14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static integer c__1 = 1;
516 static doublereal c_b12 = -1.;
517 static doublereal c_b14 = 1.;
519 /* > \brief \b DPBRFS */
521 /* =========== DOCUMENTATION =========== */
523 /* Online html documentation available at */
524 /* http://www.netlib.org/lapack/explore-html/ */
527 /* > Download DPBRFS + dependencies */
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbrfs.
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbrfs.
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbrfs.
542 /* SUBROUTINE DPBRFS( UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, */
543 /* LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO ) */
546 /* INTEGER INFO, KD, LDAB, LDAFB, LDB, LDX, N, NRHS */
547 /* INTEGER IWORK( * ) */
548 /* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */
549 /* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * ) */
552 /* > \par Purpose: */
557 /* > DPBRFS improves the computed solution to a system of linear */
558 /* > equations when the coefficient matrix is symmetric positive definite */
559 /* > and banded, and provides error bounds and backward error estimates */
560 /* > for the solution. */
566 /* > \param[in] UPLO */
568 /* > UPLO is CHARACTER*1 */
569 /* > = 'U': Upper triangle of A is stored; */
570 /* > = 'L': Lower triangle of A is stored. */
576 /* > The order of the matrix A. N >= 0. */
579 /* > \param[in] KD */
581 /* > KD is INTEGER */
582 /* > The number of superdiagonals of the matrix A if UPLO = 'U', */
583 /* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
586 /* > \param[in] NRHS */
588 /* > NRHS is INTEGER */
589 /* > The number of right hand sides, i.e., the number of columns */
590 /* > of the matrices B and X. NRHS >= 0. */
593 /* > \param[in] AB */
595 /* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */
596 /* > The upper or lower triangle of the symmetric band matrix A, */
597 /* > stored in the first KD+1 rows of the array. The j-th column */
598 /* > of A is stored in the j-th column of the array AB as follows: */
599 /* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
600 /* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
603 /* > \param[in] LDAB */
605 /* > LDAB is INTEGER */
606 /* > The leading dimension of the array AB. LDAB >= KD+1. */
609 /* > \param[in] AFB */
611 /* > AFB is DOUBLE PRECISION array, dimension (LDAFB,N) */
612 /* > The triangular factor U or L from the Cholesky factorization */
613 /* > A = U**T*U or A = L*L**T of the band matrix A as computed by */
614 /* > DPBTRF, in the same storage format as A (see AB). */
617 /* > \param[in] LDAFB */
619 /* > LDAFB is INTEGER */
620 /* > The leading dimension of the array AFB. LDAFB >= KD+1. */
625 /* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
626 /* > The right hand side matrix B. */
629 /* > \param[in] LDB */
631 /* > LDB is INTEGER */
632 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
635 /* > \param[in,out] X */
637 /* > X is DOUBLE PRECISION array, dimension (LDX,NRHS) */
638 /* > On entry, the solution matrix X, as computed by DPBTRS. */
639 /* > On exit, the improved solution matrix X. */
642 /* > \param[in] LDX */
644 /* > LDX is INTEGER */
645 /* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
648 /* > \param[out] FERR */
650 /* > FERR is DOUBLE PRECISION array, dimension (NRHS) */
651 /* > The estimated forward error bound for each solution vector */
652 /* > X(j) (the j-th column of the solution matrix X). */
653 /* > If XTRUE is the true solution corresponding to X(j), FERR(j) */
654 /* > is an estimated upper bound for the magnitude of the largest */
655 /* > element in (X(j) - XTRUE) divided by the magnitude of the */
656 /* > largest element in X(j). The estimate is as reliable as */
657 /* > the estimate for RCOND, and is almost always a slight */
658 /* > overestimate of the true error. */
661 /* > \param[out] BERR */
663 /* > BERR is DOUBLE PRECISION array, dimension (NRHS) */
664 /* > The componentwise relative backward error of each solution */
665 /* > vector X(j) (i.e., the smallest relative change in */
666 /* > any element of A or B that makes X(j) an exact solution). */
669 /* > \param[out] WORK */
671 /* > WORK is DOUBLE PRECISION array, dimension (3*N) */
674 /* > \param[out] IWORK */
676 /* > IWORK is INTEGER array, dimension (N) */
679 /* > \param[out] INFO */
681 /* > INFO is INTEGER */
682 /* > = 0: successful exit */
683 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
686 /* > \par Internal Parameters: */
687 /* ========================= */
690 /* > ITMAX is the maximum number of steps of iterative refinement. */
696 /* > \author Univ. of Tennessee */
697 /* > \author Univ. of California Berkeley */
698 /* > \author Univ. of Colorado Denver */
699 /* > \author NAG Ltd. */
701 /* > \date December 2016 */
703 /* > \ingroup doubleOTHERcomputational */
705 /* ===================================================================== */
706 /* Subroutine */ int dpbrfs_(char *uplo, integer *n, integer *kd, integer *
707 nrhs, doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb,
708 doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
709 ferr, doublereal *berr, doublereal *work, integer *iwork, integer *
712 /* System generated locals */
713 integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
714 x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
715 doublereal d__1, d__2, d__3;
717 /* Local variables */
719 doublereal safe1, safe2;
720 integer i__, j, k, l;
722 extern logical lsame_(char *, char *);
724 extern /* Subroutine */ int dsbmv_(char *, integer *, integer *,
725 doublereal *, doublereal *, integer *, doublereal *, integer *,
726 doublereal *, doublereal *, integer *), dcopy_(integer *,
727 doublereal *, integer *, doublereal *, integer *), daxpy_(integer
728 *, doublereal *, doublereal *, integer *, doublereal *, integer *)
732 extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *,
733 integer *, doublereal *, integer *, integer *);
734 extern doublereal dlamch_(char *);
738 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpbtrs_(
739 char *, integer *, integer *, integer *, doublereal *, integer *,
740 doublereal *, integer *, integer *);
741 doublereal lstres, eps;
744 /* -- LAPACK computational routine (version 3.7.0) -- */
745 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
746 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
750 /* ===================================================================== */
753 /* Test the input parameters. */
755 /* Parameter adjustments */
757 ab_offset = 1 + ab_dim1 * 1;
760 afb_offset = 1 + afb_dim1 * 1;
763 b_offset = 1 + b_dim1 * 1;
766 x_offset = 1 + x_dim1 * 1;
775 upper = lsame_(uplo, "U");
776 if (! upper && ! lsame_(uplo, "L")) {
780 } else if (*kd < 0) {
782 } else if (*nrhs < 0) {
784 } else if (*ldab < *kd + 1) {
786 } else if (*ldafb < *kd + 1) {
788 } else if (*ldb < f2cmax(1,*n)) {
790 } else if (*ldx < f2cmax(1,*n)) {
795 xerbla_("DPBRFS", &i__1, (ftnlen)6);
799 /* Quick return if possible */
801 if (*n == 0 || *nrhs == 0) {
803 for (j = 1; j <= i__1; ++j) {
811 /* NZ = maximum number of nonzero elements in each row of A, plus 1 */
814 i__1 = *n + 1, i__2 = (*kd << 1) + 2;
815 nz = f2cmin(i__1,i__2);
816 eps = dlamch_("Epsilon");
817 safmin = dlamch_("Safe minimum");
821 /* Do for each right hand side */
824 for (j = 1; j <= i__1; ++j) {
830 /* Loop until stopping criterion is satisfied. */
832 /* Compute residual R = B - A * X */
834 dcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[*n + 1], &c__1);
835 dsbmv_(uplo, n, kd, &c_b12, &ab[ab_offset], ldab, &x[j * x_dim1 + 1],
836 &c__1, &c_b14, &work[*n + 1], &c__1);
838 /* Compute componentwise relative backward error from formula */
840 /* f2cmax(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */
842 /* where abs(Z) is the componentwise absolute value of the matrix */
843 /* or vector Z. If the i-th component of the denominator is less */
844 /* than SAFE2, then SAFE1 is added to the i-th components of the */
845 /* numerator and denominator before dividing. */
848 for (i__ = 1; i__ <= i__2; ++i__) {
849 work[i__] = (d__1 = b[i__ + j * b_dim1], abs(d__1));
853 /* Compute abs(A)*abs(X) + abs(B). */
857 for (k = 1; k <= i__2; ++k) {
859 xk = (d__1 = x[k + j * x_dim1], abs(d__1));
862 i__3 = 1, i__4 = k - *kd;
864 for (i__ = f2cmax(i__3,i__4); i__ <= i__5; ++i__) {
865 work[i__] += (d__1 = ab[l + i__ + k * ab_dim1], abs(d__1))
867 s += (d__1 = ab[l + i__ + k * ab_dim1], abs(d__1)) * (
868 d__2 = x[i__ + j * x_dim1], abs(d__2));
871 work[k] = work[k] + (d__1 = ab[*kd + 1 + k * ab_dim1], abs(
877 for (k = 1; k <= i__2; ++k) {
879 xk = (d__1 = x[k + j * x_dim1], abs(d__1));
880 work[k] += (d__1 = ab[k * ab_dim1 + 1], abs(d__1)) * xk;
883 i__3 = *n, i__4 = k + *kd;
884 i__5 = f2cmin(i__3,i__4);
885 for (i__ = k + 1; i__ <= i__5; ++i__) {
886 work[i__] += (d__1 = ab[l + i__ + k * ab_dim1], abs(d__1))
888 s += (d__1 = ab[l + i__ + k * ab_dim1], abs(d__1)) * (
889 d__2 = x[i__ + j * x_dim1], abs(d__2));
898 for (i__ = 1; i__ <= i__2; ++i__) {
899 if (work[i__] > safe2) {
901 d__2 = s, d__3 = (d__1 = work[*n + i__], abs(d__1)) / work[
903 s = f2cmax(d__2,d__3);
906 d__2 = s, d__3 = ((d__1 = work[*n + i__], abs(d__1)) + safe1)
907 / (work[i__] + safe1);
908 s = f2cmax(d__2,d__3);
914 /* Test stopping criterion. Continue iterating if */
915 /* 1) The residual BERR(J) is larger than machine epsilon, and */
916 /* 2) BERR(J) decreased by at least a factor of 2 during the */
917 /* last iteration, and */
918 /* 3) At most ITMAX iterations tried. */
920 if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) {
922 /* Update solution and try again. */
924 dpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[*n + 1]
926 daxpy_(n, &c_b14, &work[*n + 1], &c__1, &x[j * x_dim1 + 1], &c__1)
933 /* Bound error from formula */
935 /* norm(X - XTRUE) / norm(X) .le. FERR = */
936 /* norm( abs(inv(A))* */
937 /* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */
940 /* norm(Z) is the magnitude of the largest component of Z */
941 /* inv(A) is the inverse of A */
942 /* abs(Z) is the componentwise absolute value of the matrix or */
944 /* NZ is the maximum number of nonzeros in any row of A, plus 1 */
945 /* EPS is machine epsilon */
947 /* The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */
948 /* is incremented by SAFE1 if the i-th component of */
949 /* abs(A)*abs(X) + abs(B) is less than SAFE2. */
951 /* Use DLACN2 to estimate the infinity-norm of the matrix */
952 /* inv(A) * diag(W), */
953 /* where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */
956 for (i__ = 1; i__ <= i__2; ++i__) {
957 if (work[i__] > safe2) {
958 work[i__] = (d__1 = work[*n + i__], abs(d__1)) + nz * eps *
961 work[i__] = (d__1 = work[*n + i__], abs(d__1)) + nz * eps *
969 dlacn2_(n, &work[(*n << 1) + 1], &work[*n + 1], &iwork[1], &ferr[j], &
974 /* Multiply by diag(W)*inv(A**T). */
976 dpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[*n
979 for (i__ = 1; i__ <= i__2; ++i__) {
980 work[*n + i__] *= work[i__];
983 } else if (kase == 2) {
985 /* Multiply by inv(A)*diag(W). */
988 for (i__ = 1; i__ <= i__2; ++i__) {
989 work[*n + i__] *= work[i__];
992 dpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[*n
998 /* Normalize error. */
1002 for (i__ = 1; i__ <= i__2; ++i__) {
1004 d__2 = lstres, d__3 = (d__1 = x[i__ + j * x_dim1], abs(d__1));
1005 lstres = f2cmax(d__2,d__3);