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 doublereal c_b4 = -1.;
516 static doublereal c_b5 = 1.;
517 static integer c__1 = 1;
518 static doublereal c_b38 = 0.;
520 /* > \brief \b DLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below th
521 e k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformati
522 on to the unreduced part of A. */
524 /* =========== DOCUMENTATION =========== */
526 /* Online html documentation available at */
527 /* http://www.netlib.org/lapack/explore-html/ */
530 /* > Download DLAHRD + dependencies */
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahrd.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlahrd.
537 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlahrd.
545 /* SUBROUTINE DLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) */
547 /* INTEGER K, LDA, LDT, LDY, N, NB */
548 /* DOUBLE PRECISION A( LDA, * ), T( LDT, NB ), TAU( NB ), */
552 /* > \par Purpose: */
557 /* > This routine is deprecated and has been replaced by routine DLAHR2. */
559 /* > DLAHRD reduces the first NB columns of a real general n-by-(n-k+1) */
560 /* > matrix A so that elements below the k-th subdiagonal are zero. The */
561 /* > reduction is performed by an orthogonal similarity transformation */
562 /* > Q**T * A * Q. The routine returns the matrices V and T which determine */
563 /* > Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T. */
572 /* > The order of the matrix A. */
578 /* > The offset for the reduction. Elements below the k-th */
579 /* > subdiagonal in the first NB columns are reduced to zero. */
582 /* > \param[in] NB */
584 /* > NB is INTEGER */
585 /* > The number of columns to be reduced. */
588 /* > \param[in,out] A */
590 /* > A is DOUBLE PRECISION array, dimension (LDA,N-K+1) */
591 /* > On entry, the n-by-(n-k+1) general matrix A. */
592 /* > On exit, the elements on and above the k-th subdiagonal in */
593 /* > the first NB columns are overwritten with the corresponding */
594 /* > elements of the reduced matrix; the elements below the k-th */
595 /* > subdiagonal, with the array TAU, represent the matrix Q as a */
596 /* > product of elementary reflectors. The other columns of A are */
597 /* > unchanged. 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] TAU */
608 /* > TAU is DOUBLE PRECISION array, dimension (NB) */
609 /* > The scalar factors of the elementary reflectors. See Further */
613 /* > \param[out] T */
615 /* > T is DOUBLE PRECISION array, dimension (LDT,NB) */
616 /* > The upper triangular matrix T. */
619 /* > \param[in] LDT */
621 /* > LDT is INTEGER */
622 /* > The leading dimension of the array T. LDT >= NB. */
625 /* > \param[out] Y */
627 /* > Y is DOUBLE PRECISION array, dimension (LDY,NB) */
628 /* > The n-by-nb matrix Y. */
631 /* > \param[in] LDY */
633 /* > LDY is INTEGER */
634 /* > The leading dimension of the array Y. LDY >= N. */
640 /* > \author Univ. of Tennessee */
641 /* > \author Univ. of California Berkeley */
642 /* > \author Univ. of Colorado Denver */
643 /* > \author NAG Ltd. */
645 /* > \date December 2016 */
647 /* > \ingroup doubleOTHERauxiliary */
649 /* > \par Further Details: */
650 /* ===================== */
654 /* > The matrix Q is represented as a product of nb elementary reflectors */
656 /* > Q = H(1) H(2) . . . H(nb). */
658 /* > Each H(i) has the form */
660 /* > H(i) = I - tau * v * v**T */
662 /* > where tau is a real scalar, and v is a real vector with */
663 /* > v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in */
664 /* > A(i+k+1:n,i), and tau in TAU(i). */
666 /* > The elements of the vectors v together form the (n-k+1)-by-nb matrix */
667 /* > V which is needed, with T and Y, to apply the transformation to the */
668 /* > unreduced part of the matrix, using an update of the form: */
669 /* > A := (I - V*T*V**T) * (A - Y*V**T). */
671 /* > The contents of A on exit are illustrated by the following example */
672 /* > with n = 7, k = 3 and nb = 2: */
674 /* > ( a h a a a ) */
675 /* > ( a h a a a ) */
676 /* > ( a h a a a ) */
677 /* > ( h h a a a ) */
678 /* > ( v1 h a a a ) */
679 /* > ( v1 v2 a a a ) */
680 /* > ( v1 v2 a a a ) */
682 /* > where a denotes an element of the original matrix A, h denotes a */
683 /* > modified element of the upper Hessenberg matrix H, and vi denotes an */
684 /* > element of the vector defining H(i). */
687 /* ===================================================================== */
688 /* Subroutine */ int dlahrd_(integer *n, integer *k, integer *nb, doublereal *
689 a, integer *lda, doublereal *tau, doublereal *t, integer *ldt,
690 doublereal *y, integer *ldy)
692 /* System generated locals */
693 integer a_dim1, a_offset, t_dim1, t_offset, y_dim1, y_offset, i__1, i__2,
697 /* Local variables */
699 extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
700 integer *), dgemv_(char *, integer *, integer *, doublereal *,
701 doublereal *, integer *, doublereal *, integer *, doublereal *,
702 doublereal *, integer *), dcopy_(integer *, doublereal *,
703 integer *, doublereal *, integer *), daxpy_(integer *, doublereal
704 *, doublereal *, integer *, doublereal *, integer *), dtrmv_(char
705 *, char *, char *, integer *, doublereal *, integer *, doublereal
708 extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *,
709 integer *, doublereal *);
712 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
713 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
714 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
718 /* ===================================================================== */
721 /* Quick return if possible */
723 /* Parameter adjustments */
726 a_offset = 1 + a_dim1 * 1;
729 t_offset = 1 + t_dim1 * 1;
732 y_offset = 1 + y_dim1 * 1;
741 for (i__ = 1; i__ <= i__1; ++i__) {
744 /* Update A(1:n,i) */
746 /* Compute i-th column of A - Y * V**T */
749 dgemv_("No transpose", n, &i__2, &c_b4, &y[y_offset], ldy, &a[*k
750 + i__ - 1 + a_dim1], lda, &c_b5, &a[i__ * a_dim1 + 1], &
753 /* Apply I - V * T**T * V**T to this column (call it b) from the */
754 /* left, using the last column of T as workspace */
756 /* Let V = ( V1 ) and b = ( b1 ) (first I-1 rows) */
759 /* where V1 is unit lower triangular */
761 /* w := V1**T * b1 */
764 dcopy_(&i__2, &a[*k + 1 + i__ * a_dim1], &c__1, &t[*nb * t_dim1 +
767 dtrmv_("Lower", "Transpose", "Unit", &i__2, &a[*k + 1 + a_dim1],
768 lda, &t[*nb * t_dim1 + 1], &c__1);
770 /* w := w + V2**T *b2 */
772 i__2 = *n - *k - i__ + 1;
774 dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[*k + i__ + a_dim1],
775 lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b5, &t[*nb *
781 dtrmv_("Upper", "Transpose", "Non-unit", &i__2, &t[t_offset], ldt,
782 &t[*nb * t_dim1 + 1], &c__1);
784 /* b2 := b2 - V2*w */
786 i__2 = *n - *k - i__ + 1;
788 dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[*k + i__ + a_dim1],
789 lda, &t[*nb * t_dim1 + 1], &c__1, &c_b5, &a[*k + i__ +
790 i__ * a_dim1], &c__1);
792 /* b1 := b1 - V1*w */
795 dtrmv_("Lower", "No transpose", "Unit", &i__2, &a[*k + 1 + a_dim1]
796 , lda, &t[*nb * t_dim1 + 1], &c__1);
798 daxpy_(&i__2, &c_b4, &t[*nb * t_dim1 + 1], &c__1, &a[*k + 1 + i__
801 a[*k + i__ - 1 + (i__ - 1) * a_dim1] = ei;
804 /* Generate the elementary reflector H(i) to annihilate */
807 i__2 = *n - *k - i__ + 1;
810 dlarfg_(&i__2, &a[*k + i__ + i__ * a_dim1], &a[f2cmin(i__3,*n) + i__ *
811 a_dim1], &c__1, &tau[i__]);
812 ei = a[*k + i__ + i__ * a_dim1];
813 a[*k + i__ + i__ * a_dim1] = 1.;
815 /* Compute Y(1:n,i) */
817 i__2 = *n - *k - i__ + 1;
818 dgemv_("No transpose", n, &i__2, &c_b5, &a[(i__ + 1) * a_dim1 + 1],
819 lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b38, &y[i__ *
821 i__2 = *n - *k - i__ + 1;
823 dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[*k + i__ + a_dim1], lda, &
824 a[*k + i__ + i__ * a_dim1], &c__1, &c_b38, &t[i__ * t_dim1 +
827 dgemv_("No transpose", n, &i__2, &c_b4, &y[y_offset], ldy, &t[i__ *
828 t_dim1 + 1], &c__1, &c_b5, &y[i__ * y_dim1 + 1], &c__1);
829 dscal_(n, &tau[i__], &y[i__ * y_dim1 + 1], &c__1);
831 /* Compute T(1:i,i) */
835 dscal_(&i__2, &d__1, &t[i__ * t_dim1 + 1], &c__1);
837 dtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[t_offset], ldt,
838 &t[i__ * t_dim1 + 1], &c__1)
840 t[i__ + i__ * t_dim1] = tau[i__];
844 a[*k + *nb + *nb * a_dim1] = ei;