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 /* > \brief <b> DPOSVX computes the solution to system of linear equations A * X = B for PO matrices</b> */
515 /* =========== DOCUMENTATION =========== */
517 /* Online html documentation available at */
518 /* http://www.netlib.org/lapack/explore-html/ */
521 /* > Download DPOSVX + dependencies */
522 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dposvx.
525 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dposvx.
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dposvx.
536 /* SUBROUTINE DPOSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED, */
537 /* S, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, */
540 /* CHARACTER EQUED, FACT, UPLO */
541 /* INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS */
542 /* DOUBLE PRECISION RCOND */
543 /* INTEGER IWORK( * ) */
544 /* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), */
545 /* $ BERR( * ), FERR( * ), S( * ), WORK( * ), */
549 /* > \par Purpose: */
554 /* > DPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to */
555 /* > compute the solution to a real system of linear equations */
557 /* > where A is an N-by-N symmetric positive definite matrix and X and B */
558 /* > are N-by-NRHS matrices. */
560 /* > Error bounds on the solution and a condition estimate are also */
564 /* > \par Description: */
565 /* ================= */
569 /* > The following steps are performed: */
571 /* > 1. If FACT = 'E', real scaling factors are computed to equilibrate */
573 /* > diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B */
574 /* > Whether or not the system will be equilibrated depends on the */
575 /* > scaling of the matrix A, but if equilibration is used, A is */
576 /* > overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */
578 /* > 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
579 /* > factor the matrix A (after equilibration if FACT = 'E') as */
580 /* > A = U**T* U, if UPLO = 'U', or */
581 /* > A = L * L**T, if UPLO = 'L', */
582 /* > where U is an upper triangular matrix and L is a lower triangular */
585 /* > 3. If the leading i-by-i principal minor is not positive definite, */
586 /* > then the routine returns with INFO = i. Otherwise, the factored */
587 /* > form of A is used to estimate the condition number of the matrix */
588 /* > A. If the reciprocal of the condition number is less than machine */
589 /* > precision, INFO = N+1 is returned as a warning, but the routine */
590 /* > still goes on to solve for X and compute error bounds as */
591 /* > described below. */
593 /* > 4. The system of equations is solved for X using the factored form */
596 /* > 5. Iterative refinement is applied to improve the computed solution */
597 /* > matrix and calculate error bounds and backward error estimates */
600 /* > 6. If equilibration was used, the matrix X is premultiplied by */
601 /* > diag(S) so that it solves the original system before */
602 /* > equilibration. */
608 /* > \param[in] FACT */
610 /* > FACT is CHARACTER*1 */
611 /* > Specifies whether or not the factored form of the matrix A is */
612 /* > supplied on entry, and if not, whether the matrix A should be */
613 /* > equilibrated before it is factored. */
614 /* > = 'F': On entry, AF contains the factored form of A. */
615 /* > If EQUED = 'Y', the matrix A has been equilibrated */
616 /* > with scaling factors given by S. A and AF will not */
618 /* > = 'N': The matrix A will be copied to AF and factored. */
619 /* > = 'E': The matrix A will be equilibrated if necessary, then */
620 /* > copied to AF and factored. */
623 /* > \param[in] UPLO */
625 /* > UPLO is CHARACTER*1 */
626 /* > = 'U': Upper triangle of A is stored; */
627 /* > = 'L': Lower triangle of A is stored. */
633 /* > The number of linear equations, i.e., the order of the */
634 /* > matrix A. N >= 0. */
637 /* > \param[in] NRHS */
639 /* > NRHS is INTEGER */
640 /* > The number of right hand sides, i.e., the number of columns */
641 /* > of the matrices B and X. NRHS >= 0. */
644 /* > \param[in,out] A */
646 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
647 /* > On entry, the symmetric matrix A, except if FACT = 'F' and */
648 /* > EQUED = 'Y', then A must contain the equilibrated matrix */
649 /* > diag(S)*A*diag(S). If UPLO = 'U', the leading */
650 /* > N-by-N upper triangular part of A contains the upper */
651 /* > triangular part of the matrix A, and the strictly lower */
652 /* > triangular part of A is not referenced. If UPLO = 'L', the */
653 /* > leading N-by-N lower triangular part of A contains the lower */
654 /* > triangular part of the matrix A, and the strictly upper */
655 /* > triangular part of A is not referenced. A is not modified if */
656 /* > FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
658 /* > On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
659 /* > diag(S)*A*diag(S). */
662 /* > \param[in] LDA */
664 /* > LDA is INTEGER */
665 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
668 /* > \param[in,out] AF */
670 /* > AF is DOUBLE PRECISION array, dimension (LDAF,N) */
671 /* > If FACT = 'F', then AF is an input argument and on entry */
672 /* > contains the triangular factor U or L from the Cholesky */
673 /* > factorization A = U**T*U or A = L*L**T, in the same storage */
674 /* > format as A. If EQUED .ne. 'N', then AF is the factored form */
675 /* > of the equilibrated matrix diag(S)*A*diag(S). */
677 /* > If FACT = 'N', then AF is an output argument and on exit */
678 /* > returns the triangular factor U or L from the Cholesky */
679 /* > factorization A = U**T*U or A = L*L**T of the original */
682 /* > If FACT = 'E', then AF is an output argument and on exit */
683 /* > returns the triangular factor U or L from the Cholesky */
684 /* > factorization A = U**T*U or A = L*L**T of the equilibrated */
685 /* > matrix A (see the description of A for the form of the */
686 /* > equilibrated matrix). */
689 /* > \param[in] LDAF */
691 /* > LDAF is INTEGER */
692 /* > The leading dimension of the array AF. LDAF >= f2cmax(1,N). */
695 /* > \param[in,out] EQUED */
697 /* > EQUED is CHARACTER*1 */
698 /* > Specifies the form of equilibration that was done. */
699 /* > = 'N': No equilibration (always true if FACT = 'N'). */
700 /* > = 'Y': Equilibration was done, i.e., A has been replaced by */
701 /* > diag(S) * A * diag(S). */
702 /* > EQUED is an input argument if FACT = 'F'; otherwise, it is an */
703 /* > output argument. */
706 /* > \param[in,out] S */
708 /* > S is DOUBLE PRECISION array, dimension (N) */
709 /* > The scale factors for A; not accessed if EQUED = 'N'. S is */
710 /* > an input argument if FACT = 'F'; otherwise, S is an output */
711 /* > argument. If FACT = 'F' and EQUED = 'Y', each element of S */
712 /* > must be positive. */
715 /* > \param[in,out] B */
717 /* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
718 /* > On entry, the N-by-NRHS right hand side matrix B. */
719 /* > On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', */
720 /* > B is overwritten by diag(S) * B. */
723 /* > \param[in] LDB */
725 /* > LDB is INTEGER */
726 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
729 /* > \param[out] X */
731 /* > X is DOUBLE PRECISION array, dimension (LDX,NRHS) */
732 /* > If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to */
733 /* > the original system of equations. Note that if EQUED = 'Y', */
734 /* > A and B are modified on exit, and the solution to the */
735 /* > equilibrated system is inv(diag(S))*X. */
738 /* > \param[in] LDX */
740 /* > LDX is INTEGER */
741 /* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
744 /* > \param[out] RCOND */
746 /* > RCOND is DOUBLE PRECISION */
747 /* > The estimate of the reciprocal condition number of the matrix */
748 /* > A after equilibration (if done). If RCOND is less than the */
749 /* > machine precision (in particular, if RCOND = 0), the matrix */
750 /* > is singular to working precision. This condition is */
751 /* > indicated by a return code of INFO > 0. */
754 /* > \param[out] FERR */
756 /* > FERR is DOUBLE PRECISION array, dimension (NRHS) */
757 /* > The estimated forward error bound for each solution vector */
758 /* > X(j) (the j-th column of the solution matrix X). */
759 /* > If XTRUE is the true solution corresponding to X(j), FERR(j) */
760 /* > is an estimated upper bound for the magnitude of the largest */
761 /* > element in (X(j) - XTRUE) divided by the magnitude of the */
762 /* > largest element in X(j). The estimate is as reliable as */
763 /* > the estimate for RCOND, and is almost always a slight */
764 /* > overestimate of the true error. */
767 /* > \param[out] BERR */
769 /* > BERR is DOUBLE PRECISION array, dimension (NRHS) */
770 /* > The componentwise relative backward error of each solution */
771 /* > vector X(j) (i.e., the smallest relative change in */
772 /* > any element of A or B that makes X(j) an exact solution). */
775 /* > \param[out] WORK */
777 /* > WORK is DOUBLE PRECISION array, dimension (3*N) */
780 /* > \param[out] IWORK */
782 /* > IWORK is INTEGER array, dimension (N) */
785 /* > \param[out] INFO */
787 /* > INFO is INTEGER */
788 /* > = 0: successful exit */
789 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
790 /* > > 0: if INFO = i, and i is */
791 /* > <= N: the leading minor of order i of A is */
792 /* > not positive definite, so the factorization */
793 /* > could not be completed, and the solution has not */
794 /* > been computed. RCOND = 0 is returned. */
795 /* > = N+1: U is nonsingular, but RCOND is less than machine */
796 /* > precision, meaning that the matrix is singular */
797 /* > to working precision. Nevertheless, the */
798 /* > solution and error bounds are computed because */
799 /* > there are a number of situations where the */
800 /* > computed solution can be more accurate than the */
801 /* > value of RCOND would suggest. */
807 /* > \author Univ. of Tennessee */
808 /* > \author Univ. of California Berkeley */
809 /* > \author Univ. of Colorado Denver */
810 /* > \author NAG Ltd. */
812 /* > \date April 2012 */
814 /* > \ingroup doublePOsolve */
816 /* ===================================================================== */
817 /* Subroutine */ int dposvx_(char *fact, char *uplo, integer *n, integer *
818 nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf,
819 char *equed, doublereal *s, doublereal *b, integer *ldb, doublereal *
820 x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *
821 berr, doublereal *work, integer *iwork, integer *info)
823 /* System generated locals */
824 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
825 x_offset, i__1, i__2;
826 doublereal d__1, d__2;
828 /* Local variables */
829 doublereal amax, smin, smax;
831 extern logical lsame_(char *, char *);
832 doublereal scond, anorm;
833 logical equil, rcequ;
834 extern doublereal dlamch_(char *);
836 extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
837 doublereal *, integer *, doublereal *, integer *),
838 xerbla_(char *, integer *, ftnlen);
840 extern /* Subroutine */ int dpocon_(char *, integer *, doublereal *,
841 integer *, doublereal *, doublereal *, doublereal *, integer *,
844 extern doublereal dlansy_(char *, char *, integer *, doublereal *,
845 integer *, doublereal *);
846 extern /* Subroutine */ int dlaqsy_(char *, integer *, doublereal *,
847 integer *, doublereal *, doublereal *, doublereal *, char *), dpoequ_(integer *, doublereal *, integer *,
848 doublereal *, doublereal *, doublereal *, integer *), dporfs_(
849 char *, integer *, integer *, doublereal *, integer *, doublereal
850 *, integer *, doublereal *, integer *, doublereal *, integer *,
851 doublereal *, doublereal *, doublereal *, integer *, integer *), dpotrf_(char *, integer *, doublereal *, integer *,
854 extern /* Subroutine */ int dpotrs_(char *, integer *, integer *,
855 doublereal *, integer *, doublereal *, integer *, integer *);
858 /* -- LAPACK driver routine (version 3.7.0) -- */
859 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
860 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
864 /* ===================================================================== */
867 /* Parameter adjustments */
869 a_offset = 1 + a_dim1 * 1;
872 af_offset = 1 + af_dim1 * 1;
876 b_offset = 1 + b_dim1 * 1;
879 x_offset = 1 + x_dim1 * 1;
888 nofact = lsame_(fact, "N");
889 equil = lsame_(fact, "E");
890 if (nofact || equil) {
891 *(unsigned char *)equed = 'N';
894 rcequ = lsame_(equed, "Y");
895 smlnum = dlamch_("Safe minimum");
896 bignum = 1. / smlnum;
899 /* Test the input parameters. */
901 if (! nofact && ! equil && ! lsame_(fact, "F")) {
903 } else if (! lsame_(uplo, "U") && ! lsame_(uplo,
908 } else if (*nrhs < 0) {
910 } else if (*lda < f2cmax(1,*n)) {
912 } else if (*ldaf < f2cmax(1,*n)) {
914 } else if (lsame_(fact, "F") && ! (rcequ || lsame_(
922 for (j = 1; j <= i__1; ++j) {
924 d__1 = smin, d__2 = s[j];
925 smin = f2cmin(d__1,d__2);
927 d__1 = smax, d__2 = s[j];
928 smax = f2cmax(d__1,d__2);
934 scond = f2cmax(smin,smlnum) / f2cmin(smax,bignum);
940 if (*ldb < f2cmax(1,*n)) {
942 } else if (*ldx < f2cmax(1,*n)) {
950 xerbla_("DPOSVX", &i__1, (ftnlen)6);
956 /* Compute row and column scalings to equilibrate the matrix A. */
958 dpoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
961 /* Equilibrate the matrix. */
963 dlaqsy_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
964 rcequ = lsame_(equed, "Y");
968 /* Scale the right hand side. */
972 for (j = 1; j <= i__1; ++j) {
974 for (i__ = 1; i__ <= i__2; ++i__) {
975 b[i__ + j * b_dim1] = s[i__] * b[i__ + j * b_dim1];
982 if (nofact || equil) {
984 /* Compute the Cholesky factorization A = U**T *U or A = L*L**T. */
986 dlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
987 dpotrf_(uplo, n, &af[af_offset], ldaf, info);
989 /* Return if INFO is non-zero. */
997 /* Compute the norm of the matrix A. */
999 anorm = dlansy_("1", uplo, n, &a[a_offset], lda, &work[1]);
1001 /* Compute the reciprocal of the condition number of A. */
1003 dpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1],
1006 /* Compute the solution matrix X. */
1008 dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
1009 dpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
1011 /* Use iterative refinement to improve the computed solution and */
1012 /* compute error bounds and backward error estimates for it. */
1014 dporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &b[
1015 b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], &
1018 /* Transform the solution matrix X to a solution of the original */
1023 for (j = 1; j <= i__1; ++j) {
1025 for (i__ = 1; i__ <= i__2; ++i__) {
1026 x[i__ + j * x_dim1] = s[i__] * x[i__ + j * x_dim1];
1032 for (j = 1; j <= i__1; ++j) {
1038 /* Set INFO = N+1 if the matrix is singular to working precision. */
1040 if (*rcond < dlamch_("Epsilon")) {