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 integer c__4 = 4;
516 static integer c_n1 = -1;
517 static integer c__1 = 1;
518 static real c_b17 = 0.f;
519 static real c_b23 = 1.f;
520 static real c_b39 = -.5f;
521 static real c_b42 = -1.f;
523 /* > \brief \b SSYTRD_SY2SB */
525 /* @generated from zhetrd_he2hb.f, fortran z -> s, Wed Dec 7 08:22:40 2016 */
527 /* =========== DOCUMENTATION =========== */
529 /* Online html documentation available at */
530 /* http://www.netlib.org/lapack/explore-html/ */
533 /* > Download SSYTRD_SY2SB + dependencies */
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssytrd.
537 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssytrd.
540 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssytrd.
548 /* SUBROUTINE SSYTRD_SY2SB( UPLO, N, KD, A, LDA, AB, LDAB, TAU, */
549 /* WORK, LWORK, INFO ) */
554 /* INTEGER INFO, LDA, LDAB, LWORK, N, KD */
555 /* REAL A( LDA, * ), AB( LDAB, * ), */
556 /* TAU( * ), WORK( * ) */
559 /* > \par Purpose: */
564 /* > SSYTRD_SY2SB reduces a real symmetric matrix A to real symmetric */
565 /* > band-diagonal form AB by a orthogonal similarity transformation: */
566 /* > Q**T * A * Q = AB. */
572 /* > \param[in] UPLO */
574 /* > UPLO is CHARACTER*1 */
575 /* > = 'U': Upper triangle of A is stored; */
576 /* > = 'L': Lower triangle of A is stored. */
582 /* > The order of the matrix A. N >= 0. */
585 /* > \param[in] KD */
587 /* > KD is INTEGER */
588 /* > The number of superdiagonals of the reduced matrix if UPLO = 'U', */
589 /* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
590 /* > The reduced matrix is stored in the array AB. */
593 /* > \param[in,out] A */
595 /* > A is REAL array, dimension (LDA,N) */
596 /* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */
597 /* > N-by-N upper triangular part of A contains the upper */
598 /* > triangular part of the matrix A, and the strictly lower */
599 /* > triangular part of A is not referenced. If UPLO = 'L', the */
600 /* > leading N-by-N lower triangular part of A contains the lower */
601 /* > triangular part of the matrix A, and the strictly upper */
602 /* > triangular part of A is not referenced. */
603 /* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */
604 /* > of A are overwritten by the corresponding elements of the */
605 /* > tridiagonal matrix T, and the elements above the first */
606 /* > superdiagonal, with the array TAU, represent the orthogonal */
607 /* > matrix Q as a product of elementary reflectors; if UPLO */
608 /* > = 'L', the diagonal and first subdiagonal of A are over- */
609 /* > written by the corresponding elements of the tridiagonal */
610 /* > matrix T, and the elements below the first subdiagonal, with */
611 /* > the array TAU, represent the orthogonal matrix Q as a product */
612 /* > of elementary reflectors. See Further Details. */
615 /* > \param[in] LDA */
617 /* > LDA is INTEGER */
618 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
621 /* > \param[out] AB */
623 /* > AB is REAL array, dimension (LDAB,N) */
624 /* > On exit, the upper or lower triangle of the symmetric band */
625 /* > matrix A, stored in the first KD+1 rows of the array. The */
626 /* > j-th column of A is stored in the j-th column of the array AB */
628 /* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
629 /* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
632 /* > \param[in] LDAB */
634 /* > LDAB is INTEGER */
635 /* > The leading dimension of the array AB. LDAB >= KD+1. */
638 /* > \param[out] TAU */
640 /* > TAU is REAL array, dimension (N-KD) */
641 /* > The scalar factors of the elementary reflectors (see Further */
645 /* > \param[out] WORK */
647 /* > WORK is REAL array, dimension (LWORK) */
648 /* > On exit, if INFO = 0, or if LWORK=-1, */
649 /* > WORK(1) returns the size of LWORK. */
652 /* > \param[in] LWORK */
654 /* > LWORK is INTEGER */
655 /* > The dimension of the array WORK which should be calculated */
656 /* > by a workspace query. LWORK = MAX(1, LWORK_QUERY) */
657 /* > If LWORK = -1, then a workspace query is assumed; the routine */
658 /* > only calculates the optimal size of the WORK array, returns */
659 /* > this value as the first entry of the WORK array, and no error */
660 /* > message related to LWORK is issued by XERBLA. */
661 /* > LWORK_QUERY = N*KD + N*f2cmax(KD,FACTOPTNB) + 2*KD*KD */
662 /* > where FACTOPTNB is the blocking used by the QR or LQ */
663 /* > algorithm, usually FACTOPTNB=128 is a good choice otherwise */
664 /* > putting LWORK=-1 will provide the size of WORK. */
667 /* > \param[out] INFO */
669 /* > INFO is INTEGER */
670 /* > = 0: successful exit */
671 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
677 /* > \author Univ. of Tennessee */
678 /* > \author Univ. of California Berkeley */
679 /* > \author Univ. of Colorado Denver */
680 /* > \author NAG Ltd. */
682 /* > \date November 2017 */
684 /* > \ingroup realSYcomputational */
686 /* > \par Further Details: */
687 /* ===================== */
691 /* > Implemented by Azzam Haidar. */
693 /* > All details are available on technical report, SC11, SC13 papers. */
695 /* > Azzam Haidar, Hatem Ltaief, and Jack Dongarra. */
696 /* > Parallel reduction to condensed forms for symmetric eigenvalue problems */
697 /* > using aggregated fine-grained and memory-aware kernels. In Proceedings */
698 /* > of 2011 International Conference for High Performance Computing, */
699 /* > Networking, Storage and Analysis (SC '11), New York, NY, USA, */
700 /* > Article 8 , 11 pages. */
701 /* > http://doi.acm.org/10.1145/2063384.2063394 */
703 /* > A. Haidar, J. Kurzak, P. Luszczek, 2013. */
704 /* > An improved parallel singular value algorithm and its implementation */
705 /* > for multicore hardware, In Proceedings of 2013 International Conference */
706 /* > for High Performance Computing, Networking, Storage and Analysis (SC '13). */
707 /* > Denver, Colorado, USA, 2013. */
708 /* > Article 90, 12 pages. */
709 /* > http://doi.acm.org/10.1145/2503210.2503292 */
711 /* > A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. */
712 /* > A novel hybrid CPU-GPU generalized eigensolver for electronic structure */
713 /* > calculations based on fine-grained memory aware tasks. */
714 /* > International Journal of High Performance Computing Applications. */
715 /* > Volume 28 Issue 2, Pages 196-209, May 2014. */
716 /* > http://hpc.sagepub.com/content/28/2/196 */
722 /* > If UPLO = 'U', the matrix Q is represented as a product of elementary */
725 /* > Q = H(k)**T . . . H(2)**T H(1)**T, where k = n-kd. */
727 /* > Each H(i) has the form */
729 /* > H(i) = I - tau * v * v**T */
731 /* > where tau is a real scalar, and v is a real vector with */
732 /* > v(1:i+kd-1) = 0 and v(i+kd) = 1; conjg(v(i+kd+1:n)) is stored on exit in */
733 /* > A(i,i+kd+1:n), and tau in TAU(i). */
735 /* > If UPLO = 'L', the matrix Q is represented as a product of elementary */
738 /* > Q = H(1) H(2) . . . H(k), where k = n-kd. */
740 /* > Each H(i) has the form */
742 /* > H(i) = I - tau * v * v**T */
744 /* > where tau is a real scalar, and v is a real vector with */
745 /* > v(kd+1:i) = 0 and v(i+kd+1) = 1; v(i+kd+2:n) is stored on exit in */
746 /* > A(i+kd+2:n,i), and tau in TAU(i). */
748 /* > The contents of A on exit are illustrated by the following examples */
751 /* > if UPLO = 'U': if UPLO = 'L': */
753 /* > ( ab ab/v1 v1 v1 v1 ) ( ab ) */
754 /* > ( ab ab/v2 v2 v2 ) ( ab/v1 ab ) */
755 /* > ( ab ab/v3 v3 ) ( v1 ab/v2 ab ) */
756 /* > ( ab ab/v4 ) ( v1 v2 ab/v3 ab ) */
757 /* > ( ab ) ( v1 v2 v3 ab/v4 ab ) */
759 /* > where d and e denote diagonal and off-diagonal elements of T, and vi */
760 /* > denotes an element of the vector defining H(i). */
763 /* ===================================================================== */
764 /* Subroutine */ int ssytrd_sy2sb_(char *uplo, integer *n, integer *kd, real
765 *a, integer *lda, real *ab, integer *ldab, real *tau, real *work,
766 integer *lwork, integer *info)
768 /* System generated locals */
769 integer a_dim1, a_offset, ab_dim1, ab_offset, i__1, i__2, i__3, i__4,
772 /* Local variables */
773 extern integer ilaenv2stage_(integer *, char *, char *, integer *,
774 integer *, integer *, integer *);
775 integer tpos, wpos, s1pos, s2pos, i__, j;
776 extern logical lsame_(char *, char *);
778 extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
779 integer *, real *, real *, integer *, real *, integer *, real *,
783 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
784 integer *), ssymm_(char *, char *, integer *, integer *, real *,
785 real *, integer *, real *, integer *, real *, real *, integer *);
787 extern /* Subroutine */ int ssyr2k_(char *, char *, integer *, integer *,
788 real *, real *, integer *, real *, integer *, real *, real *,
791 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), sgelqf_(
792 integer *, integer *, real *, integer *, real *, real *, integer *
793 , integer *), sgeqrf_(integer *, integer *, real *, integer *,
794 real *, real *, integer *, integer *), slarft_(char *, char *,
795 integer *, integer *, real *, integer *, real *, real *, integer *
796 ), slaset_(char *, integer *, integer *, real *,
797 real *, real *, integer *);
800 integer ls2, ldt, ldw, lds1, lds2;
804 /* -- LAPACK computational routine (version 3.8.0) -- */
805 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
806 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
810 /* ===================================================================== */
813 /* Determine the minimal workspace size required */
814 /* and test the input parameters */
816 /* Parameter adjustments */
818 a_offset = 1 + a_dim1 * 1;
821 ab_offset = 1 + ab_dim1 * 1;
828 upper = lsame_(uplo, "U");
829 lquery = *lwork == -1;
830 lwmin = ilaenv2stage_(&c__4, "SSYTRD_SY2SB", "", n, kd, &c_n1, &c_n1);
831 if (! upper && ! lsame_(uplo, "L")) {
835 } else if (*kd < 0) {
837 } else if (*lda < f2cmax(1,*n)) {
839 } else /* if(complicated condition) */ {
841 i__1 = 1, i__2 = *kd + 1;
842 if (*ldab < f2cmax(i__1,i__2)) {
844 } else if (*lwork < lwmin && ! lquery) {
851 xerbla_("SSYTRD_SY2SB", &i__1, (ftnlen)12);
854 work[1] = (real) lwmin;
858 /* Quick return if possible */
859 /* Copy the upper/lower portion of A into AB */
864 for (i__ = 1; i__ <= i__1; ++i__) {
867 lk = f2cmin(i__2,i__);
868 scopy_(&lk, &a[i__ - lk + 1 + i__ * a_dim1], &c__1, &ab[*kd +
869 1 - lk + 1 + i__ * ab_dim1], &c__1);
874 for (i__ = 1; i__ <= i__1; ++i__) {
876 i__2 = *kd + 1, i__3 = *n - i__ + 1;
877 lk = f2cmin(i__2,i__3);
878 scopy_(&lk, &a[i__ + i__ * a_dim1], &c__1, &ab[i__ * ab_dim1
887 /* Determine the pointer position for the workspace */
894 ls2 = lwmin - lt - lw - ls1;
895 /* LS2 = N*MAX(KD,FACTOPTNB) */
909 /* Set the workspace of the triangular matrix T to zero once such a */
910 /* way every time T is generated the upper/lower portion will be always zero */
912 slaset_("A", &ldt, kd, &c_b17, &c_b17, &work[tpos], &ldt);
917 for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
918 pn = *n - i__ - *kd + 1;
920 i__3 = *n - i__ - *kd + 1;
921 pk = f2cmin(i__3,*kd);
923 /* Compute the LQ factorization of the current block */
925 sgelqf_(kd, &pn, &a[i__ + (i__ + *kd) * a_dim1], lda, &tau[i__], &
926 work[s2pos], &ls2, &iinfo);
928 /* Copy the upper portion of A into AB */
931 for (j = i__; j <= i__3; ++j) {
933 i__4 = *kd, i__5 = *n - j;
934 lk = f2cmin(i__4,i__5) + 1;
936 scopy_(&lk, &a[j + j * a_dim1], lda, &ab[*kd + 1 + j *
941 slaset_("Lower", &pk, &pk, &c_b17, &c_b23, &a[i__ + (i__ + *kd) *
944 /* Form the matrix T */
946 slarft_("Forward", "Rowwise", &pn, &pk, &a[i__ + (i__ + *kd) *
947 a_dim1], lda, &tau[i__], &work[tpos], &ldt);
951 sgemm_("Conjugate", "No transpose", &pk, &pn, &pk, &c_b23, &work[
952 tpos], &ldt, &a[i__ + (i__ + *kd) * a_dim1], lda, &c_b17,
953 &work[s2pos], &lds2);
955 ssymm_("Right", uplo, &pk, &pn, &c_b23, &a[i__ + *kd + (i__ + *kd)
956 * a_dim1], lda, &work[s2pos], &lds2, &c_b17, &work[wpos],
959 sgemm_("No transpose", "Conjugate", &pk, &pk, &pn, &c_b23, &work[
960 wpos], &ldw, &work[s2pos], &lds2, &c_b17, &work[s1pos], &
963 sgemm_("No transpose", "No transpose", &pk, &pn, &pk, &c_b39, &
964 work[s1pos], &lds1, &a[i__ + (i__ + *kd) * a_dim1], lda, &
965 c_b23, &work[wpos], &ldw);
968 /* Update the unreduced submatrix A(i+kd:n,i+kd:n), using */
969 /* an update of the form: A := A - V'*W - W'*V */
971 ssyr2k_(uplo, "Conjugate", &pn, &pk, &c_b42, &a[i__ + (i__ + *kd)
972 * a_dim1], lda, &work[wpos], &ldw, &c_b23, &a[i__ + *kd +
973 (i__ + *kd) * a_dim1], lda);
977 /* Copy the upper band to AB which is the band storage matrix */
980 for (j = *n - *kd + 1; j <= i__2; ++j) {
982 i__1 = *kd, i__3 = *n - j;
983 lk = f2cmin(i__1,i__3) + 1;
985 scopy_(&lk, &a[j + j * a_dim1], lda, &ab[*kd + 1 + j * ab_dim1], &
992 /* Reduce the lower triangle of A to lower band matrix */
996 for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
997 pn = *n - i__ - *kd + 1;
999 i__3 = *n - i__ - *kd + 1;
1000 pk = f2cmin(i__3,*kd);
1002 /* Compute the QR factorization of the current block */
1004 sgeqrf_(&pn, kd, &a[i__ + *kd + i__ * a_dim1], lda, &tau[i__], &
1005 work[s2pos], &ls2, &iinfo);
1007 /* Copy the upper portion of A into AB */
1009 i__3 = i__ + pk - 1;
1010 for (j = i__; j <= i__3; ++j) {
1012 i__4 = *kd, i__5 = *n - j;
1013 lk = f2cmin(i__4,i__5) + 1;
1014 scopy_(&lk, &a[j + j * a_dim1], &c__1, &ab[j * ab_dim1 + 1], &
1019 slaset_("Upper", &pk, &pk, &c_b17, &c_b23, &a[i__ + *kd + i__ *
1022 /* Form the matrix T */
1024 slarft_("Forward", "Columnwise", &pn, &pk, &a[i__ + *kd + i__ *
1025 a_dim1], lda, &tau[i__], &work[tpos], &ldt);
1029 sgemm_("No transpose", "No transpose", &pn, &pk, &pk, &c_b23, &a[
1030 i__ + *kd + i__ * a_dim1], lda, &work[tpos], &ldt, &c_b17,
1031 &work[s2pos], &lds2);
1033 ssymm_("Left", uplo, &pn, &pk, &c_b23, &a[i__ + *kd + (i__ + *kd)
1034 * a_dim1], lda, &work[s2pos], &lds2, &c_b17, &work[wpos],
1037 sgemm_("Conjugate", "No transpose", &pk, &pk, &pn, &c_b23, &work[
1038 s2pos], &lds2, &work[wpos], &ldw, &c_b17, &work[s1pos], &
1041 sgemm_("No transpose", "No transpose", &pn, &pk, &pk, &c_b39, &a[
1042 i__ + *kd + i__ * a_dim1], lda, &work[s1pos], &lds1, &
1043 c_b23, &work[wpos], &ldw);
1046 /* Update the unreduced submatrix A(i+kd:n,i+kd:n), using */
1047 /* an update of the form: A := A - V*W' - W*V' */
1049 ssyr2k_(uplo, "No transpose", &pn, &pk, &c_b42, &a[i__ + *kd +
1050 i__ * a_dim1], lda, &work[wpos], &ldw, &c_b23, &a[i__ + *
1051 kd + (i__ + *kd) * a_dim1], lda);
1052 /* ================================================================== */
1053 /* RESTORE A FOR COMPARISON AND CHECKING TO BE REMOVED */
1054 /* DO 45 J = I, I+PK-1 */
1055 /* LK = MIN( KD, N-J ) + 1 */
1056 /* CALL SCOPY( LK, AB( 1, J ), 1, A( J, J ), 1 ) */
1058 /* ================================================================== */
1062 /* Copy the lower band to AB which is the band storage matrix */
1065 for (j = *n - *kd + 1; j <= i__1; ++j) {
1067 i__2 = *kd, i__3 = *n - j;
1068 lk = f2cmin(i__2,i__3) + 1;
1069 scopy_(&lk, &a[j + j * a_dim1], &c__1, &ab[j * ab_dim1 + 1], &
1075 work[1] = (real) lwmin;
1078 /* End of SSYTRD_SY2SB */
1080 } /* ssytrd_sy2sb__ */