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1]
1041 , &c__1, &c_b1, &y[i__ + 1 + i__ * y_dim1], &c__1);
1044 cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1
1045 + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &
1046 c_b1, &y[i__ * y_dim1 + 1], &c__1);
1049 q__1.r = -1.f, q__1.i = 0.f;
1050 cgemv_("No transpose", &i__2, &i__3, &q__1, &y[i__ + 1 +
1051 y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b2, &y[
1052 i__ + 1 + i__ * y_dim1], &c__1);
1054 cgemv_("Conjugate transpose", &i__2, &i__, &c_b2, &x[i__ + 1
1055 + x_dim1], ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &
1056 c_b1, &y[i__ * y_dim1 + 1], &c__1);
1058 q__1.r = -1.f, q__1.i = 0.f;
1059 cgemv_("Conjugate transpose", &i__, &i__2, &q__1, &a[(i__ + 1)
1060 * a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &
1061 c_b2, &y[i__ + 1 + i__ * y_dim1], &c__1);
1063 cscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
1065 i__2 = *n - i__ + 1;
1066 clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);