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_b12 = 1.;
516 static doublereal c_b15 = -1.;
518 /* > \brief \b DPFTRF */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download DPFTRF + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpftrf.
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpftrf.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpftrf.
541 /* SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, INFO ) */
543 /* CHARACTER TRANSR, UPLO */
544 /* INTEGER N, INFO */
545 /* DOUBLE PRECISION A( 0: * ) */
548 /* > \par Purpose: */
553 /* > DPFTRF computes the Cholesky factorization of a real symmetric */
554 /* > positive definite matrix A. */
556 /* > The factorization has the form */
557 /* > A = U**T * U, if UPLO = 'U', or */
558 /* > A = L * L**T, if UPLO = 'L', */
559 /* > where U is an upper triangular matrix and L is lower triangular. */
561 /* > This is the block version of the algorithm, calling Level 3 BLAS. */
567 /* > \param[in] TRANSR */
569 /* > TRANSR is CHARACTER*1 */
570 /* > = 'N': The Normal TRANSR of RFP A is stored; */
571 /* > = 'T': The Transpose TRANSR of RFP A is stored. */
574 /* > \param[in] UPLO */
576 /* > UPLO is CHARACTER*1 */
577 /* > = 'U': Upper triangle of RFP A is stored; */
578 /* > = 'L': Lower triangle of RFP A is stored. */
584 /* > The order of the matrix A. N >= 0. */
587 /* > \param[in,out] A */
589 /* > A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ); */
590 /* > On entry, the symmetric matrix A in RFP format. RFP format is */
591 /* > described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' */
592 /* > then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is */
593 /* > (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is */
594 /* > the transpose of RFP A as defined when */
595 /* > TRANSR = 'N'. The contents of RFP A are defined by UPLO as */
596 /* > follows: If UPLO = 'U' the RFP A contains the NT elements of */
597 /* > upper packed A. If UPLO = 'L' the RFP A contains the elements */
598 /* > of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = */
599 /* > 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N */
600 /* > is odd. See the Note below for more details. */
602 /* > On exit, if INFO = 0, the factor U or L from the Cholesky */
603 /* > factorization RFP A = U**T*U or RFP A = L*L**T. */
606 /* > \param[out] INFO */
608 /* > INFO is INTEGER */
609 /* > = 0: successful exit */
610 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
611 /* > > 0: if INFO = i, the leading minor of order i is not */
612 /* > positive definite, and the factorization could not be */
619 /* > \author Univ. of Tennessee */
620 /* > \author Univ. of California Berkeley */
621 /* > \author Univ. of Colorado Denver */
622 /* > \author NAG Ltd. */
624 /* > \date December 2016 */
626 /* > \ingroup doubleOTHERcomputational */
628 /* > \par Further Details: */
629 /* ===================== */
633 /* > We first consider Rectangular Full Packed (RFP) Format when N is */
634 /* > even. We give an example where N = 6. */
636 /* > AP is Upper AP is Lower */
638 /* > 00 01 02 03 04 05 00 */
639 /* > 11 12 13 14 15 10 11 */
640 /* > 22 23 24 25 20 21 22 */
641 /* > 33 34 35 30 31 32 33 */
642 /* > 44 45 40 41 42 43 44 */
643 /* > 55 50 51 52 53 54 55 */
646 /* > Let TRANSR = 'N'. RFP holds AP as follows: */
647 /* > For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
648 /* > three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
649 /* > the transpose of the first three columns of AP upper. */
650 /* > For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
651 /* > three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
652 /* > the transpose of the last three columns of AP lower. */
653 /* > This covers the case N even and TRANSR = 'N'. */
657 /* > 03 04 05 33 43 53 */
658 /* > 13 14 15 00 44 54 */
659 /* > 23 24 25 10 11 55 */
660 /* > 33 34 35 20 21 22 */
661 /* > 00 44 45 30 31 32 */
662 /* > 01 11 55 40 41 42 */
663 /* > 02 12 22 50 51 52 */
665 /* > Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
666 /* > transpose of RFP A above. One therefore gets: */
671 /* > 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */
672 /* > 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */
673 /* > 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */
676 /* > We then consider Rectangular Full Packed (RFP) Format when N is */
677 /* > odd. We give an example where N = 5. */
679 /* > AP is Upper AP is Lower */
681 /* > 00 01 02 03 04 00 */
682 /* > 11 12 13 14 10 11 */
683 /* > 22 23 24 20 21 22 */
684 /* > 33 34 30 31 32 33 */
685 /* > 44 40 41 42 43 44 */
688 /* > Let TRANSR = 'N'. RFP holds AP as follows: */
689 /* > For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
690 /* > three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
691 /* > the transpose of the first two columns of AP upper. */
692 /* > For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
693 /* > three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
694 /* > the transpose of the last two columns of AP lower. */
695 /* > This covers the case N odd and TRANSR = 'N'. */
699 /* > 02 03 04 00 33 43 */
700 /* > 12 13 14 10 11 44 */
701 /* > 22 23 24 20 21 22 */
702 /* > 00 33 34 30 31 32 */
703 /* > 01 11 44 40 41 42 */
705 /* > Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
706 /* > transpose of RFP A above. One therefore gets: */
710 /* > 02 12 22 00 01 00 10 20 30 40 50 */
711 /* > 03 13 23 33 11 33 11 21 31 41 51 */
712 /* > 04 14 24 34 44 43 44 22 32 42 52 */
715 /* ===================================================================== */
716 /* Subroutine */ int dpftrf_(char *transr, char *uplo, integer *n, doublereal
719 /* System generated locals */
722 /* Local variables */
724 logical normaltransr;
725 extern logical lsame_(char *, char *);
727 extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
728 integer *, integer *, doublereal *, doublereal *, integer *,
729 doublereal *, integer *), dsyrk_(
730 char *, char *, integer *, integer *, doublereal *, doublereal *,
731 integer *, doublereal *, doublereal *, integer *);
733 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
735 extern /* Subroutine */ int dpotrf_(char *, integer *, doublereal *,
736 integer *, integer *);
739 /* -- LAPACK computational routine (version 3.7.0) -- */
740 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
741 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
745 /* ===================================================================== */
748 /* Test the input parameters. */
751 normaltransr = lsame_(transr, "N");
752 lower = lsame_(uplo, "L");
753 if (! normaltransr && ! lsame_(transr, "T")) {
755 } else if (! lower && ! lsame_(uplo, "U")) {
762 xerbla_("DPFTRF", &i__1, (ftnlen)6);
766 /* Quick return if possible */
772 /* If N is odd, set NISODD = .TRUE. */
773 /* If N is even, set K = N/2 and NISODD = .FALSE. */
782 /* Set N1 and N2 depending on LOWER */
792 /* start execution: there are eight cases */
800 /* N is odd and TRANSR = 'N' */
804 /* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) */
805 /* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) */
806 /* T1 -> a(0), T2 -> a(n), S -> a(n1) */
808 dpotrf_("L", &n1, a, n, info);
812 dtrsm_("R", "L", "T", "N", &n2, &n1, &c_b12, a, n, &a[n1], n);
813 dsyrk_("U", "N", &n2, &n1, &c_b15, &a[n1], n, &c_b12, &a[*n],
815 dpotrf_("U", &n2, &a[*n], n, info);
822 /* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) */
823 /* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) */
824 /* T1 -> a(n2), T2 -> a(n1), S -> a(0) */
826 dpotrf_("L", &n1, &a[n2], n, info);
830 dtrsm_("L", "L", "N", "N", &n1, &n2, &c_b12, &a[n2], n, a, n);
831 dsyrk_("U", "T", &n2, &n1, &c_b15, a, n, &c_b12, &a[n1], n);
832 dpotrf_("U", &n2, &a[n1], n, info);
841 /* N is odd and TRANSR = 'T' */
845 /* SRPA for LOWER, TRANSPOSE and N is odd */
846 /* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) */
847 /* T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1 */
849 dpotrf_("U", &n1, a, &n1, info);
853 dtrsm_("L", "U", "T", "N", &n1, &n2, &c_b12, a, &n1, &a[n1 *
855 dsyrk_("L", "T", &n2, &n1, &c_b15, &a[n1 * n1], &n1, &c_b12, &
857 dpotrf_("L", &n2, &a[1], &n1, info);
864 /* SRPA for UPPER, TRANSPOSE and N is odd */
865 /* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) */
866 /* T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2 */
868 dpotrf_("U", &n1, &a[n2 * n2], &n2, info);
872 dtrsm_("R", "U", "N", "N", &n2, &n1, &c_b12, &a[n2 * n2], &n2,
874 dsyrk_("L", "N", &n2, &n1, &c_b15, a, &n2, &c_b12, &a[n1 * n2]
876 dpotrf_("L", &n2, &a[n1 * n2], &n2, info);
891 /* N is even and TRANSR = 'N' */
895 /* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
896 /* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) */
897 /* T1 -> a(1), T2 -> a(0), S -> a(k+1) */
900 dpotrf_("L", &k, &a[1], &i__1, info);
906 dtrsm_("R", "L", "T", "N", &k, &k, &c_b12, &a[1], &i__1, &a[k
910 dsyrk_("U", "N", &k, &k, &c_b15, &a[k + 1], &i__1, &c_b12, a,
913 dpotrf_("U", &k, a, &i__1, info);
920 /* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
921 /* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) */
922 /* T1 -> a(k+1), T2 -> a(k), S -> a(0) */
925 dpotrf_("L", &k, &a[k + 1], &i__1, info);
931 dtrsm_("L", "L", "N", "N", &k, &k, &c_b12, &a[k + 1], &i__1,
935 dsyrk_("U", "T", &k, &k, &c_b15, a, &i__1, &c_b12, &a[k], &
938 dpotrf_("U", &k, &a[k], &i__1, info);
947 /* N is even and TRANSR = 'T' */
951 /* SRPA for LOWER, TRANSPOSE and N is even (see paper) */
952 /* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) */
953 /* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k */
955 dpotrf_("U", &k, &a[k], &k, info);
959 dtrsm_("L", "U", "T", "N", &k, &k, &c_b12, &a[k], &n1, &a[k *
961 dsyrk_("L", "T", &k, &k, &c_b15, &a[k * (k + 1)], &k, &c_b12,
963 dpotrf_("L", &k, a, &k, info);
970 /* SRPA for UPPER, TRANSPOSE and N is even (see paper) */
971 /* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0) */
972 /* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k */
974 dpotrf_("U", &k, &a[k * (k + 1)], &k, info);
978 dtrsm_("R", "U", "N", "N", &k, &k, &c_b12, &a[k * (k + 1)], &
980 dsyrk_("L", "N", &k, &k, &c_b15, a, &k, &c_b12, &a[k * k], &k);
981 dpotrf_("L", &k, &a[k * k], &k, info);