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;
517 /* > \brief \b DSPTRF */
519 /* =========== DOCUMENTATION =========== */
521 /* Online html documentation available at */
522 /* http://www.netlib.org/lapack/explore-html/ */
525 /* > Download DSPTRF + dependencies */
526 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsptrf.
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsptrf.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsptrf.
540 /* SUBROUTINE DSPTRF( UPLO, N, AP, IPIV, INFO ) */
543 /* INTEGER INFO, N */
544 /* INTEGER IPIV( * ) */
545 /* DOUBLE PRECISION AP( * ) */
548 /* > \par Purpose: */
553 /* > DSPTRF computes the factorization of a real symmetric matrix A stored */
554 /* > in packed format using the Bunch-Kaufman diagonal pivoting method: */
556 /* > A = U*D*U**T or A = L*D*L**T */
558 /* > where U (or L) is a product of permutation and unit upper (lower) */
559 /* > triangular matrices, and D is symmetric and block diagonal with */
560 /* > 1-by-1 and 2-by-2 diagonal blocks. */
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,out] AP */
581 /* > AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) */
582 /* > On entry, the upper or lower triangle of the symmetric matrix */
583 /* > A, packed columnwise in a linear array. The j-th column of A */
584 /* > is stored in the array AP as follows: */
585 /* > if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
586 /* > if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
588 /* > On exit, the block diagonal matrix D and the multipliers used */
589 /* > to obtain the factor U or L, stored as a packed triangular */
590 /* > matrix overwriting A (see below for further details). */
593 /* > \param[out] IPIV */
595 /* > IPIV is INTEGER array, dimension (N) */
596 /* > Details of the interchanges and the block structure of D. */
597 /* > If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
598 /* > interchanged and D(k,k) is a 1-by-1 diagonal block. */
599 /* > If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
600 /* > columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
601 /* > is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */
602 /* > IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
603 /* > interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
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, D(i,i) is exactly zero. The factorization */
612 /* > has been completed, but the block diagonal matrix D is */
613 /* > exactly singular, and division by zero will occur if it */
614 /* > is used to solve a system of equations. */
620 /* > \author Univ. of Tennessee */
621 /* > \author Univ. of California Berkeley */
622 /* > \author Univ. of Colorado Denver */
623 /* > \author NAG Ltd. */
625 /* > \date December 2016 */
627 /* > \ingroup doubleOTHERcomputational */
629 /* > \par Further Details: */
630 /* ===================== */
634 /* > If UPLO = 'U', then A = U*D*U**T, where */
635 /* > U = P(n)*U(n)* ... *P(k)U(k)* ..., */
636 /* > i.e., U is a product of terms P(k)*U(k), where k decreases from n to */
637 /* > 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
638 /* > and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */
639 /* > defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */
640 /* > that if the diagonal block D(k) is of order s (s = 1 or 2), then */
642 /* > ( I v 0 ) k-s */
643 /* > U(k) = ( 0 I 0 ) s */
644 /* > ( 0 0 I ) n-k */
647 /* > If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */
648 /* > If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */
649 /* > and A(k,k), and v overwrites A(1:k-2,k-1:k). */
651 /* > If UPLO = 'L', then A = L*D*L**T, where */
652 /* > L = P(1)*L(1)* ... *P(k)*L(k)* ..., */
653 /* > i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */
654 /* > n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
655 /* > and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */
656 /* > defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */
657 /* > that if the diagonal block D(k) is of order s (s = 1 or 2), then */
659 /* > ( I 0 0 ) k-1 */
660 /* > L(k) = ( 0 I 0 ) s */
661 /* > ( 0 v I ) n-k-s+1 */
662 /* > k-1 s n-k-s+1 */
664 /* > If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */
665 /* > If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */
666 /* > and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */
669 /* > \par Contributors: */
670 /* ================== */
672 /* > J. Lewis, Boeing Computer Services Company */
674 /* ===================================================================== */
675 /* Subroutine */ int dsptrf_(char *uplo, integer *n, doublereal *ap, integer *
678 /* System generated locals */
680 doublereal d__1, d__2, d__3;
682 /* Local variables */
684 extern /* Subroutine */ int dspr_(char *, integer *, doublereal *,
685 doublereal *, integer *, doublereal *);
688 extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
690 extern logical lsame_(char *, char *);
691 extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
692 doublereal *, integer *);
695 doublereal r1, d11, d12, d21, d22;
697 doublereal absakk, wk;
699 extern integer idamax_(integer *, doublereal *, integer *);
700 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
701 doublereal colmax, rowmax;
702 integer knc, kpc, npp;
703 doublereal wkm1, wkp1;
706 /* -- LAPACK computational routine (version 3.7.0) -- */
707 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
708 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
712 /* ===================================================================== */
715 /* Test the input parameters. */
717 /* Parameter adjustments */
723 upper = lsame_(uplo, "U");
724 if (! upper && ! lsame_(uplo, "L")) {
731 xerbla_("DSPTRF", &i__1, (ftnlen)6);
735 /* Initialize ALPHA for use in choosing pivot block size. */
737 alpha = (sqrt(17.) + 1.) / 8.;
741 /* Factorize A as U*D*U**T using the upper triangle of A */
743 /* K is the main loop index, decreasing from N to 1 in steps of */
747 kc = (*n - 1) * *n / 2 + 1;
751 /* If K < 1, exit from loop */
758 /* Determine rows and columns to be interchanged and whether */
759 /* a 1-by-1 or 2-by-2 pivot block will be used */
761 absakk = (d__1 = ap[kc + k - 1], abs(d__1));
763 /* IMAX is the row-index of the largest off-diagonal element in */
764 /* column K, and COLMAX is its absolute value */
768 imax = idamax_(&i__1, &ap[kc], &c__1);
769 colmax = (d__1 = ap[kc + imax - 1], abs(d__1));
774 if (f2cmax(absakk,colmax) == 0.) {
776 /* Column K is zero: set INFO and continue */
783 if (absakk >= alpha * colmax) {
785 /* no interchange, use 1-by-1 pivot block */
792 kx = imax * (imax + 1) / 2 + imax;
794 for (j = imax + 1; j <= i__1; ++j) {
795 if ((d__1 = ap[kx], abs(d__1)) > rowmax) {
796 rowmax = (d__1 = ap[kx], abs(d__1));
802 kpc = (imax - 1) * imax / 2 + 1;
805 jmax = idamax_(&i__1, &ap[kpc], &c__1);
807 d__2 = rowmax, d__3 = (d__1 = ap[kpc + jmax - 1], abs(
809 rowmax = f2cmax(d__2,d__3);
812 if (absakk >= alpha * colmax * (colmax / rowmax)) {
814 /* no interchange, use 1-by-1 pivot block */
817 } else if ((d__1 = ap[kpc + imax - 1], abs(d__1)) >= alpha *
820 /* interchange rows and columns K and IMAX, use 1-by-1 */
826 /* interchange rows and columns K-1 and IMAX, use 2-by-2 */
840 /* Interchange rows and columns KK and KP in the leading */
841 /* submatrix A(1:k,1:k) */
844 dswap_(&i__1, &ap[knc], &c__1, &ap[kpc], &c__1);
847 for (j = kp + 1; j <= i__1; ++j) {
850 ap[knc + j - 1] = ap[kx];
854 t = ap[knc + kk - 1];
855 ap[knc + kk - 1] = ap[kpc + kp - 1];
856 ap[kpc + kp - 1] = t;
859 ap[kc + k - 2] = ap[kc + kp - 1];
864 /* Update the leading submatrix */
868 /* 1-by-1 pivot block D(k): column k now holds */
870 /* W(k) = U(k)*D(k) */
872 /* where U(k) is the k-th column of U */
874 /* Perform a rank-1 update of A(1:k-1,1:k-1) as */
876 /* A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T */
878 r1 = 1. / ap[kc + k - 1];
881 dspr_(uplo, &i__1, &d__1, &ap[kc], &c__1, &ap[1]);
883 /* Store U(k) in column k */
886 dscal_(&i__1, &r1, &ap[kc], &c__1);
889 /* 2-by-2 pivot block D(k): columns k and k-1 now hold */
891 /* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) */
893 /* where U(k) and U(k-1) are the k-th and (k-1)-th columns */
896 /* Perform a rank-2 update of A(1:k-2,1:k-2) as */
898 /* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T */
899 /* = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T */
903 d12 = ap[k - 1 + (k - 1) * k / 2];
904 d22 = ap[k - 1 + (k - 2) * (k - 1) / 2] / d12;
905 d11 = ap[k + (k - 1) * k / 2] / d12;
906 t = 1. / (d11 * d22 - 1.);
909 for (j = k - 2; j >= 1; --j) {
910 wkm1 = d12 * (d11 * ap[j + (k - 2) * (k - 1) / 2] -
911 ap[j + (k - 1) * k / 2]);
912 wk = d12 * (d22 * ap[j + (k - 1) * k / 2] - ap[j + (k
913 - 2) * (k - 1) / 2]);
914 for (i__ = j; i__ >= 1; --i__) {
915 ap[i__ + (j - 1) * j / 2] = ap[i__ + (j - 1) * j /
916 2] - ap[i__ + (k - 1) * k / 2] * wk - ap[
917 i__ + (k - 2) * (k - 1) / 2] * wkm1;
920 ap[j + (k - 1) * k / 2] = wk;
921 ap[j + (k - 2) * (k - 1) / 2] = wkm1;
930 /* Store details of the interchanges in IPIV */
939 /* Decrease K and return to the start of the main loop */
947 /* Factorize A as L*D*L**T using the lower triangle of A */
949 /* K is the main loop index, increasing from 1 to N in steps of */
954 npp = *n * (*n + 1) / 2;
958 /* If K > N, exit from loop */
965 /* Determine rows and columns to be interchanged and whether */
966 /* a 1-by-1 or 2-by-2 pivot block will be used */
968 absakk = (d__1 = ap[kc], abs(d__1));
970 /* IMAX is the row-index of the largest off-diagonal element in */
971 /* column K, and COLMAX is its absolute value */
975 imax = k + idamax_(&i__1, &ap[kc + 1], &c__1);
976 colmax = (d__1 = ap[kc + imax - k], abs(d__1));
981 if (f2cmax(absakk,colmax) == 0.) {
983 /* Column K is zero: set INFO and continue */
990 if (absakk >= alpha * colmax) {
992 /* no interchange, use 1-by-1 pivot block */
997 /* JMAX is the column-index of the largest off-diagonal */
998 /* element in row IMAX, and ROWMAX is its absolute value */
1003 for (j = k; j <= i__1; ++j) {
1004 if ((d__1 = ap[kx], abs(d__1)) > rowmax) {
1005 rowmax = (d__1 = ap[kx], abs(d__1));
1011 kpc = npp - (*n - imax + 1) * (*n - imax + 2) / 2 + 1;
1014 jmax = imax + idamax_(&i__1, &ap[kpc + 1], &c__1);
1016 d__2 = rowmax, d__3 = (d__1 = ap[kpc + jmax - imax], abs(
1018 rowmax = f2cmax(d__2,d__3);
1021 if (absakk >= alpha * colmax * (colmax / rowmax)) {
1023 /* no interchange, use 1-by-1 pivot block */
1026 } else if ((d__1 = ap[kpc], abs(d__1)) >= alpha * rowmax) {
1028 /* interchange rows and columns K and IMAX, use 1-by-1 */
1034 /* interchange rows and columns K+1 and IMAX, use 2-by-2 */
1044 knc = knc + *n - k + 1;
1048 /* Interchange rows and columns KK and KP in the trailing */
1049 /* submatrix A(k:n,k:n) */
1053 dswap_(&i__1, &ap[knc + kp - kk + 1], &c__1, &ap[kpc + 1],
1058 for (j = kk + 1; j <= i__1; ++j) {
1059 kx = kx + *n - j + 1;
1060 t = ap[knc + j - kk];
1061 ap[knc + j - kk] = ap[kx];
1070 ap[kc + 1] = ap[kc + kp - k];
1071 ap[kc + kp - k] = t;
1075 /* Update the trailing submatrix */
1079 /* 1-by-1 pivot block D(k): column k now holds */
1081 /* W(k) = L(k)*D(k) */
1083 /* where L(k) is the k-th column of L */
1087 /* Perform a rank-1 update of A(k+1:n,k+1:n) as */
1089 /* A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T */
1094 dspr_(uplo, &i__1, &d__1, &ap[kc + 1], &c__1, &ap[kc + *n
1097 /* Store L(k) in column K */
1100 dscal_(&i__1, &r1, &ap[kc + 1], &c__1);
1104 /* 2-by-2 pivot block D(k): columns K and K+1 now hold */
1106 /* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) */
1108 /* where L(k) and L(k+1) are the k-th and (k+1)-th columns */
1113 /* Perform a rank-2 update of A(k+2:n,k+2:n) as */
1115 /* A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T */
1116 /* = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T */
1118 /* where L(k) and L(k+1) are the k-th and (k+1)-th */
1121 d21 = ap[k + 1 + (k - 1) * ((*n << 1) - k) / 2];
1122 d11 = ap[k + 1 + k * ((*n << 1) - k - 1) / 2] / d21;
1123 d22 = ap[k + (k - 1) * ((*n << 1) - k) / 2] / d21;
1124 t = 1. / (d11 * d22 - 1.);
1128 for (j = k + 2; j <= i__1; ++j) {
1129 wk = d21 * (d11 * ap[j + (k - 1) * ((*n << 1) - k) /
1130 2] - ap[j + k * ((*n << 1) - k - 1) / 2]);
1131 wkp1 = d21 * (d22 * ap[j + k * ((*n << 1) - k - 1) /
1132 2] - ap[j + (k - 1) * ((*n << 1) - k) / 2]);
1135 for (i__ = j; i__ <= i__2; ++i__) {
1136 ap[i__ + (j - 1) * ((*n << 1) - j) / 2] = ap[i__
1137 + (j - 1) * ((*n << 1) - j) / 2] - ap[i__
1138 + (k - 1) * ((*n << 1) - k) / 2] * wk -
1139 ap[i__ + k * ((*n << 1) - k - 1) / 2] *
1144 ap[j + (k - 1) * ((*n << 1) - k) / 2] = wk;
1145 ap[j + k * ((*n << 1) - k - 1) / 2] = wkp1;
1153 /* Store details of the interchanges in IPIV */
1162 /* Increase K and return to the start of the main loop */
1165 kc = knc + *n - k + 2;