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 ZLARFB_GETT */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download ZLARFB_GETT + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb_
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfb_
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfb_
541 /* SUBROUTINE ZLARFB_GETT( IDENT, M, N, K, T, LDT, A, LDA, B, LDB, */
542 /* $ WORK, LDWORK ) */
545 /* CHARACTER IDENT */
546 /* INTEGER K, LDA, LDB, LDT, LDWORK, M, N */
547 /* COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * ), */
548 /* $ WORK( LDWORK, * ) */
550 /* > \par Purpose: */
555 /* > ZLARFB_GETT applies a complex Householder block reflector H from the */
556 /* > left to a complex (K+M)-by-N "triangular-pentagonal" matrix */
557 /* > composed of two block matrices: an upper trapezoidal K-by-N matrix A */
558 /* > stored in the array A, and a rectangular M-by-(N-K) matrix B, stored */
559 /* > in the array B. The block reflector H is stored in a compact */
560 /* > WY-representation, where the elementary reflectors are in the */
561 /* > arrays A, B and T. See Further Details section. */
567 /* > \param[in] IDENT */
569 /* > IDENT is CHARACTER*1 */
570 /* > If IDENT = not 'I', or not 'i', then V1 is unit */
571 /* > lower-triangular and stored in the left K-by-K block of */
572 /* > the input matrix A, */
573 /* > If IDENT = 'I' or 'i', then V1 is an identity matrix and */
575 /* > See Further Details section. */
581 /* > The number of rows of the matrix B. */
588 /* > The number of columns of the matrices A and B. */
595 /* > The number or rows of the matrix A. */
596 /* > K is also order of the matrix T, i.e. the number of */
597 /* > elementary reflectors whose product defines the block */
598 /* > reflector. 0 <= K <= N. */
603 /* > T is COMPLEX*16 array, dimension (LDT,K) */
604 /* > The upper-triangular K-by-K matrix T in the representation */
605 /* > of the block reflector. */
608 /* > \param[in] LDT */
610 /* > LDT is INTEGER */
611 /* > The leading dimension of the array T. LDT >= K. */
614 /* > \param[in,out] A */
616 /* > A is COMPLEX*16 array, dimension (LDA,N) */
619 /* > a) In the K-by-N upper-trapezoidal part A: input matrix A. */
620 /* > b) In the columns below the diagonal: columns of V1 */
621 /* > (ones are not stored on the diagonal). */
624 /* > A is overwritten by rectangular K-by-N product H*A. */
626 /* > See Further Details section. */
629 /* > \param[in] LDA */
631 /* > LDB is INTEGER */
632 /* > The leading dimension of the array A. LDA >= f2cmax(1,K). */
635 /* > \param[in,out] B */
637 /* > B is COMPLEX*16 array, dimension (LDB,N) */
640 /* > a) In the M-by-(N-K) right block: input matrix B. */
641 /* > b) In the M-by-N left block: columns of V2. */
644 /* > B is overwritten by rectangular M-by-N product H*B. */
646 /* > See Further Details section. */
649 /* > \param[in] LDB */
651 /* > LDB is INTEGER */
652 /* > The leading dimension of the array B. LDB >= f2cmax(1,M). */
655 /* > \param[out] WORK */
657 /* > WORK is COMPLEX*16 array, */
658 /* > dimension (LDWORK,f2cmax(K,N-K)) */
661 /* > \param[in] LDWORK */
663 /* > LDWORK is INTEGER */
664 /* > The leading dimension of the array WORK. LDWORK>=f2cmax(1,K). */
671 /* > \author Univ. of Tennessee */
672 /* > \author Univ. of California Berkeley */
673 /* > \author Univ. of Colorado Denver */
674 /* > \author NAG Ltd. */
676 /* > \ingroup complex16OTHERauxiliary */
678 /* > \par Contributors: */
679 /* ================== */
683 /* > November 2020, Igor Kozachenko, */
684 /* > Computer Science Division, */
685 /* > University of California, Berkeley */
689 /* > \par Further Details: */
690 /* ===================== */
694 /* > (1) Description of the Algebraic Operation. */
696 /* > The matrix A is a K-by-N matrix composed of two column block */
697 /* > matrices, A1, which is K-by-K, and A2, which is K-by-(N-K): */
698 /* > A = ( A1, A2 ). */
699 /* > The matrix B is an M-by-N matrix composed of two column block */
700 /* > matrices, B1, which is M-by-K, and B2, which is M-by-(N-K): */
701 /* > B = ( B1, B2 ). */
703 /* > Perform the operation: */
705 /* > ( A_out ) := H * ( A_in ) = ( I - V * T * V**H ) * ( A_in ) = */
706 /* > ( B_out ) ( B_in ) ( B_in ) */
707 /* > = ( I - ( V1 ) * T * ( V1**H, V2**H ) ) * ( A_in ) */
708 /* > ( V2 ) ( B_in ) */
711 /* > a) ( A_in ) consists of two block columns: */
714 /* > ( A_in ) = (( A1_in ) ( A2_in )) = (( A1_in ) ( A2_in )) */
715 /* > ( B_in ) (( B1_in ) ( B2_in )) (( 0 ) ( B2_in )), */
717 /* > where the column blocks are: */
719 /* > ( A1_in ) is a K-by-K upper-triangular matrix stored in the */
720 /* > upper triangular part of the array A(1:K,1:K). */
721 /* > ( B1_in ) is an M-by-K rectangular ZERO matrix and not stored. */
723 /* > ( A2_in ) is a K-by-(N-K) rectangular matrix stored */
724 /* > in the array A(1:K,K+1:N). */
725 /* > ( B2_in ) is an M-by-(N-K) rectangular matrix stored */
726 /* > in the array B(1:M,K+1:N). */
728 /* > b) V = ( V1 ) */
732 /* > 1) if IDENT == 'I',V1 is a K-by-K identity matrix, not stored; */
733 /* > 2) if IDENT != 'I',V1 is a K-by-K unit lower-triangular matrix, */
734 /* > stored in the lower-triangular part of the array */
735 /* > A(1:K,1:K) (ones are not stored), */
736 /* > and V2 is an M-by-K rectangular stored the array B(1:M,1:K), */
737 /* > (because on input B1_in is a rectangular zero */
738 /* > matrix that is not stored and the space is */
739 /* > used to store V2). */
741 /* > c) T is a K-by-K upper-triangular matrix stored */
742 /* > in the array T(1:K,1:K). */
746 /* > a) ( A_out ) consists of two block columns: */
749 /* > ( A_out ) = (( A1_out ) ( A2_out )) */
750 /* > ( B_out ) (( B1_out ) ( B2_out )), */
752 /* > where the column blocks are: */
754 /* > ( A1_out ) is a K-by-K square matrix, or a K-by-K */
755 /* > upper-triangular matrix, if V1 is an */
756 /* > identity matrix. AiOut is stored in */
757 /* > the array A(1:K,1:K). */
758 /* > ( B1_out ) is an M-by-K rectangular matrix stored */
759 /* > in the array B(1:M,K:N). */
761 /* > ( A2_out ) is a K-by-(N-K) rectangular matrix stored */
762 /* > in the array A(1:K,K+1:N). */
763 /* > ( B2_out ) is an M-by-(N-K) rectangular matrix stored */
764 /* > in the array B(1:M,K+1:N). */
767 /* > The operation above can be represented as the same operation */
768 /* > on each block column: */
770 /* > ( A1_out ) := H * ( A1_in ) = ( I - V * T * V**H ) * ( A1_in ) */
771 /* > ( B1_out ) ( 0 ) ( 0 ) */
773 /* > ( A2_out ) := H * ( A2_in ) = ( I - V * T * V**H ) * ( A2_in ) */
774 /* > ( B2_out ) ( B2_in ) ( B2_in ) */
776 /* > If IDENT != 'I': */
778 /* > The computation for column block 1: */
780 /* > A1_out: = A1_in - V1*T*(V1**H)*A1_in */
782 /* > B1_out: = - V2*T*(V1**H)*A1_in */
784 /* > The computation for column block 2, which exists if N > K: */
786 /* > A2_out: = A2_in - V1*T*( (V1**H)*A2_in + (V2**H)*B2_in ) */
788 /* > B2_out: = B2_in - V2*T*( (V1**H)*A2_in + (V2**H)*B2_in ) */
790 /* > If IDENT == 'I': */
792 /* > The operation for column block 1: */
794 /* > A1_out: = A1_in - V1*T*A1_in */
796 /* > B1_out: = - V2*T*A1_in */
798 /* > The computation for column block 2, which exists if N > K: */
800 /* > A2_out: = A2_in - T*( A2_in + (V2**H)*B2_in ) */
802 /* > B2_out: = B2_in - V2*T*( A2_in + (V2**H)*B2_in ) */
804 /* > (2) Description of the Algorithmic Computation. */
806 /* > In the first step, we compute column block 2, i.e. A2 and B2. */
807 /* > Here, we need to use the K-by-(N-K) rectangular workspace */
808 /* > matrix W2 that is of the same size as the matrix A2. */
809 /* > W2 is stored in the array WORK(1:K,1:(N-K)). */
811 /* > In the second step, we compute column block 1, i.e. A1 and B1. */
812 /* > Here, we need to use the K-by-K square workspace matrix W1 */
813 /* > that is of the same size as the as the matrix A1. */
814 /* > W1 is stored in the array WORK(1:K,1:K). */
816 /* > NOTE: Hence, in this routine, we need the workspace array WORK */
817 /* > only of size WORK(1:K,1:f2cmax(K,N-K)) so it can hold both W2 from */
818 /* > the first step and W1 from the second step. */
820 /* > Case (A), when V1 is unit lower-triangular, i.e. IDENT != 'I', */
821 /* > more computations than in the Case (B). */
823 /* > if( IDENT != 'I' ) then */
824 /* > if ( N > K ) then */
825 /* > (First Step - column block 2) */
826 /* > col2_(1) W2: = A2 */
827 /* > col2_(2) W2: = (V1**H) * W2 = (unit_lower_tr_of_(A1)**H) * W2 */
828 /* > col2_(3) W2: = W2 + (V2**H) * B2 = W2 + (B1**H) * B2 */
829 /* > col2_(4) W2: = T * W2 */
830 /* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */
831 /* > col2_(6) W2: = V1 * W2 = unit_lower_tr_of_(A1) * W2 */
832 /* > col2_(7) A2: = A2 - W2 */
834 /* > (Second Step - column block 1) */
835 /* > col1_(1) W1: = A1 */
836 /* > col1_(2) W1: = (V1**H) * W1 = (unit_lower_tr_of_(A1)**H) * W1 */
837 /* > col1_(3) W1: = T * W1 */
838 /* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */
839 /* > col1_(5) square W1: = V1 * W1 = unit_lower_tr_of_(A1) * W1 */
840 /* > col1_(6) square A1: = A1 - W1 */
844 /* > Case (B), when V1 is an identity matrix, i.e. IDENT == 'I', */
845 /* > less computations than in the Case (A) */
847 /* > if( IDENT == 'I' ) then */
848 /* > if ( N > K ) then */
849 /* > (First Step - column block 2) */
850 /* > col2_(1) W2: = A2 */
851 /* > col2_(3) W2: = W2 + (V2**H) * B2 = W2 + (B1**H) * B2 */
852 /* > col2_(4) W2: = T * W2 */
853 /* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */
854 /* > col2_(7) A2: = A2 - W2 */
856 /* > (Second Step - column block 1) */
857 /* > col1_(1) W1: = A1 */
858 /* > col1_(3) W1: = T * W1 */
859 /* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */
860 /* > col1_(6) upper-triangular_of_(A1): = A1 - W1 */
864 /* > Combine these cases (A) and (B) together, this is the resulting */
867 /* > if ( N > K ) then */
869 /* > (First Step - column block 2) */
871 /* > col2_(1) W2: = A2 */
872 /* > if( IDENT != 'I' ) then */
873 /* > col2_(2) W2: = (V1**H) * W2 */
874 /* > = (unit_lower_tr_of_(A1)**H) * W2 */
876 /* > col2_(3) W2: = W2 + (V2**H) * B2 = W2 + (B1**H) * B2] */
877 /* > col2_(4) W2: = T * W2 */
878 /* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */
879 /* > if( IDENT != 'I' ) then */
880 /* > col2_(6) W2: = V1 * W2 = unit_lower_tr_of_(A1) * W2 */
882 /* > col2_(7) A2: = A2 - W2 */
886 /* > (Second Step - column block 1) */
888 /* > col1_(1) W1: = A1 */
889 /* > if( IDENT != 'I' ) then */
890 /* > col1_(2) W1: = (V1**H) * W1 */
891 /* > = (unit_lower_tr_of_(A1)**H) * W1 */
893 /* > col1_(3) W1: = T * W1 */
894 /* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */
895 /* > if( IDENT != 'I' ) then */
896 /* > col1_(5) square W1: = V1 * W1 = unit_lower_tr_of_(A1) * W1 */
897 /* > col1_(6_a) below_diag_of_(A1): = - below_diag_of_(W1) */
899 /* > col1_(6_b) up_tr_of_(A1): = up_tr_of_(A1) - up_tr_of_(W1) */
905 /* ===================================================================== */
906 /* Subroutine */ int zlarfb_gett_(char *ident, integer *m, integer *n,
907 integer *k, doublecomplex *t, integer *ldt, doublecomplex *a, integer
908 *lda, doublecomplex *b, integer *ldb, doublecomplex *work, integer *
911 /* System generated locals */
912 integer a_dim1, a_offset, b_dim1, b_offset, t_dim1, t_offset, work_dim1,
913 work_offset, i__1, i__2, i__3, i__4, i__5;
916 /* Local variables */
918 extern logical lsame_(char *, char *);
919 extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
920 integer *, doublecomplex *, doublecomplex *, integer *,
921 doublecomplex *, integer *, doublecomplex *, doublecomplex *,
922 integer *), zcopy_(integer *, doublecomplex *,
923 integer *, doublecomplex *, integer *), ztrmm_(char *, char *,
924 char *, char *, integer *, integer *, doublecomplex *,
925 doublecomplex *, integer *, doublecomplex *, integer *);
929 /* -- LAPACK auxiliary routine -- */
930 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
931 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
934 /* ===================================================================== */
937 /* Quick return if possible */
939 /* Parameter adjustments */
941 t_offset = 1 + t_dim1 * 1;
944 a_offset = 1 + a_dim1 * 1;
947 b_offset = 1 + b_dim1 * 1;
950 work_offset = 1 + work_dim1 * 1;
954 if (*m < 0 || *n <= 0 || *k == 0 || *k > *n) {
958 lnotident = ! lsame_(ident, "I");
960 /* ------------------------------------------------------------------ */
962 /* First Step. Computation of the Column Block 2: */
964 /* ( A2 ) := H * ( A2 ) */
967 /* ------------------------------------------------------------------ */
971 /* col2_(1) Compute W2: = A2. Therefore, copy A2 = A(1:K, K+1:N) */
972 /* into W2=WORK(1:K, 1:N-K) column-by-column. */
975 for (j = 1; j <= i__1; ++j) {
976 zcopy_(k, &a[(*k + j) * a_dim1 + 1], &c__1, &work[j * work_dim1 +
981 /* col2_(2) Compute W2: = (V1**H) * W2 = (A1**H) * W2, */
982 /* V1 is not an identy matrix, but unit lower-triangular */
983 /* V1 stored in A1 (diagonal ones are not stored). */
987 ztrmm_("L", "L", "C", "U", k, &i__1, &c_b1, &a[a_offset], lda, &
988 work[work_offset], ldwork);
991 /* col2_(3) Compute W2: = W2 + (V2**H) * B2 = W2 + (B1**H) * B2 */
992 /* V2 stored in B1. */
996 zgemm_("C", "N", k, &i__1, m, &c_b1, &b[b_offset], ldb, &b[(*k +
997 1) * b_dim1 + 1], ldb, &c_b1, &work[work_offset], ldwork);
1000 /* col2_(4) Compute W2: = T * W2, */
1001 /* T is upper-triangular. */
1004 ztrmm_("L", "U", "N", "N", k, &i__1, &c_b1, &t[t_offset], ldt, &work[
1005 work_offset], ldwork);
1007 /* col2_(5) Compute B2: = B2 - V2 * W2 = B2 - B1 * W2, */
1008 /* V2 stored in B1. */
1012 z__1.r = -1., z__1.i = 0.;
1013 zgemm_("N", "N", m, &i__1, k, &z__1, &b[b_offset], ldb, &work[
1014 work_offset], ldwork, &c_b1, &b[(*k + 1) * b_dim1 + 1],
1020 /* col2_(6) Compute W2: = V1 * W2 = A1 * W2, */
1021 /* V1 is not an identity matrix, but unit lower-triangular, */
1022 /* V1 stored in A1 (diagonal ones are not stored). */
1025 ztrmm_("L", "L", "N", "U", k, &i__1, &c_b1, &a[a_offset], lda, &
1026 work[work_offset], ldwork);
1029 /* col2_(7) Compute A2: = A2 - W2 = */
1030 /* = A(1:K, K+1:N-K) - WORK(1:K, 1:N-K), */
1031 /* column-by-column. */
1034 for (j = 1; j <= i__1; ++j) {
1036 for (i__ = 1; i__ <= i__2; ++i__) {
1037 i__3 = i__ + (*k + j) * a_dim1;
1038 i__4 = i__ + (*k + j) * a_dim1;
1039 i__5 = i__ + j * work_dim1;
1040 z__1.r = a[i__4].r - work[i__5].r, z__1.i = a[i__4].i - work[
1042 a[i__3].r = z__1.r, a[i__3].i = z__1.i;
1048 /* ------------------------------------------------------------------ */
1050 /* Second Step. Computation of the Column Block 1: */
1052 /* ( A1 ) := H * ( A1 ) */
1055 /* ------------------------------------------------------------------ */
1057 /* col1_(1) Compute W1: = A1. Copy the upper-triangular */
1058 /* A1 = A(1:K, 1:K) into the upper-triangular */
1059 /* W1 = WORK(1:K, 1:K) column-by-column. */
1062 for (j = 1; j <= i__1; ++j) {
1063 zcopy_(&j, &a[j * a_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1)
1067 /* Set the subdiagonal elements of W1 to zero column-by-column. */
1070 for (j = 1; j <= i__1; ++j) {
1072 for (i__ = j + 1; i__ <= i__2; ++i__) {
1073 i__3 = i__ + j * work_dim1;
1074 work[i__3].r = 0., work[i__3].i = 0.;
1080 /* col1_(2) Compute W1: = (V1**H) * W1 = (A1**H) * W1, */
1081 /* V1 is not an identity matrix, but unit lower-triangular */
1082 /* V1 stored in A1 (diagonal ones are not stored), */
1083 /* W1 is upper-triangular with zeroes below the diagonal. */
1085 ztrmm_("L", "L", "C", "U", k, k, &c_b1, &a[a_offset], lda, &work[
1086 work_offset], ldwork);
1089 /* col1_(3) Compute W1: = T * W1, */
1090 /* T is upper-triangular, */
1091 /* W1 is upper-triangular with zeroes below the diagonal. */
1093 ztrmm_("L", "U", "N", "N", k, k, &c_b1, &t[t_offset], ldt, &work[
1094 work_offset], ldwork);
1096 /* col1_(4) Compute B1: = - V2 * W1 = - B1 * W1, */
1097 /* V2 = B1, W1 is upper-triangular with zeroes below the diagonal. */
1100 z__1.r = -1., z__1.i = 0.;
1101 ztrmm_("R", "U", "N", "N", m, k, &z__1, &work[work_offset], ldwork, &
1107 /* col1_(5) Compute W1: = V1 * W1 = A1 * W1, */
1108 /* V1 is not an identity matrix, but unit lower-triangular */
1109 /* V1 stored in A1 (diagonal ones are not stored), */
1110 /* W1 is upper-triangular on input with zeroes below the diagonal, */
1111 /* and square on output. */
1113 ztrmm_("L", "L", "N", "U", k, k, &c_b1, &a[a_offset], lda, &work[
1114 work_offset], ldwork);
1116 /* col1_(6) Compute A1: = A1 - W1 = A(1:K, 1:K) - WORK(1:K, 1:K) */
1117 /* column-by-column. A1 is upper-triangular on input. */
1118 /* If IDENT, A1 is square on output, and W1 is square, */
1119 /* if NOT IDENT, A1 is upper-triangular on output, */
1120 /* W1 is upper-triangular. */
1122 /* col1_(6)_a Compute elements of A1 below the diagonal. */
1125 for (j = 1; j <= i__1; ++j) {
1127 for (i__ = j + 1; i__ <= i__2; ++i__) {
1128 i__3 = i__ + j * a_dim1;
1129 i__4 = i__ + j * work_dim1;
1130 z__1.r = -work[i__4].r, z__1.i = -work[i__4].i;
1131 a[i__3].r = z__1.r, a[i__3].i = z__1.i;
1137 /* col1_(6)_b Compute elements of A1 on and above the diagonal. */
1140 for (j = 1; j <= i__1; ++j) {
1142 for (i__ = 1; i__ <= i__2; ++i__) {
1143 i__3 = i__ + j * a_dim1;
1144 i__4 = i__ + j * a_dim1;
1145 i__5 = i__ + j * work_dim1;
1146 z__1.r = a[i__4].r - work[i__5].r, z__1.i = a[i__4].i - work[i__5]
1148 a[i__3].r = z__1.r, a[i__3].i = z__1.i;
1154 /* End of ZLARFB_GETT */
1156 } /* zlarfb_gett__ */