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]/Cd(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)
514 /* Table of constant values */
516 static integer c__1 = 1;
517 static integer c_n1 = -1;
518 static doublereal c_b23 = -1.;
519 static doublereal c_b25 = 1.;
521 /* > \brief \b DPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive
522 semidefinite matrix. */
525 /* =========== DOCUMENTATION =========== */
527 /* Online html documentation available at */
528 /* http://www.netlib.org/lapack/explore-html/ */
531 /* > Download DPSTRF + dependencies */
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpstrf.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpstrf.
538 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpstrf.
546 /* SUBROUTINE DPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) */
548 /* DOUBLE PRECISION TOL */
549 /* INTEGER INFO, LDA, N, RANK */
551 /* DOUBLE PRECISION A( LDA, * ), WORK( 2*N ) */
552 /* INTEGER PIV( N ) */
555 /* > \par Purpose: */
560 /* > DPSTRF computes the Cholesky factorization with complete */
561 /* > pivoting of a real symmetric positive semidefinite matrix A. */
563 /* > The factorization has the form */
564 /* > P**T * A * P = U**T * U , if UPLO = 'U', */
565 /* > P**T * A * P = L * L**T, if UPLO = 'L', */
566 /* > where U is an upper triangular matrix and L is lower triangular, and */
567 /* > P is stored as vector PIV. */
569 /* > This algorithm does not attempt to check that A is positive */
570 /* > semidefinite. This version of the algorithm calls level 3 BLAS. */
576 /* > \param[in] UPLO */
578 /* > UPLO is CHARACTER*1 */
579 /* > Specifies whether the upper or lower triangular part of the */
580 /* > symmetric matrix A is stored. */
581 /* > = 'U': Upper triangular */
582 /* > = 'L': Lower triangular */
588 /* > The order of the matrix A. N >= 0. */
591 /* > \param[in,out] A */
593 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
594 /* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */
595 /* > n by n upper triangular part of A contains the upper */
596 /* > triangular part of the matrix A, and the strictly lower */
597 /* > triangular part of A is not referenced. If UPLO = 'L', the */
598 /* > leading n by n lower triangular part of A contains the lower */
599 /* > triangular part of the matrix A, and the strictly upper */
600 /* > triangular part of A is not referenced. */
602 /* > On exit, if INFO = 0, the factor U or L from the Cholesky */
603 /* > factorization as above. */
606 /* > \param[in] LDA */
608 /* > LDA is INTEGER */
609 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
612 /* > \param[out] PIV */
614 /* > PIV is INTEGER array, dimension (N) */
615 /* > PIV is such that the nonzero entries are P( PIV(K), K ) = 1. */
618 /* > \param[out] RANK */
620 /* > RANK is INTEGER */
621 /* > The rank of A given by the number of steps the algorithm */
625 /* > \param[in] TOL */
627 /* > TOL is DOUBLE PRECISION */
628 /* > User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) */
629 /* > will be used. The algorithm terminates at the (K-1)st step */
630 /* > if the pivot <= TOL. */
633 /* > \param[out] WORK */
635 /* > WORK is DOUBLE PRECISION array, dimension (2*N) */
639 /* > \param[out] INFO */
641 /* > INFO is INTEGER */
642 /* > < 0: If INFO = -K, the K-th argument had an illegal value, */
643 /* > = 0: algorithm completed successfully, and */
644 /* > > 0: the matrix A is either rank deficient with computed rank */
645 /* > as returned in RANK, or is not positive semidefinite. See */
646 /* > Section 7 of LAPACK Working Note #161 for further */
653 /* > \author Univ. of Tennessee */
654 /* > \author Univ. of California Berkeley */
655 /* > \author Univ. of Colorado Denver */
656 /* > \author NAG Ltd. */
658 /* > \date December 2016 */
660 /* > \ingroup doubleOTHERcomputational */
662 /* ===================================================================== */
663 /* Subroutine */ int dpstrf_(char *uplo, integer *n, doublereal *a, integer *
664 lda, integer *piv, integer *rank, doublereal *tol, doublereal *work,
667 /* System generated locals */
668 integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
671 /* Local variables */
674 extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
676 extern logical lsame_(char *, char *);
677 extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
678 doublereal *, doublereal *, integer *, doublereal *, integer *,
679 doublereal *, doublereal *, integer *);
682 extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
683 doublereal *, integer *);
686 extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *,
687 doublereal *, doublereal *, integer *, doublereal *, doublereal *,
688 integer *), dpstf2_(char *, integer *,
689 doublereal *, integer *, integer *, integer *, doublereal *,
690 doublereal *, integer *);
692 extern doublereal dlamch_(char *);
693 extern logical disnan_(doublereal *);
694 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
695 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
696 integer *, integer *, ftnlen, ftnlen);
701 /* -- LAPACK computational routine (version 3.7.0) -- */
702 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
703 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
707 /* ===================================================================== */
710 /* Test the input parameters. */
712 /* Parameter adjustments */
716 a_offset = 1 + a_dim1 * 1;
721 upper = lsame_(uplo, "U");
722 if (! upper && ! lsame_(uplo, "L")) {
726 } else if (*lda < f2cmax(1,*n)) {
731 xerbla_("DPSTRF", &i__1, (ftnlen)6);
735 /* Quick return if possible */
743 nb = ilaenv_(&c__1, "DPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
745 if (nb <= 1 || nb >= *n) {
747 /* Use unblocked code */
749 dpstf2_(uplo, n, &a[a_dim1 + 1], lda, &piv[1], rank, tol, &work[1],
758 for (i__ = 1; i__ <= i__1; ++i__) {
763 /* Compute stopping value */
766 ajj = a[pvt + pvt * a_dim1];
768 for (i__ = 2; i__ <= i__1; ++i__) {
769 if (a[i__ + i__ * a_dim1] > ajj) {
771 ajj = a[pvt + pvt * a_dim1];
774 if (ajj <= 0. || disnan_(&ajj)) {
780 /* Compute stopping value if not supplied */
783 dstop = *n * dlamch_("Epsilon") * ajj;
791 /* Compute the Cholesky factorization P**T * A * P = U**T * U */
795 for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
797 /* Account for last block not being NB wide */
800 i__3 = nb, i__4 = *n - k + 1;
801 jb = f2cmin(i__3,i__4);
803 /* Set relevant part of first half of WORK to zero, */
804 /* holds dot products */
807 for (i__ = k; i__ <= i__3; ++i__) {
813 for (j = k; j <= i__3; ++j) {
815 /* Find pivot, test for exit, else swap rows and columns */
816 /* Update dot products, compute possible pivots which are */
817 /* stored in the second half of WORK */
820 for (i__ = j; i__ <= i__4; ++i__) {
823 /* Computing 2nd power */
824 d__1 = a[j - 1 + i__ * a_dim1];
825 work[i__] += d__1 * d__1;
827 work[*n + i__] = a[i__ + i__ * a_dim1] - work[i__];
835 itemp = mymaxloc_(&work[1], &i__4, &i__5, &c__1);
837 ajj = work[*n + pvt];
838 if (ajj <= dstop || disnan_(&ajj)) {
839 a[j + j * a_dim1] = ajj;
846 /* Pivot OK, so can now swap pivot rows and columns */
848 a[pvt + pvt * a_dim1] = a[j + j * a_dim1];
850 dswap_(&i__4, &a[j * a_dim1 + 1], &c__1, &a[pvt *
854 dswap_(&i__4, &a[j + (pvt + 1) * a_dim1], lda, &a[
855 pvt + (pvt + 1) * a_dim1], lda);
858 dswap_(&i__4, &a[j + (j + 1) * a_dim1], lda, &a[j + 1
859 + pvt * a_dim1], &c__1);
861 /* Swap dot products and PIV */
872 a[j + j * a_dim1] = ajj;
874 /* Compute elements J+1:N of row J. */
879 dgemv_("Trans", &i__4, &i__5, &c_b23, &a[k + (j + 1) *
880 a_dim1], lda, &a[k + j * a_dim1], &c__1, &
881 c_b25, &a[j + (j + 1) * a_dim1], lda);
884 dscal_(&i__4, &d__1, &a[j + (j + 1) * a_dim1], lda);
890 /* Update trailing matrix, J already incremented */
894 dsyrk_("Upper", "Trans", &i__3, &jb, &c_b23, &a[k + j *
895 a_dim1], lda, &c_b25, &a[j + j * a_dim1], lda);
903 /* Compute the Cholesky factorization P**T * A * P = L * L**T */
907 for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
909 /* Account for last block not being NB wide */
912 i__3 = nb, i__4 = *n - k + 1;
913 jb = f2cmin(i__3,i__4);
915 /* Set relevant part of first half of WORK to zero, */
916 /* holds dot products */
919 for (i__ = k; i__ <= i__3; ++i__) {
925 for (j = k; j <= i__3; ++j) {
927 /* Find pivot, test for exit, else swap rows and columns */
928 /* Update dot products, compute possible pivots which are */
929 /* stored in the second half of WORK */
932 for (i__ = j; i__ <= i__4; ++i__) {
935 /* Computing 2nd power */
936 d__1 = a[i__ + (j - 1) * a_dim1];
937 work[i__] += d__1 * d__1;
939 work[*n + i__] = a[i__ + i__ * a_dim1] - work[i__];
947 itemp = mymaxloc_(&work[1], &i__4, &i__5, &c__1);
949 ajj = work[*n + pvt];
950 if (ajj <= dstop || disnan_(&ajj)) {
951 a[j + j * a_dim1] = ajj;
958 /* Pivot OK, so can now swap pivot rows and columns */
960 a[pvt + pvt * a_dim1] = a[j + j * a_dim1];
962 dswap_(&i__4, &a[j + a_dim1], lda, &a[pvt + a_dim1],
966 dswap_(&i__4, &a[pvt + 1 + j * a_dim1], &c__1, &a[
967 pvt + 1 + pvt * a_dim1], &c__1);
970 dswap_(&i__4, &a[j + 1 + j * a_dim1], &c__1, &a[pvt +
971 (j + 1) * a_dim1], lda);
973 /* Swap dot products and PIV */
984 a[j + j * a_dim1] = ajj;
986 /* Compute elements J+1:N of column J. */
991 dgemv_("No Trans", &i__4, &i__5, &c_b23, &a[j + 1 + k
992 * a_dim1], lda, &a[j + k * a_dim1], lda, &
993 c_b25, &a[j + 1 + j * a_dim1], &c__1);
996 dscal_(&i__4, &d__1, &a[j + 1 + j * a_dim1], &c__1);
1002 /* Update trailing matrix, J already incremented */
1006 dsyrk_("Lower", "No Trans", &i__3, &jb, &c_b23, &a[j + k *
1007 a_dim1], lda, &c_b25, &a[j + j * a_dim1], lda);
1016 /* Ran to completion, A has full rank */
1023 /* Rank is the number of steps completed. Set INFO = 1 to signal */
1024 /* that the factorization cannot be used to solve a system. */