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 integer c__1 = 1;
517 static integer c__5 = 5;
518 static logical c_true = TRUE_;
519 static logical c_false = FALSE_;
521 /* > \brief \b CLATMS */
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
531 /* SUBROUTINE CLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, */
532 /* KL, KU, PACK, A, LDA, WORK, INFO ) */
534 /* CHARACTER DIST, PACK, SYM */
535 /* INTEGER INFO, KL, KU, LDA, M, MODE, N */
536 /* REAL COND, DMAX */
537 /* INTEGER ISEED( 4 ) */
539 /* COMPLEX A( LDA, * ), WORK( * ) */
542 /* > \par Purpose: */
547 /* > CLATMS generates random matrices with specified singular values */
548 /* > (or hermitian with specified eigenvalues) */
549 /* > for testing LAPACK programs. */
551 /* > CLATMS operates by applying the following sequence of */
554 /* > Set the diagonal to D, where D may be input or */
555 /* > computed according to MODE, COND, DMAX, and SYM */
556 /* > as described below. */
558 /* > Generate a matrix with the appropriate band structure, by one */
559 /* > of two methods: */
562 /* > Generate a dense M x N matrix by multiplying D on the left */
563 /* > and the right by random unitary matrices, then: */
565 /* > Reduce the bandwidth according to KL and KU, using */
566 /* > Householder transformations. */
569 /* > Convert the bandwidth-0 (i.e., diagonal) matrix to a */
570 /* > bandwidth-1 matrix using Givens rotations, "chasing" */
571 /* > out-of-band elements back, much as in QR; then convert */
572 /* > the bandwidth-1 to a bandwidth-2 matrix, etc. Note */
573 /* > that for reasonably small bandwidths (relative to M and */
574 /* > N) this requires less storage, as a dense matrix is not */
575 /* > generated. Also, for hermitian or symmetric matrices, */
576 /* > only one triangle is generated. */
578 /* > Method A is chosen if the bandwidth is a large fraction of the */
579 /* > order of the matrix, and LDA is at least M (so a dense */
580 /* > matrix can be stored.) Method B is chosen if the bandwidth */
581 /* > is small (< 1/2 N for hermitian or symmetric, < .3 N+M for */
582 /* > non-symmetric), or LDA is less than M and not less than the */
585 /* > Pack the matrix if desired. Options specified by PACK are: */
587 /* > zero out upper half (if hermitian) */
588 /* > zero out lower half (if hermitian) */
589 /* > store the upper half columnwise (if hermitian or upper */
591 /* > store the lower half columnwise (if hermitian or lower */
593 /* > store the lower triangle in banded format (if hermitian or */
594 /* > lower triangular) */
595 /* > store the upper triangle in banded format (if hermitian or */
596 /* > upper triangular) */
597 /* > store the entire matrix in banded format */
598 /* > If Method B is chosen, and band format is specified, then the */
599 /* > matrix will be generated in the band format, so no repacking */
600 /* > will be necessary. */
609 /* > The number of rows of A. Not modified. */
615 /* > The number of columns of A. N must equal M if the matrix */
616 /* > is symmetric or hermitian (i.e., if SYM is not 'N') */
617 /* > Not modified. */
620 /* > \param[in] DIST */
622 /* > DIST is CHARACTER*1 */
623 /* > On entry, DIST specifies the type of distribution to be used */
624 /* > to generate the random eigen-/singular values. */
625 /* > 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) */
626 /* > 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) */
627 /* > 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) */
628 /* > Not modified. */
631 /* > \param[in,out] ISEED */
633 /* > ISEED is INTEGER array, dimension ( 4 ) */
634 /* > On entry ISEED specifies the seed of the random number */
635 /* > generator. They should lie between 0 and 4095 inclusive, */
636 /* > and ISEED(4) should be odd. The random number generator */
637 /* > uses a linear congruential sequence limited to small */
638 /* > integers, and so should produce machine independent */
639 /* > random numbers. The values of ISEED are changed on */
640 /* > exit, and can be used in the next call to CLATMS */
641 /* > to continue the same random number sequence. */
642 /* > Changed on exit. */
645 /* > \param[in] SYM */
647 /* > SYM is CHARACTER*1 */
648 /* > If SYM='H', the generated matrix is hermitian, with */
649 /* > eigenvalues specified by D, COND, MODE, and DMAX; they */
650 /* > may be positive, negative, or zero. */
651 /* > If SYM='P', the generated matrix is hermitian, with */
652 /* > eigenvalues (= singular values) specified by D, COND, */
653 /* > MODE, and DMAX; they will not be negative. */
654 /* > If SYM='N', the generated matrix is nonsymmetric, with */
655 /* > singular values specified by D, COND, MODE, and DMAX; */
656 /* > they will not be negative. */
657 /* > If SYM='S', the generated matrix is (complex) symmetric, */
658 /* > with singular values specified by D, COND, MODE, and */
659 /* > DMAX; they will not be negative. */
660 /* > Not modified. */
663 /* > \param[in,out] D */
665 /* > D is REAL array, dimension ( MIN( M, N ) ) */
666 /* > This array is used to specify the singular values or */
667 /* > eigenvalues of A (see SYM, above.) If MODE=0, then D is */
668 /* > assumed to contain the singular/eigenvalues, otherwise */
669 /* > they will be computed according to MODE, COND, and DMAX, */
670 /* > and placed in D. */
671 /* > Modified if MODE is nonzero. */
674 /* > \param[in] MODE */
676 /* > MODE is INTEGER */
677 /* > On entry this describes how the singular/eigenvalues are to */
678 /* > be specified: */
679 /* > MODE = 0 means use D as input */
680 /* > MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND */
681 /* > MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND */
682 /* > MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) */
683 /* > MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) */
684 /* > MODE = 5 sets D to random numbers in the range */
685 /* > ( 1/COND , 1 ) such that their logarithms */
686 /* > are uniformly distributed. */
687 /* > MODE = 6 set D to random numbers from same distribution */
688 /* > as the rest of the matrix. */
689 /* > MODE < 0 has the same meaning as ABS(MODE), except that */
690 /* > the order of the elements of D is reversed. */
691 /* > Thus if MODE is positive, D has entries ranging from */
692 /* > 1 to 1/COND, if negative, from 1/COND to 1, */
693 /* > If SYM='H', and MODE is neither 0, 6, nor -6, then */
694 /* > the elements of D will also be multiplied by a random */
695 /* > sign (i.e., +1 or -1.) */
696 /* > Not modified. */
699 /* > \param[in] COND */
702 /* > On entry, this is used as described under MODE above. */
703 /* > If used, it must be >= 1. Not modified. */
706 /* > \param[in] DMAX */
709 /* > If MODE is neither -6, 0 nor 6, the contents of D, as */
710 /* > computed according to MODE and COND, will be scaled by */
711 /* > DMAX / f2cmax(abs(D(i))); thus, the maximum absolute eigen- or */
712 /* > singular value (which is to say the norm) will be abs(DMAX). */
713 /* > Note that DMAX need not be positive: if DMAX is negative */
714 /* > (or zero), D will be scaled by a negative number (or zero). */
715 /* > Not modified. */
718 /* > \param[in] KL */
720 /* > KL is INTEGER */
721 /* > This specifies the lower bandwidth of the matrix. For */
722 /* > example, KL=0 implies upper triangular, KL=1 implies upper */
723 /* > Hessenberg, and KL being at least M-1 means that the matrix */
724 /* > has full lower bandwidth. KL must equal KU if the matrix */
725 /* > is symmetric or hermitian. */
726 /* > Not modified. */
729 /* > \param[in] KU */
731 /* > KU is INTEGER */
732 /* > This specifies the upper bandwidth of the matrix. For */
733 /* > example, KU=0 implies lower triangular, KU=1 implies lower */
734 /* > Hessenberg, and KU being at least N-1 means that the matrix */
735 /* > has full upper bandwidth. KL must equal KU if the matrix */
736 /* > is symmetric or hermitian. */
737 /* > Not modified. */
740 /* > \param[in] PACK */
742 /* > PACK is CHARACTER*1 */
743 /* > This specifies packing of matrix as follows: */
744 /* > 'N' => no packing */
745 /* > 'U' => zero out all subdiagonal entries (if symmetric */
746 /* > or hermitian) */
747 /* > 'L' => zero out all superdiagonal entries (if symmetric */
748 /* > or hermitian) */
749 /* > 'C' => store the upper triangle columnwise (only if the */
750 /* > matrix is symmetric, hermitian, or upper triangular) */
751 /* > 'R' => store the lower triangle columnwise (only if the */
752 /* > matrix is symmetric, hermitian, or lower triangular) */
753 /* > 'B' => store the lower triangle in band storage scheme */
754 /* > (only if the matrix is symmetric, hermitian, or */
755 /* > lower triangular) */
756 /* > 'Q' => store the upper triangle in band storage scheme */
757 /* > (only if the matrix is symmetric, hermitian, or */
758 /* > upper triangular) */
759 /* > 'Z' => store the entire matrix in band storage scheme */
760 /* > (pivoting can be provided for by using this */
761 /* > option to store A in the trailing rows of */
762 /* > the allocated storage) */
764 /* > Using these options, the various LAPACK packed and banded */
765 /* > storage schemes can be obtained: */
767 /* > PB, SB, HB, or TB - use 'B' or 'Q' */
768 /* > PP, SP, HB, or TP - use 'C' or 'R' */
770 /* > If two calls to CLATMS differ only in the PACK parameter, */
771 /* > they will generate mathematically equivalent matrices. */
772 /* > Not modified. */
775 /* > \param[in,out] A */
777 /* > A is COMPLEX array, dimension ( LDA, N ) */
778 /* > On exit A is the desired test matrix. A is first generated */
779 /* > in full (unpacked) form, and then packed, if so specified */
780 /* > by PACK. Thus, the first M elements of the first N */
781 /* > columns will always be modified. If PACK specifies a */
782 /* > packed or banded storage scheme, all LDA elements of the */
783 /* > first N columns will be modified; the elements of the */
784 /* > array which do not correspond to elements of the generated */
785 /* > matrix are set to zero. */
789 /* > \param[in] LDA */
791 /* > LDA is INTEGER */
792 /* > LDA specifies the first dimension of A as declared in the */
793 /* > calling program. If PACK='N', 'U', 'L', 'C', or 'R', then */
794 /* > LDA must be at least M. If PACK='B' or 'Q', then LDA must */
795 /* > be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). */
796 /* > If PACK='Z', LDA must be large enough to hold the packed */
797 /* > array: MIN( KU, N-1) + MIN( KL, M-1) + 1. */
798 /* > Not modified. */
801 /* > \param[out] WORK */
803 /* > WORK is COMPLEX array, dimension ( 3*MAX( N, M ) ) */
808 /* > \param[out] INFO */
810 /* > INFO is INTEGER */
811 /* > Error code. On exit, INFO will be set to one of the */
812 /* > following values: */
813 /* > 0 => normal return */
814 /* > -1 => M negative or unequal to N and SYM='S', 'H', or 'P' */
815 /* > -2 => N negative */
816 /* > -3 => DIST illegal string */
817 /* > -5 => SYM illegal string */
818 /* > -7 => MODE not in range -6 to 6 */
819 /* > -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 */
820 /* > -10 => KL negative */
821 /* > -11 => KU negative, or SYM is not 'N' and KU is not equal to */
823 /* > -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; */
824 /* > or PACK='C' or 'Q' and SYM='N' and KL is not zero; */
825 /* > or PACK='R' or 'B' and SYM='N' and KU is not zero; */
826 /* > or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not */
828 /* > -14 => LDA is less than M, or PACK='Z' and LDA is less than */
829 /* > MIN(KU,N-1) + MIN(KL,M-1) + 1. */
830 /* > 1 => Error return from SLATM1 */
831 /* > 2 => Cannot scale to DMAX (f2cmax. sing. value is 0) */
832 /* > 3 => Error return from CLAGGE, CLAGHE or CLAGSY */
838 /* > \author Univ. of Tennessee */
839 /* > \author Univ. of California Berkeley */
840 /* > \author Univ. of Colorado Denver */
841 /* > \author NAG Ltd. */
843 /* > \date December 2016 */
845 /* > \ingroup complex_matgen */
847 /* ===================================================================== */
848 /* Subroutine */ int clatms_(integer *m, integer *n, char *dist, integer *
849 iseed, char *sym, real *d__, integer *mode, real *cond, real *dmax__,
850 integer *kl, integer *ku, char *pack, complex *a, integer *lda,
851 complex *work, integer *info)
853 /* System generated locals */
854 integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
855 real r__1, r__2, r__3;
856 complex q__1, q__2, q__3;
859 /* Local variables */
871 extern logical lsame_(char *, char *);
873 extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
875 integer idist, mnmin, iskew;
876 complex extra, dummy;
877 extern /* Subroutine */ int slatm1_(integer *, real *, integer *, integer
878 *, integer *, real *, integer *, integer *);
880 extern /* Subroutine */ int clagge_(integer *, integer *, integer *,
881 integer *, real *, complex *, integer *, integer *, complex *,
882 integer *), claghe_(integer *, integer *, real *, complex *,
883 integer *, integer *, complex *, integer *);
886 integer iendch, ir, jr, ipackg, mr;
887 //extern /* Complex */ VOID clarnd_(complex *, integer *, integer *);
888 extern complex clarnd_(integer *, integer *);
891 extern /* Subroutine */ int claset_(char *, integer *, integer *, complex
892 *, complex *, complex *, integer *), clartg_(complex *,
893 complex *, real *, complex *, complex *), xerbla_(char *, integer
894 *), clagsy_(integer *, integer *, real *, complex *,
895 integer *, integer *, complex *, integer *);
896 extern real slarnd_(integer *, integer *);
897 extern /* Subroutine */ int clarot_(logical *, logical *, logical *,
898 integer *, complex *, complex *, complex *, integer *, complex *,
900 logical iltemp, givens;
901 integer ioffst, irsign;
902 logical ilextr, topdwn;
903 integer ir1, ir2, isympk, jch, llb, jkl, jku, uub;
906 /* -- LAPACK computational routine (version 3.7.0) -- */
907 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
908 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
912 /* ===================================================================== */
915 /* 1) Decode and Test the input parameters. */
916 /* Initialize flags & seed. */
918 /* Parameter adjustments */
922 a_offset = 1 + a_dim1 * 1;
929 /* Quick return if possible */
931 if (*m == 0 || *n == 0) {
937 if (lsame_(dist, "U")) {
939 } else if (lsame_(dist, "S")) {
941 } else if (lsame_(dist, "N")) {
949 if (lsame_(sym, "N")) {
953 } else if (lsame_(sym, "P")) {
957 } else if (lsame_(sym, "S")) {
961 } else if (lsame_(sym, "H")) {
972 if (lsame_(pack, "N")) {
974 } else if (lsame_(pack, "U")) {
977 } else if (lsame_(pack, "L")) {
980 } else if (lsame_(pack, "C")) {
983 } else if (lsame_(pack, "R")) {
986 } else if (lsame_(pack, "B")) {
989 } else if (lsame_(pack, "Q")) {
992 } else if (lsame_(pack, "Z")) {
998 /* Set certain internal parameters */
1000 mnmin = f2cmin(*m,*n);
1002 i__1 = *kl, i__2 = *m - 1;
1003 llb = f2cmin(i__1,i__2);
1005 i__1 = *ku, i__2 = *n - 1;
1006 uub = f2cmin(i__1,i__2);
1008 i__1 = *m, i__2 = *n + llb;
1009 mr = f2cmin(i__1,i__2);
1011 i__1 = *n, i__2 = *m + uub;
1012 nc = f2cmin(i__1,i__2);
1014 if (ipack == 5 || ipack == 6) {
1016 } else if (ipack == 7) {
1017 minlda = llb + uub + 1;
1022 /* Use Givens rotation method if bandwidth small enough, */
1023 /* or if LDA is too small to store the matrix unpacked. */
1028 i__1 = 1, i__2 = mr + nc;
1029 if ((real) (llb + uub) < (real) f2cmax(i__1,i__2) * .3f) {
1033 if (llb << 1 < *m) {
1037 if (*lda < *m && *lda >= minlda) {
1041 /* Set INFO if an error */
1045 } else if (*m != *n && isym != 1) {
1047 } else if (*n < 0) {
1049 } else if (idist == -1) {
1051 } else if (isym == -1) {
1053 } else if (abs(*mode) > 6) {
1055 } else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.f) {
1057 } else if (*kl < 0) {
1059 } else if (*ku < 0 || isym != 1 && *kl != *ku) {
1061 } else if (ipack == -1 || isympk == 1 && isym == 1 || isympk == 2 && isym
1062 == 1 && *kl > 0 || isympk == 3 && isym == 1 && *ku > 0 || isympk
1065 } else if (*lda < f2cmax(1,minlda)) {
1071 xerbla_("CLATMS", &i__1);
1075 /* Initialize random number generator */
1077 for (i__ = 1; i__ <= 4; ++i__) {
1078 iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096;
1082 if (iseed[4] % 2 != 1) {
1086 /* 2) Set up D if indicated. */
1088 /* Compute D according to COND and MODE */
1090 slatm1_(mode, cond, &irsign, &idist, &iseed[1], &d__[1], &mnmin, &iinfo);
1096 /* Choose Top-Down if D is (apparently) increasing, */
1097 /* Bottom-Up if D is (apparently) decreasing. */
1099 if (abs(d__[1]) <= (r__1 = d__[mnmin], abs(r__1))) {
1105 if (*mode != 0 && abs(*mode) != 6) {
1111 for (i__ = 2; i__ <= i__1; ++i__) {
1113 r__2 = temp, r__3 = (r__1 = d__[i__], abs(r__1));
1114 temp = f2cmax(r__2,r__3);
1119 alpha = *dmax__ / temp;
1125 sscal_(&mnmin, &alpha, &d__[1], &c__1);
1129 claset_("Full", lda, n, &c_b1, &c_b1, &a[a_offset], lda);
1131 /* 3) Generate Banded Matrix using Givens rotations. */
1132 /* Also the special case of UUB=LLB=0 */
1134 /* Compute Addressing constants to cover all */
1135 /* storage formats. Whether GE, HE, SY, GB, HB, or SB, */
1136 /* upper or lower triangle or both, */
1137 /* the (i,j)-th element is in */
1138 /* A( i - ISKEW*j + IOFFST, j ) */
1154 /* IPACKG is the format that the matrix is generated in. If this is */
1155 /* different from IPACK, then the matrix must be repacked at the */
1156 /* end. It also signals how to compute the norm, for scaling. */
1160 /* Diagonal Matrix -- We are done, unless it */
1161 /* is to be stored HP/SP/PP/TP (PACK='R' or 'C') */
1163 if (llb == 0 && uub == 0) {
1165 for (j = 1; j <= i__1; ++j) {
1166 i__2 = (1 - iskew) * j + ioffst + j * a_dim1;
1168 q__1.r = d__[i__3], q__1.i = 0.f;
1169 a[i__2].r = q__1.r, a[i__2].i = q__1.i;
1173 if (ipack <= 2 || ipack >= 5) {
1177 } else if (givens) {
1179 /* Check whether to use Givens rotations, */
1180 /* Householder transformations, or nothing. */
1184 /* Non-symmetric -- A = U D V */
1193 for (j = 1; j <= i__1; ++j) {
1194 i__2 = (1 - iskew) * j + ioffst + j * a_dim1;
1196 q__1.r = d__[i__3], q__1.i = 0.f;
1197 a[i__2].r = q__1.r, a[i__2].i = q__1.i;
1204 for (jku = 1; jku <= i__1; ++jku) {
1206 /* Transform from bandwidth JKL, JKU-1 to JKL, JKU */
1208 /* Last row actually rotated is M */
1209 /* Last column actually rotated is MIN( M+JKU, N ) */
1213 i__2 = f2cmin(i__3,*n) + jkl - 1;
1214 for (jr = 1; jr <= i__2; ++jr) {
1215 extra.r = 0.f, extra.i = 0.f;
1216 angle = slarnd_(&c__1, &iseed[1]) *
1217 6.2831853071795864769252867663f;
1219 //clarnd_(&q__2, &c__5, &iseed[1]);
1220 q__2=clarnd_(&c__5, &iseed[1]);
1221 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1222 c__.r = q__1.r, c__.i = q__1.i;
1224 //clarnd_(&q__2, &c__5, &iseed[1]);
1225 q__2=clarnd_(&c__5, &iseed[1]);
1226 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1227 s.r = q__1.r, s.i = q__1.i;
1229 i__3 = 1, i__4 = jr - jkl;
1230 icol = f2cmax(i__3,i__4);
1233 i__3 = *n, i__4 = jr + jku;
1234 il = f2cmin(i__3,i__4) + 1 - icol;
1236 clarot_(&c_true, &L__1, &c_false, &il, &c__, &s, &
1237 a[jr - iskew * icol + ioffst + icol *
1238 a_dim1], &ilda, &extra, &dummy);
1241 /* Chase "EXTRA" back up */
1246 for (jch = jr - jkl; i__3 < 0 ? jch >= 1 : jch <= 1;
1249 clartg_(&a[ir + 1 - iskew * (ic + 1) + ioffst
1250 + (ic + 1) * a_dim1], &extra, &realc,
1252 //clarnd_(&q__1, &c__5, &iseed[1]);
1253 q__1=clarnd_(&c__5, &iseed[1]);
1254 dummy.r = q__1.r, dummy.i = q__1.i;
1255 q__2.r = realc * dummy.r, q__2.i = realc *
1257 r_cnjg(&q__1, &q__2);
1258 c__.r = q__1.r, c__.i = q__1.i;
1259 q__3.r = -s.r, q__3.i = -s.i;
1260 q__2.r = q__3.r * dummy.r - q__3.i * dummy.i,
1261 q__2.i = q__3.r * dummy.i + q__3.i *
1263 r_cnjg(&q__1, &q__2);
1264 s.r = q__1.r, s.i = q__1.i;
1267 i__4 = 1, i__5 = jch - jku;
1268 irow = f2cmax(i__4,i__5);
1270 ctemp.r = 0.f, ctemp.i = 0.f;
1272 clarot_(&c_false, &iltemp, &c_true, &il, &c__, &s,
1273 &a[irow - iskew * ic + ioffst + ic *
1274 a_dim1], &ilda, &ctemp, &extra);
1276 clartg_(&a[irow + 1 - iskew * (ic + 1) +
1277 ioffst + (ic + 1) * a_dim1], &ctemp, &
1279 //clarnd_(&q__1, &c__5, &iseed[1]);
1280 q__1=clarnd_(&c__5, &iseed[1]);
1281 dummy.r = q__1.r, dummy.i = q__1.i;
1282 q__2.r = realc * dummy.r, q__2.i = realc *
1284 r_cnjg(&q__1, &q__2);
1285 c__.r = q__1.r, c__.i = q__1.i;
1286 q__3.r = -s.r, q__3.i = -s.i;
1287 q__2.r = q__3.r * dummy.r - q__3.i * dummy.i,
1288 q__2.i = q__3.r * dummy.i + q__3.i *
1290 r_cnjg(&q__1, &q__2);
1291 s.r = q__1.r, s.i = q__1.i;
1294 i__4 = 1, i__5 = jch - jku - jkl;
1295 icol = f2cmax(i__4,i__5);
1297 extra.r = 0.f, extra.i = 0.f;
1298 L__1 = jch > jku + jkl;
1299 clarot_(&c_true, &L__1, &c_true, &il, &c__, &
1300 s, &a[irow - iskew * icol + ioffst +
1301 icol * a_dim1], &ilda, &extra, &ctemp)
1315 for (jkl = 1; jkl <= i__1; ++jkl) {
1317 /* Transform from bandwidth JKL-1, JKU to JKL, JKU */
1321 i__2 = f2cmin(i__3,*m) + jku - 1;
1322 for (jc = 1; jc <= i__2; ++jc) {
1323 extra.r = 0.f, extra.i = 0.f;
1324 angle = slarnd_(&c__1, &iseed[1]) *
1325 6.2831853071795864769252867663f;
1327 //clarnd_(&q__2, &c__5, &iseed[1]);
1328 q__2=clarnd_(&c__5, &iseed[1]);
1329 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1330 c__.r = q__1.r, c__.i = q__1.i;
1332 //clarnd_(&q__2, &c__5, &iseed[1]);
1333 q__2=clarnd_(&c__5, &iseed[1]);
1334 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1335 s.r = q__1.r, s.i = q__1.i;
1337 i__3 = 1, i__4 = jc - jku;
1338 irow = f2cmax(i__3,i__4);
1341 i__3 = *m, i__4 = jc + jkl;
1342 il = f2cmin(i__3,i__4) + 1 - irow;
1344 clarot_(&c_false, &L__1, &c_false, &il, &c__, &s,
1345 &a[irow - iskew * jc + ioffst + jc *
1346 a_dim1], &ilda, &extra, &dummy);
1349 /* Chase "EXTRA" back up */
1354 for (jch = jc - jku; i__3 < 0 ? jch >= 1 : jch <= 1;
1357 clartg_(&a[ir + 1 - iskew * (ic + 1) + ioffst
1358 + (ic + 1) * a_dim1], &extra, &realc,
1360 //clarnd_(&q__1, &c__5, &iseed[1]);
1361 q__1=clarnd_(&c__5, &iseed[1]);
1362 dummy.r = q__1.r, dummy.i = q__1.i;
1363 q__2.r = realc * dummy.r, q__2.i = realc *
1365 r_cnjg(&q__1, &q__2);
1366 c__.r = q__1.r, c__.i = q__1.i;
1367 q__3.r = -s.r, q__3.i = -s.i;
1368 q__2.r = q__3.r * dummy.r - q__3.i * dummy.i,
1369 q__2.i = q__3.r * dummy.i + q__3.i *
1371 r_cnjg(&q__1, &q__2);
1372 s.r = q__1.r, s.i = q__1.i;
1375 i__4 = 1, i__5 = jch - jkl;
1376 icol = f2cmax(i__4,i__5);
1378 ctemp.r = 0.f, ctemp.i = 0.f;
1380 clarot_(&c_true, &iltemp, &c_true, &il, &c__, &s,
1381 &a[ir - iskew * icol + ioffst + icol *
1382 a_dim1], &ilda, &ctemp, &extra);
1384 clartg_(&a[ir + 1 - iskew * (icol + 1) +
1385 ioffst + (icol + 1) * a_dim1], &ctemp,
1386 &realc, &s, &dummy);
1387 //clarnd_(&q__1, &c__5, &iseed[1]);
1388 q__1=clarnd_(&c__5, &iseed[1]);
1389 dummy.r = q__1.r, dummy.i = q__1.i;
1390 q__2.r = realc * dummy.r, q__2.i = realc *
1392 r_cnjg(&q__1, &q__2);
1393 c__.r = q__1.r, c__.i = q__1.i;
1394 q__3.r = -s.r, q__3.i = -s.i;
1395 q__2.r = q__3.r * dummy.r - q__3.i * dummy.i,
1396 q__2.i = q__3.r * dummy.i + q__3.i *
1398 r_cnjg(&q__1, &q__2);
1399 s.r = q__1.r, s.i = q__1.i;
1401 i__4 = 1, i__5 = jch - jkl - jku;
1402 irow = f2cmax(i__4,i__5);
1404 extra.r = 0.f, extra.i = 0.f;
1405 L__1 = jch > jkl + jku;
1406 clarot_(&c_false, &L__1, &c_true, &il, &c__, &
1407 s, &a[irow - iskew * icol + ioffst +
1408 icol * a_dim1], &ilda, &extra, &ctemp)
1422 /* Bottom-Up -- Start at the bottom right. */
1426 for (jku = 1; jku <= i__1; ++jku) {
1428 /* Transform from bandwidth JKL, JKU-1 to JKL, JKU */
1430 /* First row actually rotated is M */
1431 /* First column actually rotated is MIN( M+JKU, N ) */
1434 i__2 = *m, i__3 = *n + jkl;
1435 iendch = f2cmin(i__2,i__3) - 1;
1439 for (jc = f2cmin(i__2,*n) - 1; jc >= i__3; --jc) {
1440 extra.r = 0.f, extra.i = 0.f;
1441 angle = slarnd_(&c__1, &iseed[1]) *
1442 6.2831853071795864769252867663f;
1444 //clarnd_(&q__2, &c__5, &iseed[1]);
1445 q__2=clarnd_(&c__5, &iseed[1]);
1446 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1447 c__.r = q__1.r, c__.i = q__1.i;
1449 //clarnd_(&q__2, &c__5, &iseed[1]);
1450 q__2=clarnd_(&c__5, &iseed[1]);
1451 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1452 s.r = q__1.r, s.i = q__1.i;
1454 i__2 = 1, i__4 = jc - jku + 1;
1455 irow = f2cmax(i__2,i__4);
1458 i__2 = *m, i__4 = jc + jkl + 1;
1459 il = f2cmin(i__2,i__4) + 1 - irow;
1460 L__1 = jc + jkl < *m;
1461 clarot_(&c_false, &c_false, &L__1, &il, &c__, &s,
1462 &a[irow - iskew * jc + ioffst + jc *
1463 a_dim1], &ilda, &dummy, &extra);
1466 /* Chase "EXTRA" back down */
1471 for (jch = jc + jkl; i__4 < 0 ? jch >= i__2 : jch <=
1472 i__2; jch += i__4) {
1475 clartg_(&a[jch - iskew * ic + ioffst + ic *
1476 a_dim1], &extra, &realc, &s, &dummy);
1477 //clarnd_(&q__1, &c__5, &iseed[1]);
1478 q__1=clarnd_(&c__5, &iseed[1]);
1479 dummy.r = q__1.r, dummy.i = q__1.i;
1480 q__1.r = realc * dummy.r, q__1.i = realc *
1482 c__.r = q__1.r, c__.i = q__1.i;
1483 q__1.r = s.r * dummy.r - s.i * dummy.i,
1484 q__1.i = s.r * dummy.i + s.i *
1486 s.r = q__1.r, s.i = q__1.i;
1490 i__5 = *n - 1, i__6 = jch + jku;
1491 icol = f2cmin(i__5,i__6);
1492 iltemp = jch + jku < *n;
1493 ctemp.r = 0.f, ctemp.i = 0.f;
1494 i__5 = icol + 2 - ic;
1495 clarot_(&c_true, &ilextr, &iltemp, &i__5, &c__, &
1496 s, &a[jch - iskew * ic + ioffst + ic *
1497 a_dim1], &ilda, &extra, &ctemp);
1499 clartg_(&a[jch - iskew * icol + ioffst + icol
1500 * a_dim1], &ctemp, &realc, &s, &dummy)
1502 //clarnd_(&q__1, &c__5, &iseed[1]);
1503 q__1=clarnd_(&c__5, &iseed[1]);
1504 dummy.r = q__1.r, dummy.i = q__1.i;
1505 q__1.r = realc * dummy.r, q__1.i = realc *
1507 c__.r = q__1.r, c__.i = q__1.i;
1508 q__1.r = s.r * dummy.r - s.i * dummy.i,
1509 q__1.i = s.r * dummy.i + s.i *
1511 s.r = q__1.r, s.i = q__1.i;
1513 i__5 = iendch, i__6 = jch + jkl + jku;
1514 il = f2cmin(i__5,i__6) + 2 - jch;
1515 extra.r = 0.f, extra.i = 0.f;
1516 L__1 = jch + jkl + jku <= iendch;
1517 clarot_(&c_false, &c_true, &L__1, &il, &c__, &
1518 s, &a[jch - iskew * icol + ioffst +
1519 icol * a_dim1], &ilda, &ctemp, &extra)
1532 for (jkl = 1; jkl <= i__1; ++jkl) {
1534 /* Transform from bandwidth JKL-1, JKU to JKL, JKU */
1536 /* First row actually rotated is MIN( N+JKL, M ) */
1537 /* First column actually rotated is N */
1540 i__3 = *n, i__4 = *m + jku;
1541 iendch = f2cmin(i__3,i__4) - 1;
1545 for (jr = f2cmin(i__3,*m) - 1; jr >= i__4; --jr) {
1546 extra.r = 0.f, extra.i = 0.f;
1547 angle = slarnd_(&c__1, &iseed[1]) *
1548 6.2831853071795864769252867663f;
1550 //clarnd_(&q__2, &c__5, &iseed[1]);
1551 q__2=clarnd_(&c__5, &iseed[1]);
1552 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1553 c__.r = q__1.r, c__.i = q__1.i;
1555 //clarnd_(&q__2, &c__5, &iseed[1]);
1556 q__2=clarnd_(&c__5, &iseed[1]);
1557 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1558 s.r = q__1.r, s.i = q__1.i;
1560 i__3 = 1, i__2 = jr - jkl + 1;
1561 icol = f2cmax(i__3,i__2);
1564 i__3 = *n, i__2 = jr + jku + 1;
1565 il = f2cmin(i__3,i__2) + 1 - icol;
1566 L__1 = jr + jku < *n;
1567 clarot_(&c_true, &c_false, &L__1, &il, &c__, &s, &
1568 a[jr - iskew * icol + ioffst + icol *
1569 a_dim1], &ilda, &dummy, &extra);
1572 /* Chase "EXTRA" back down */
1577 for (jch = jr + jku; i__2 < 0 ? jch >= i__3 : jch <=
1578 i__3; jch += i__2) {
1581 clartg_(&a[ir - iskew * jch + ioffst + jch *
1582 a_dim1], &extra, &realc, &s, &dummy);
1583 //clarnd_(&q__1, &c__5, &iseed[1]);
1584 q__1=clarnd_(&c__5, &iseed[1]);
1585 dummy.r = q__1.r, dummy.i = q__1.i;
1586 q__1.r = realc * dummy.r, q__1.i = realc *
1588 c__.r = q__1.r, c__.i = q__1.i;
1589 q__1.r = s.r * dummy.r - s.i * dummy.i,
1590 q__1.i = s.r * dummy.i + s.i *
1592 s.r = q__1.r, s.i = q__1.i;
1596 i__5 = *m - 1, i__6 = jch + jkl;
1597 irow = f2cmin(i__5,i__6);
1598 iltemp = jch + jkl < *m;
1599 ctemp.r = 0.f, ctemp.i = 0.f;
1600 i__5 = irow + 2 - ir;
1601 clarot_(&c_false, &ilextr, &iltemp, &i__5, &c__, &
1602 s, &a[ir - iskew * jch + ioffst + jch *
1603 a_dim1], &ilda, &extra, &ctemp);
1605 clartg_(&a[irow - iskew * jch + ioffst + jch *
1606 a_dim1], &ctemp, &realc, &s, &dummy);
1607 //clarnd_(&q__1, &c__5, &iseed[1]);
1608 q__1=clarnd_(&c__5, &iseed[1]);
1609 dummy.r = q__1.r, dummy.i = q__1.i;
1610 q__1.r = realc * dummy.r, q__1.i = realc *
1612 c__.r = q__1.r, c__.i = q__1.i;
1613 q__1.r = s.r * dummy.r - s.i * dummy.i,
1614 q__1.i = s.r * dummy.i + s.i *
1616 s.r = q__1.r, s.i = q__1.i;
1618 i__5 = iendch, i__6 = jch + jkl + jku;
1619 il = f2cmin(i__5,i__6) + 2 - jch;
1620 extra.r = 0.f, extra.i = 0.f;
1621 L__1 = jch + jkl + jku <= iendch;
1622 clarot_(&c_true, &c_true, &L__1, &il, &c__, &
1623 s, &a[irow - iskew * jch + ioffst +
1624 jch * a_dim1], &ilda, &ctemp, &extra);
1638 /* Symmetric -- A = U D U' */
1639 /* Hermitian -- A = U D U* */
1646 /* Top-Down -- Generate Upper triangle only */
1656 for (j = 1; j <= i__1; ++j) {
1657 i__4 = (1 - iskew) * j + ioffg + j * a_dim1;
1659 q__1.r = d__[i__2], q__1.i = 0.f;
1660 a[i__4].r = q__1.r, a[i__4].i = q__1.i;
1665 for (k = 1; k <= i__1; ++k) {
1667 for (jc = 1; jc <= i__4; ++jc) {
1669 i__2 = 1, i__3 = jc - k;
1670 irow = f2cmax(i__2,i__3);
1672 i__2 = jc + 1, i__3 = k + 2;
1673 il = f2cmin(i__2,i__3);
1674 extra.r = 0.f, extra.i = 0.f;
1675 i__2 = jc - iskew * (jc + 1) + ioffg + (jc + 1) *
1677 ctemp.r = a[i__2].r, ctemp.i = a[i__2].i;
1678 angle = slarnd_(&c__1, &iseed[1]) *
1679 6.2831853071795864769252867663f;
1681 //clarnd_(&q__2, &c__5, &iseed[1]);
1682 q__2=clarnd_(&c__5, &iseed[1]);
1683 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1684 c__.r = q__1.r, c__.i = q__1.i;
1686 //clarnd_(&q__2, &c__5, &iseed[1]);
1687 q__2=clarnd_(&c__5, &iseed[1]);
1688 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1689 s.r = q__1.r, s.i = q__1.i;
1691 ct.r = c__.r, ct.i = c__.i;
1692 st.r = s.r, st.i = s.i;
1694 r_cnjg(&q__1, &ctemp);
1695 ctemp.r = q__1.r, ctemp.i = q__1.i;
1696 r_cnjg(&q__1, &c__);
1697 ct.r = q__1.r, ct.i = q__1.i;
1699 st.r = q__1.r, st.i = q__1.i;
1702 clarot_(&c_false, &L__1, &c_true, &il, &c__, &s, &a[
1703 irow - iskew * jc + ioffg + jc * a_dim1], &
1704 ilda, &extra, &ctemp);
1706 i__3 = k, i__5 = *n - jc;
1707 i__2 = f2cmin(i__3,i__5) + 1;
1708 clarot_(&c_true, &c_true, &c_false, &i__2, &ct, &st, &
1709 a[(1 - iskew) * jc + ioffg + jc * a_dim1], &
1710 ilda, &ctemp, &dummy);
1712 /* Chase EXTRA back up the matrix */
1716 for (jch = jc - k; i__2 < 0 ? jch >= 1 : jch <= 1;
1718 clartg_(&a[jch + 1 - iskew * (icol + 1) + ioffg +
1719 (icol + 1) * a_dim1], &extra, &realc, &s,
1721 //clarnd_(&q__1, &c__5, &iseed[1]);
1722 q__1=clarnd_(&c__5, &iseed[1]);
1723 dummy.r = q__1.r, dummy.i = q__1.i;
1724 q__2.r = realc * dummy.r, q__2.i = realc *
1726 r_cnjg(&q__1, &q__2);
1727 c__.r = q__1.r, c__.i = q__1.i;
1728 q__3.r = -s.r, q__3.i = -s.i;
1729 q__2.r = q__3.r * dummy.r - q__3.i * dummy.i,
1730 q__2.i = q__3.r * dummy.i + q__3.i *
1732 r_cnjg(&q__1, &q__2);
1733 s.r = q__1.r, s.i = q__1.i;
1734 i__3 = jch - iskew * (jch + 1) + ioffg + (jch + 1)
1736 ctemp.r = a[i__3].r, ctemp.i = a[i__3].i;
1738 ct.r = c__.r, ct.i = c__.i;
1739 st.r = s.r, st.i = s.i;
1741 r_cnjg(&q__1, &ctemp);
1742 ctemp.r = q__1.r, ctemp.i = q__1.i;
1743 r_cnjg(&q__1, &c__);
1744 ct.r = q__1.r, ct.i = q__1.i;
1746 st.r = q__1.r, st.i = q__1.i;
1749 clarot_(&c_true, &c_true, &c_true, &i__3, &c__, &
1750 s, &a[(1 - iskew) * jch + ioffg + jch *
1751 a_dim1], &ilda, &ctemp, &extra);
1753 i__3 = 1, i__5 = jch - k;
1754 irow = f2cmax(i__3,i__5);
1756 i__3 = jch + 1, i__5 = k + 2;
1757 il = f2cmin(i__3,i__5);
1758 extra.r = 0.f, extra.i = 0.f;
1760 clarot_(&c_false, &L__1, &c_true, &il, &ct, &st, &
1761 a[irow - iskew * jch + ioffg + jch *
1762 a_dim1], &ilda, &extra, &ctemp);
1771 /* If we need lower triangle, copy from upper. Note that */
1772 /* the order of copying is chosen to work for 'q' -> 'b' */
1774 if (ipack != ipackg && ipack != 3) {
1776 for (jc = 1; jc <= i__1; ++jc) {
1777 irow = ioffst - iskew * jc;
1780 i__2 = *n, i__3 = jc + uub;
1781 i__4 = f2cmin(i__2,i__3);
1782 for (jr = jc; jr <= i__4; ++jr) {
1783 i__2 = jr + irow + jc * a_dim1;
1784 i__3 = jc - iskew * jr + ioffg + jr * a_dim1;
1785 a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
1790 i__2 = *n, i__3 = jc + uub;
1791 i__4 = f2cmin(i__2,i__3);
1792 for (jr = jc; jr <= i__4; ++jr) {
1793 i__2 = jr + irow + jc * a_dim1;
1794 r_cnjg(&q__1, &a[jc - iskew * jr + ioffg + jr
1796 a[i__2].r = q__1.r, a[i__2].i = q__1.i;
1804 for (jc = *n - uub + 1; jc <= i__1; ++jc) {
1806 for (jr = *n + 2 - jc; jr <= i__4; ++jr) {
1807 i__2 = jr + jc * a_dim1;
1808 a[i__2].r = 0.f, a[i__2].i = 0.f;
1822 /* Bottom-Up -- Generate Lower triangle only */
1834 for (j = 1; j <= i__1; ++j) {
1835 i__4 = (1 - iskew) * j + ioffg + j * a_dim1;
1837 q__1.r = d__[i__2], q__1.i = 0.f;
1838 a[i__4].r = q__1.r, a[i__4].i = q__1.i;
1843 for (k = 1; k <= i__1; ++k) {
1844 for (jc = *n - 1; jc >= 1; --jc) {
1846 i__4 = *n + 1 - jc, i__2 = k + 2;
1847 il = f2cmin(i__4,i__2);
1848 extra.r = 0.f, extra.i = 0.f;
1849 i__4 = (1 - iskew) * jc + 1 + ioffg + jc * a_dim1;
1850 ctemp.r = a[i__4].r, ctemp.i = a[i__4].i;
1851 angle = slarnd_(&c__1, &iseed[1]) *
1852 6.2831853071795864769252867663f;
1854 //clarnd_(&q__2, &c__5, &iseed[1]);
1855 q__2=clarnd_(&c__5, &iseed[1]);
1856 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1857 c__.r = q__1.r, c__.i = q__1.i;
1859 //clarnd_(&q__2, &c__5, &iseed[1]);
1860 q__2=clarnd_(&c__5, &iseed[1]);
1861 q__1.r = r__1 * q__2.r, q__1.i = r__1 * q__2.i;
1862 s.r = q__1.r, s.i = q__1.i;
1864 ct.r = c__.r, ct.i = c__.i;
1865 st.r = s.r, st.i = s.i;
1867 r_cnjg(&q__1, &ctemp);
1868 ctemp.r = q__1.r, ctemp.i = q__1.i;
1869 r_cnjg(&q__1, &c__);
1870 ct.r = q__1.r, ct.i = q__1.i;
1872 st.r = q__1.r, st.i = q__1.i;
1875 clarot_(&c_false, &c_true, &L__1, &il, &c__, &s, &a[(
1876 1 - iskew) * jc + ioffg + jc * a_dim1], &ilda,
1879 i__4 = 1, i__2 = jc - k + 1;
1880 icol = f2cmax(i__4,i__2);
1881 i__4 = jc + 2 - icol;
1882 clarot_(&c_true, &c_false, &c_true, &i__4, &ct, &st, &
1883 a[jc - iskew * icol + ioffg + icol * a_dim1],
1884 &ilda, &dummy, &ctemp);
1886 /* Chase EXTRA back down the matrix */
1891 for (jch = jc + k; i__2 < 0 ? jch >= i__4 : jch <=
1892 i__4; jch += i__2) {
1893 clartg_(&a[jch - iskew * icol + ioffg + icol *
1894 a_dim1], &extra, &realc, &s, &dummy);
1895 //clarnd_(&q__1, &c__5, &iseed[1]);
1896 q__1=clarnd_(&c__5, &iseed[1]);
1897 dummy.r = q__1.r, dummy.i = q__1.i;
1898 q__1.r = realc * dummy.r, q__1.i = realc *
1900 c__.r = q__1.r, c__.i = q__1.i;
1901 q__1.r = s.r * dummy.r - s.i * dummy.i, q__1.i =
1902 s.r * dummy.i + s.i * dummy.r;
1903 s.r = q__1.r, s.i = q__1.i;
1904 i__3 = (1 - iskew) * jch + 1 + ioffg + jch *
1906 ctemp.r = a[i__3].r, ctemp.i = a[i__3].i;
1908 ct.r = c__.r, ct.i = c__.i;
1909 st.r = s.r, st.i = s.i;
1911 r_cnjg(&q__1, &ctemp);
1912 ctemp.r = q__1.r, ctemp.i = q__1.i;
1913 r_cnjg(&q__1, &c__);
1914 ct.r = q__1.r, ct.i = q__1.i;
1916 st.r = q__1.r, st.i = q__1.i;
1919 clarot_(&c_true, &c_true, &c_true, &i__3, &c__, &
1920 s, &a[jch - iskew * icol + ioffg + icol *
1921 a_dim1], &ilda, &extra, &ctemp);
1923 i__3 = *n + 1 - jch, i__5 = k + 2;
1924 il = f2cmin(i__3,i__5);
1925 extra.r = 0.f, extra.i = 0.f;
1926 L__1 = *n - jch > k;
1927 clarot_(&c_false, &c_true, &L__1, &il, &ct, &st, &
1928 a[(1 - iskew) * jch + ioffg + jch *
1929 a_dim1], &ilda, &ctemp, &extra);
1938 /* If we need upper triangle, copy from lower. Note that */
1939 /* the order of copying is chosen to work for 'b' -> 'q' */
1941 if (ipack != ipackg && ipack != 4) {
1942 for (jc = *n; jc >= 1; --jc) {
1943 irow = ioffst - iskew * jc;
1946 i__2 = 1, i__4 = jc - uub;
1947 i__1 = f2cmax(i__2,i__4);
1948 for (jr = jc; jr >= i__1; --jr) {
1949 i__2 = jr + irow + jc * a_dim1;
1950 i__4 = jc - iskew * jr + ioffg + jr * a_dim1;
1951 a[i__2].r = a[i__4].r, a[i__2].i = a[i__4].i;
1956 i__2 = 1, i__4 = jc - uub;
1957 i__1 = f2cmax(i__2,i__4);
1958 for (jr = jc; jr >= i__1; --jr) {
1959 i__2 = jr + irow + jc * a_dim1;
1960 r_cnjg(&q__1, &a[jc - iskew * jr + ioffg + jr
1962 a[i__2].r = q__1.r, a[i__2].i = q__1.i;
1970 for (jc = 1; jc <= i__1; ++jc) {
1971 i__2 = uub + 1 - jc;
1972 for (jr = 1; jr <= i__2; ++jr) {
1973 i__4 = jr + jc * a_dim1;
1974 a[i__4].r = 0.f, a[i__4].i = 0.f;
1988 /* Ensure that the diagonal is real if Hermitian */
1992 for (jc = 1; jc <= i__1; ++jc) {
1993 irow = ioffst + (1 - iskew) * jc;
1994 i__2 = irow + jc * a_dim1;
1995 i__4 = irow + jc * a_dim1;
1997 q__1.r = r__1, q__1.i = 0.f;
1998 a[i__2].r = q__1.r, a[i__2].i = q__1.i;
2007 /* 4) Generate Banded Matrix by first */
2008 /* Rotating by random Unitary matrices, */
2009 /* then reducing the bandwidth using Householder */
2010 /* transformations. */
2012 /* Note: we should get here only if LDA .ge. N */
2016 /* Non-symmetric -- A = U D V */
2018 clagge_(&mr, &nc, &llb, &uub, &d__[1], &a[a_offset], lda, &iseed[
2019 1], &work[1], &iinfo);
2022 /* Symmetric -- A = U D U' or */
2023 /* Hermitian -- A = U D U* */
2026 clagsy_(m, &llb, &d__[1], &a[a_offset], lda, &iseed[1], &work[
2029 claghe_(m, &llb, &d__[1], &a[a_offset], lda, &iseed[1], &work[
2040 /* 5) Pack the matrix */
2042 if (ipack != ipackg) {
2045 /* 'U' -- Upper triangular, not packed */
2048 for (j = 1; j <= i__1; ++j) {
2050 for (i__ = j + 1; i__ <= i__2; ++i__) {
2051 i__4 = i__ + j * a_dim1;
2052 a[i__4].r = 0.f, a[i__4].i = 0.f;
2058 } else if (ipack == 2) {
2060 /* 'L' -- Lower triangular, not packed */
2063 for (j = 2; j <= i__1; ++j) {
2065 for (i__ = 1; i__ <= i__2; ++i__) {
2066 i__4 = i__ + j * a_dim1;
2067 a[i__4].r = 0.f, a[i__4].i = 0.f;
2073 } else if (ipack == 3) {
2075 /* 'C' -- Upper triangle packed Columnwise. */
2080 for (j = 1; j <= i__1; ++j) {
2082 for (i__ = 1; i__ <= i__2; ++i__) {
2088 i__4 = irow + icol * a_dim1;
2089 i__3 = i__ + j * a_dim1;
2090 a[i__4].r = a[i__3].r, a[i__4].i = a[i__3].i;
2096 } else if (ipack == 4) {
2098 /* 'R' -- Lower triangle packed Columnwise. */
2103 for (j = 1; j <= i__1; ++j) {
2105 for (i__ = j; i__ <= i__2; ++i__) {
2111 i__4 = irow + icol * a_dim1;
2112 i__3 = i__ + j * a_dim1;
2113 a[i__4].r = a[i__3].r, a[i__4].i = a[i__3].i;
2119 } else if (ipack >= 5) {
2121 /* 'B' -- The lower triangle is packed as a band matrix. */
2122 /* 'Q' -- The upper triangle is packed as a band matrix. */
2123 /* 'Z' -- The whole matrix is packed as a band matrix. */
2133 for (j = 1; j <= i__1; ++j) {
2136 for (i__ = f2cmin(i__2,*m); i__ >= 1; --i__) {
2137 i__2 = i__ - j + uub + 1 + j * a_dim1;
2138 i__4 = i__ + j * a_dim1;
2139 a[i__2].r = a[i__4].r, a[i__2].i = a[i__4].i;
2146 for (j = uub + 2; j <= i__1; ++j) {
2149 i__2 = f2cmin(i__4,*m);
2150 for (i__ = j - uub; i__ <= i__2; ++i__) {
2151 i__4 = i__ - j + uub + 1 + j * a_dim1;
2152 i__3 = i__ + j * a_dim1;
2153 a[i__4].r = a[i__3].r, a[i__4].i = a[i__3].i;
2160 /* If packed, zero out extraneous elements. */
2162 /* Symmetric/Triangular Packed -- */
2163 /* zero out everything after A(IROW,ICOL) */
2165 if (ipack == 3 || ipack == 4) {
2167 for (jc = icol; jc <= i__1; ++jc) {
2169 for (jr = irow + 1; jr <= i__2; ++jr) {
2170 i__4 = jr + jc * a_dim1;
2171 a[i__4].r = 0.f, a[i__4].i = 0.f;
2178 } else if (ipack >= 5) {
2180 /* Packed Band -- */
2181 /* 1st row is now in A( UUB+2-j, j), zero above it */
2182 /* m-th row is now in A( M+UUB-j,j), zero below it */
2183 /* last non-zero diagonal is now in A( UUB+LLB+1,j ), */
2184 /* zero below it, too. */
2186 ir1 = uub + llb + 2;
2189 for (jc = 1; jc <= i__1; ++jc) {
2190 i__2 = uub + 1 - jc;
2191 for (jr = 1; jr <= i__2; ++jr) {
2192 i__4 = jr + jc * a_dim1;
2193 a[i__4].r = 0.f, a[i__4].i = 0.f;
2198 i__3 = ir1, i__5 = ir2 - jc;
2199 i__2 = 1, i__4 = f2cmin(i__3,i__5);
2201 for (jr = f2cmax(i__2,i__4); jr <= i__6; ++jr) {
2202 i__2 = jr + jc * a_dim1;
2203 a[i__2].r = 0.f, a[i__2].i = 0.f;