14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static doublereal c_b10 = -1.;
516 static doublereal c_b11 = 1.;
517 static integer c__1 = 1;
519 /* > \brief <b> DSGESV computes the solution to system of linear equations A * X = B for GE matrices</b> (mixe
520 d precision with iterative refinement) */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download DSGESV + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsgesv.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsgesv.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsgesv.
543 /* SUBROUTINE DSGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, */
544 /* SWORK, ITER, INFO ) */
546 /* INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS */
547 /* INTEGER IPIV( * ) */
548 /* REAL SWORK( * ) */
549 /* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( N, * ), */
553 /* > \par Purpose: */
558 /* > DSGESV computes the solution to a real system of linear equations */
560 /* > where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */
562 /* > DSGESV first attempts to factorize the matrix in SINGLE PRECISION */
563 /* > and use this factorization within an iterative refinement procedure */
564 /* > to produce a solution with DOUBLE PRECISION normwise backward error */
565 /* > quality (see below). If the approach fails the method switches to a */
566 /* > DOUBLE PRECISION factorization and solve. */
568 /* > The iterative refinement is not going to be a winning strategy if */
569 /* > the ratio SINGLE PRECISION performance over DOUBLE PRECISION */
570 /* > performance is too small. A reasonable strategy should take the */
571 /* > number of right-hand sides and the size of the matrix into account. */
572 /* > This might be done with a call to ILAENV in the future. Up to now, we */
573 /* > always try iterative refinement. */
575 /* > The iterative refinement process is stopped if */
576 /* > ITER > ITERMAX */
577 /* > or for all the RHS we have: */
578 /* > RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX */
580 /* > o ITER is the number of the current iteration in the iterative */
581 /* > refinement process */
582 /* > o RNRM is the infinity-norm of the residual */
583 /* > o XNRM is the infinity-norm of the solution */
584 /* > o ANRM is the infinity-operator-norm of the matrix A */
585 /* > o EPS is the machine epsilon returned by DLAMCH('Epsilon') */
586 /* > The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 */
587 /* > respectively. */
596 /* > The number of linear equations, i.e., the order of the */
597 /* > matrix A. N >= 0. */
600 /* > \param[in] NRHS */
602 /* > NRHS is INTEGER */
603 /* > The number of right hand sides, i.e., the number of columns */
604 /* > of the matrix B. NRHS >= 0. */
607 /* > \param[in,out] A */
609 /* > A is DOUBLE PRECISION array, */
610 /* > dimension (LDA,N) */
611 /* > On entry, the N-by-N coefficient matrix A. */
612 /* > On exit, if iterative refinement has been successfully used */
613 /* > (INFO = 0 and ITER >= 0, see description below), then A is */
614 /* > unchanged, if double precision factorization has been used */
615 /* > (INFO = 0 and ITER < 0, see description below), then the */
616 /* > array A contains the factors L and U from the factorization */
617 /* > A = P*L*U; the unit diagonal elements of L are not stored. */
620 /* > \param[in] LDA */
622 /* > LDA is INTEGER */
623 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
626 /* > \param[out] IPIV */
628 /* > IPIV is INTEGER array, dimension (N) */
629 /* > The pivot indices that define the permutation matrix P; */
630 /* > row i of the matrix was interchanged with row IPIV(i). */
631 /* > Corresponds either to the single precision factorization */
632 /* > (if INFO = 0 and ITER >= 0) or the double precision */
633 /* > factorization (if INFO = 0 and ITER < 0). */
638 /* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
639 /* > The N-by-NRHS right hand side matrix B. */
642 /* > \param[in] LDB */
644 /* > LDB is INTEGER */
645 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
648 /* > \param[out] X */
650 /* > X is DOUBLE PRECISION array, dimension (LDX,NRHS) */
651 /* > If INFO = 0, the N-by-NRHS solution matrix X. */
654 /* > \param[in] LDX */
656 /* > LDX is INTEGER */
657 /* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
660 /* > \param[out] WORK */
662 /* > WORK is DOUBLE PRECISION array, dimension (N,NRHS) */
663 /* > This array is used to hold the residual vectors. */
666 /* > \param[out] SWORK */
668 /* > SWORK is REAL array, dimension (N*(N+NRHS)) */
669 /* > This array is used to use the single precision matrix and the */
670 /* > right-hand sides or solutions in single precision. */
673 /* > \param[out] ITER */
675 /* > ITER is INTEGER */
676 /* > < 0: iterative refinement has failed, double precision */
677 /* > factorization has been performed */
678 /* > -1 : the routine fell back to full precision for */
679 /* > implementation- or machine-specific reasons */
680 /* > -2 : narrowing the precision induced an overflow, */
681 /* > the routine fell back to full precision */
682 /* > -3 : failure of SGETRF */
683 /* > -31: stop the iterative refinement after the 30th */
685 /* > > 0: iterative refinement has been successfully used. */
686 /* > Returns the number of iterations */
689 /* > \param[out] INFO */
691 /* > INFO is INTEGER */
692 /* > = 0: successful exit */
693 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
694 /* > > 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is */
695 /* > exactly zero. The factorization has been completed, */
696 /* > but the factor U is exactly singular, so the solution */
697 /* > could not be computed. */
703 /* > \author Univ. of Tennessee */
704 /* > \author Univ. of California Berkeley */
705 /* > \author Univ. of Colorado Denver */
706 /* > \author NAG Ltd. */
708 /* > \date June 2016 */
710 /* > \ingroup doubleGEsolve */
712 /* ===================================================================== */
713 /* Subroutine */ int dsgesv_(integer *n, integer *nrhs, doublereal *a,
714 integer *lda, integer *ipiv, doublereal *b, integer *ldb, doublereal *
715 x, integer *ldx, doublereal *work, real *swork, integer *iter,
718 /* System generated locals */
719 integer a_dim1, a_offset, b_dim1, b_offset, work_dim1, work_offset,
720 x_dim1, x_offset, i__1;
723 /* Local variables */
726 doublereal rnrm, xnrm;
728 extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
729 integer *, doublereal *, doublereal *, integer *, doublereal *,
730 integer *, doublereal *, doublereal *, integer *);
732 extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
733 integer *, doublereal *, integer *), dlag2s_(integer *, integer *,
734 doublereal *, integer *, real *, integer *, integer *), slag2d_(
735 integer *, integer *, real *, integer *, doublereal *, integer *,
737 extern doublereal dlamch_(char *), dlange_(char *, integer *,
738 integer *, doublereal *, integer *, doublereal *);
739 extern integer idamax_(integer *, doublereal *, integer *);
740 extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
741 doublereal *, integer *, doublereal *, integer *),
742 dgetrf_(integer *, integer *, doublereal *, integer *, integer *,
743 integer *), xerbla_(char *, integer *, ftnlen), dgetrs_(char *,
744 integer *, integer *, doublereal *, integer *, integer *,
745 doublereal *, integer *, integer *), sgetrf_(integer *,
746 integer *, real *, integer *, integer *, integer *), sgetrs_(char
747 *, integer *, integer *, real *, integer *, integer *, real *,
748 integer *, integer *);
752 /* -- LAPACK driver routine (version 3.8.0) -- */
753 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
754 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
758 /* ===================================================================== */
766 /* Parameter adjustments */
768 work_offset = 1 + work_dim1 * 1;
771 a_offset = 1 + a_dim1 * 1;
775 b_offset = 1 + b_dim1 * 1;
778 x_offset = 1 + x_dim1 * 1;
786 /* Test the input parameters. */
790 } else if (*nrhs < 0) {
792 } else if (*lda < f2cmax(1,*n)) {
794 } else if (*ldb < f2cmax(1,*n)) {
796 } else if (*ldx < f2cmax(1,*n)) {
801 xerbla_("DSGESV", &i__1, (ftnlen)6);
805 /* Quick return if (N.EQ.0). */
811 /* Skip single precision iterative refinement if a priori slower */
812 /* than double precision factorization. */
819 /* Compute some constants. */
821 anrm = dlange_("I", n, n, &a[a_offset], lda, &work[work_offset]);
822 eps = dlamch_("Epsilon");
823 cte = anrm * eps * sqrt((doublereal) (*n)) * 1.;
825 /* Set the indices PTSA, PTSX for referencing SA and SX in SWORK. */
828 ptsx = ptsa + *n * *n;
830 /* Convert B from double precision to single precision and store the */
833 dlag2s_(n, nrhs, &b[b_offset], ldb, &swork[ptsx], n, info);
840 /* Convert A from double precision to single precision and store the */
843 dlag2s_(n, n, &a[a_offset], lda, &swork[ptsa], n, info);
850 /* Compute the LU factorization of SA. */
852 sgetrf_(n, n, &swork[ptsa], n, &ipiv[1], info);
859 /* Solve the system SA*SX = SB. */
861 sgetrs_("No transpose", n, nrhs, &swork[ptsa], n, &ipiv[1], &swork[ptsx],
864 /* Convert SX back to double precision */
866 slag2d_(n, nrhs, &swork[ptsx], n, &x[x_offset], ldx, info);
868 /* Compute R = B - AX (R is WORK). */
870 dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);
872 dgemm_("No Transpose", "No Transpose", n, nrhs, n, &c_b10, &a[a_offset],
873 lda, &x[x_offset], ldx, &c_b11, &work[work_offset], n);
875 /* Check whether the NRHS normwise backward errors satisfy the */
876 /* stopping criterion. If yes, set ITER=0 and return. */
879 for (i__ = 1; i__ <= i__1; ++i__) {
880 xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ *
882 rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1) +
883 i__ * work_dim1], abs(d__1));
884 if (rnrm > xnrm * cte) {
889 /* If we are here, the NRHS normwise backward errors satisfy the */
890 /* stopping criterion. We are good to exit. */
897 for (iiter = 1; iiter <= 30; ++iiter) {
899 /* Convert R (in WORK) from double precision to single precision */
900 /* and store the result in SX. */
902 dlag2s_(n, nrhs, &work[work_offset], n, &swork[ptsx], n, info);
909 /* Solve the system SA*SX = SR. */
911 sgetrs_("No transpose", n, nrhs, &swork[ptsa], n, &ipiv[1], &swork[
914 /* Convert SX back to double precision and update the current */
917 slag2d_(n, nrhs, &swork[ptsx], n, &work[work_offset], n, info);
920 for (i__ = 1; i__ <= i__1; ++i__) {
921 daxpy_(n, &c_b11, &work[i__ * work_dim1 + 1], &c__1, &x[i__ *
925 /* Compute R = B - AX (R is WORK). */
927 dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);
929 dgemm_("No Transpose", "No Transpose", n, nrhs, n, &c_b10, &a[
930 a_offset], lda, &x[x_offset], ldx, &c_b11, &work[work_offset],
933 /* Check whether the NRHS normwise backward errors satisfy the */
934 /* stopping criterion. If yes, set ITER=IITER>0 and return. */
937 for (i__ = 1; i__ <= i__1; ++i__) {
938 xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ *
940 rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1)
941 + i__ * work_dim1], abs(d__1));
942 if (rnrm > xnrm * cte) {
947 /* If we are here, the NRHS normwise backward errors satisfy the */
948 /* stopping criterion, we are good to exit. */
960 /* If we are at this place of the code, this is because we have */
961 /* performed ITER=ITERMAX iterations and never satisfied the */
962 /* stopping criterion, set up the ITER flag accordingly and follow up */
963 /* on double precision routine. */
969 /* Single-precision iterative refinement failed to converge to a */
970 /* satisfactory solution, so we resort to double precision. */
972 dgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
978 dlacpy_("All", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
979 dgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &x[x_offset]