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_b10 = 1.;
516 static doublereal c_b14 = 0.;
518 /* > \brief \b DSYTRI_3X */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download DSYTRI_3X + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytri_
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytri_
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytri_
541 /* SUBROUTINE DSYTRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO ) */
544 /* INTEGER INFO, LDA, N, NB */
545 /* INTEGER IPIV( * ) */
546 /* DOUBLE PRECISION A( LDA, * ), E( * ), WORK( N+NB+1, * ) */
549 /* > \par Purpose: */
553 /* > DSYTRI_3X computes the inverse of a real symmetric indefinite */
554 /* > matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK: */
556 /* > A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), */
558 /* > where U (or L) is unit upper (or lower) triangular matrix, */
559 /* > U**T (or L**T) is the transpose of U (or L), P is a permutation */
560 /* > matrix, P**T is the transpose of P, and D is symmetric and block */
561 /* > diagonal with 1-by-1 and 2-by-2 diagonal blocks. */
563 /* > This is the blocked version of the algorithm, calling Level 3 BLAS. */
569 /* > \param[in] UPLO */
571 /* > UPLO is CHARACTER*1 */
572 /* > Specifies whether the details of the factorization are */
573 /* > stored as an upper or lower triangular matrix. */
574 /* > = 'U': Upper triangle of A is stored; */
575 /* > = 'L': Lower triangle of A is stored. */
581 /* > The order of the matrix A. N >= 0. */
584 /* > \param[in,out] A */
586 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
587 /* > On entry, diagonal of the block diagonal matrix D and */
588 /* > factors U or L as computed by DSYTRF_RK and DSYTRF_BK: */
589 /* > a) ONLY diagonal elements of the symmetric block diagonal */
590 /* > matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); */
591 /* > (superdiagonal (or subdiagonal) elements of D */
592 /* > should be provided on entry in array E), and */
593 /* > b) If UPLO = 'U': factor U in the superdiagonal part of A. */
594 /* > If UPLO = 'L': factor L in the subdiagonal part of A. */
596 /* > On exit, if INFO = 0, the symmetric inverse of the original */
598 /* > If UPLO = 'U': the upper triangular part of the inverse */
599 /* > is formed and the part of A below the diagonal is not */
601 /* > If UPLO = 'L': the lower triangular part of the inverse */
602 /* > is formed and the part of A above the diagonal is not */
606 /* > \param[in] LDA */
608 /* > LDA is INTEGER */
609 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
614 /* > E is DOUBLE PRECISION array, dimension (N) */
615 /* > On entry, contains the superdiagonal (or subdiagonal) */
616 /* > elements of the symmetric block diagonal matrix D */
617 /* > with 1-by-1 or 2-by-2 diagonal blocks, where */
618 /* > If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) not referenced; */
619 /* > If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) not referenced. */
621 /* > NOTE: For 1-by-1 diagonal block D(k), where */
622 /* > 1 <= k <= N, the element E(k) is not referenced in both */
623 /* > UPLO = 'U' or UPLO = 'L' cases. */
626 /* > \param[in] IPIV */
628 /* > IPIV is INTEGER array, dimension (N) */
629 /* > Details of the interchanges and the block structure of D */
630 /* > as determined by DSYTRF_RK or DSYTRF_BK. */
633 /* > \param[out] WORK */
635 /* > WORK is DOUBLE PRECISION array, dimension (N+NB+1,NB+3). */
638 /* > \param[in] NB */
640 /* > NB is INTEGER */
644 /* > \param[out] INFO */
646 /* > INFO is INTEGER */
647 /* > = 0: successful exit */
648 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
649 /* > > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
650 /* > inverse could not be computed. */
656 /* > \author Univ. of Tennessee */
657 /* > \author Univ. of California Berkeley */
658 /* > \author Univ. of Colorado Denver */
659 /* > \author NAG Ltd. */
661 /* > \date June 2017 */
663 /* > \ingroup doubleSYcomputational */
665 /* > \par Contributors: */
666 /* ================== */
669 /* > June 2017, Igor Kozachenko, */
670 /* > Computer Science Division, */
671 /* > University of California, Berkeley */
675 /* ===================================================================== */
676 /* Subroutine */ int dsytri_3x_(char *uplo, integer *n, doublereal *a,
677 integer *lda, doublereal *e, integer *ipiv, doublereal *work, integer
680 /* System generated locals */
681 integer a_dim1, a_offset, work_dim1, work_offset, i__1, i__2, i__3;
683 /* Local variables */
686 extern /* Subroutine */ int dsyswapr_(char *, integer *, doublereal *,
687 integer *, integer *, integer *);
691 extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
692 integer *, doublereal *, doublereal *, integer *, doublereal *,
693 integer *, doublereal *, doublereal *, integer *);
694 extern logical lsame_(char *, char *);
695 extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *,
696 integer *, integer *, doublereal *, doublereal *, integer *,
697 doublereal *, integer *);
699 doublereal ak, u01_i_j__;
701 doublereal u11_i_j__;
703 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
705 extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal
706 *, integer *, integer *);
708 doublereal akp1, u01_ip1_j__, u11_ip1_j__;
711 /* -- LAPACK computational routine (version 3.7.1) -- */
712 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
713 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
717 /* ===================================================================== */
720 /* Test the input parameters. */
722 /* Parameter adjustments */
724 a_offset = 1 + a_dim1 * 1;
728 work_dim1 = *n + *nb + 1;
729 work_offset = 1 + work_dim1 * 1;
734 upper = lsame_(uplo, "U");
735 if (! upper && ! lsame_(uplo, "L")) {
739 } else if (*lda < f2cmax(1,*n)) {
743 /* Quick return if possible */
747 xerbla_("DSYTRI_3X", &i__1, (ftnlen)9);
754 /* Workspace got Non-diag elements of D */
757 for (k = 1; k <= i__1; ++k) {
758 work[k + work_dim1] = e[k];
761 /* Check that the diagonal matrix D is nonsingular. */
765 /* Upper triangular storage: examine D from bottom to top */
767 for (*info = *n; *info >= 1; --(*info)) {
768 if (ipiv[*info] > 0 && a[*info + *info * a_dim1] == 0.) {
774 /* Lower triangular storage: examine D from top to bottom. */
777 for (*info = 1; *info <= i__1; ++(*info)) {
778 if (ipiv[*info] > 0 && a[*info + *info * a_dim1] == 0.) {
786 /* Splitting Workspace */
787 /* U01 is a block ( N, NB+1 ) */
788 /* The first element of U01 is in WORK( 1, 1 ) */
789 /* U11 is a block ( NB+1, NB+1 ) */
790 /* The first element of U11 is in WORK( N+1, 1 ) */
794 /* INVD is a block ( N, 2 ) */
795 /* The first element of INVD is in WORK( 1, INVD ) */
802 /* invA = P * inv(U**T) * inv(D) * inv(U) * P**T. */
804 dtrtri_(uplo, "U", n, &a[a_offset], lda, info);
806 /* inv(D) and inv(D) * inv(U) */
811 /* 1 x 1 diagonal NNB */
812 work[k + invd * work_dim1] = 1. / a[k + k * a_dim1];
813 work[k + (invd + 1) * work_dim1] = 0.;
815 /* 2 x 2 diagonal NNB */
816 t = work[k + 1 + work_dim1];
817 ak = a[k + k * a_dim1] / t;
818 akp1 = a[k + 1 + (k + 1) * a_dim1] / t;
819 akkp1 = work[k + 1 + work_dim1] / t;
820 d__ = t * (ak * akp1 - 1.);
821 work[k + invd * work_dim1] = akp1 / d__;
822 work[k + 1 + (invd + 1) * work_dim1] = ak / d__;
823 work[k + (invd + 1) * work_dim1] = -akkp1 / d__;
824 work[k + 1 + invd * work_dim1] = work[k + (invd + 1) *
831 /* inv(U**T) = (inv(U))**T */
833 /* inv(U**T) * inv(D) * inv(U) */
842 /* count negative elements, */
844 for (i__ = cut + 1 - nnb; i__ <= i__1; ++i__) {
849 /* need a even number for a clear cut */
850 if (icount % 2 == 1) {
859 for (i__ = 1; i__ <= i__1; ++i__) {
861 for (j = 1; j <= i__2; ++j) {
862 work[i__ + j * work_dim1] = a[i__ + (cut + j) * a_dim1];
869 for (i__ = 1; i__ <= i__1; ++i__) {
870 work[u11 + i__ + i__ * work_dim1] = 1.;
872 for (j = 1; j <= i__2; ++j) {
873 work[u11 + i__ + j * work_dim1] = 0.;
876 for (j = i__ + 1; j <= i__2; ++j) {
877 work[u11 + i__ + j * work_dim1] = a[cut + i__ + (cut + j)
888 for (j = 1; j <= i__1; ++j) {
889 work[i__ + j * work_dim1] = work[i__ + invd *
890 work_dim1] * work[i__ + j * work_dim1];
894 for (j = 1; j <= i__1; ++j) {
895 u01_i_j__ = work[i__ + j * work_dim1];
896 u01_ip1_j__ = work[i__ + 1 + j * work_dim1];
897 work[i__ + j * work_dim1] = work[i__ + invd *
898 work_dim1] * u01_i_j__ + work[i__ + (invd + 1)
899 * work_dim1] * u01_ip1_j__;
900 work[i__ + 1 + j * work_dim1] = work[i__ + 1 + invd *
901 work_dim1] * u01_i_j__ + work[i__ + 1 + (invd
902 + 1) * work_dim1] * u01_ip1_j__;
913 if (ipiv[cut + i__] > 0) {
915 for (j = i__; j <= i__1; ++j) {
916 work[u11 + i__ + j * work_dim1] = work[cut + i__ +
917 invd * work_dim1] * work[u11 + i__ + j *
922 for (j = i__; j <= i__1; ++j) {
923 u11_i_j__ = work[u11 + i__ + j * work_dim1];
924 u11_ip1_j__ = work[u11 + i__ + 1 + j * work_dim1];
925 work[u11 + i__ + j * work_dim1] = work[cut + i__ +
926 invd * work_dim1] * work[u11 + i__ + j *
927 work_dim1] + work[cut + i__ + (invd + 1) *
928 work_dim1] * work[u11 + i__ + 1 + j *
930 work[u11 + i__ + 1 + j * work_dim1] = work[cut + i__
931 + 1 + invd * work_dim1] * u11_i_j__ + work[
932 cut + i__ + 1 + (invd + 1) * work_dim1] *
940 /* U11**T * invD1 * U11 -> U11 */
943 dtrmm_("L", "U", "T", "U", &nnb, &nnb, &c_b10, &a[cut + 1 + (cut
944 + 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
947 for (i__ = 1; i__ <= i__1; ++i__) {
949 for (j = i__; j <= i__2; ++j) {
950 a[cut + i__ + (cut + j) * a_dim1] = work[u11 + i__ + j *
955 /* U01**T * invD * U01 -> A( CUT+I, CUT+J ) */
959 dgemm_("T", "N", &nnb, &nnb, &cut, &c_b10, &a[(cut + 1) * a_dim1
960 + 1], lda, &work[work_offset], &i__1, &c_b14, &work[u11 +
961 1 + work_dim1], &i__2);
963 /* U11 = U11**T * invD1 * U11 + U01**T * invD * U01 */
966 for (i__ = 1; i__ <= i__1; ++i__) {
968 for (j = i__; j <= i__2; ++j) {
969 a[cut + i__ + (cut + j) * a_dim1] += work[u11 + i__ + j *
974 /* U01 = U00**T * invD0 * U01 */
977 dtrmm_("L", uplo, "T", "U", &cut, &nnb, &c_b10, &a[a_offset], lda,
978 &work[work_offset], &i__1);
983 for (i__ = 1; i__ <= i__1; ++i__) {
985 for (j = 1; j <= i__2; ++j) {
986 a[i__ + (cut + j) * a_dim1] = work[i__ + j * work_dim1];
994 /* Apply PERMUTATIONS P and P**T: */
995 /* P * inv(U**T) * inv(D) * inv(U) * P**T. */
996 /* Interchange rows and columns I and IPIV(I) in reverse order */
997 /* from the formation order of IPIV vector for Upper case. */
999 /* ( We can use a loop over IPIV with increment 1, */
1000 /* since the ABS value of IPIV(I) represents the row (column) */
1001 /* index of the interchange with row (column) i in both 1x1 */
1002 /* and 2x2 pivot cases, i.e. we don't need separate code branches */
1003 /* for 1x1 and 2x2 pivot cases ) */
1006 for (i__ = 1; i__ <= i__1; ++i__) {
1007 ip = (i__2 = ipiv[i__], abs(i__2));
1010 dsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
1013 dsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
1022 /* inv A = P * inv(L**T) * inv(D) * inv(L) * P**T. */
1024 dtrtri_(uplo, "U", n, &a[a_offset], lda, info);
1026 /* inv(D) and inv(D) * inv(L) */
1031 /* 1 x 1 diagonal NNB */
1032 work[k + invd * work_dim1] = 1. / a[k + k * a_dim1];
1033 work[k + (invd + 1) * work_dim1] = 0.;
1035 /* 2 x 2 diagonal NNB */
1036 t = work[k - 1 + work_dim1];
1037 ak = a[k - 1 + (k - 1) * a_dim1] / t;
1038 akp1 = a[k + k * a_dim1] / t;
1039 akkp1 = work[k - 1 + work_dim1] / t;
1040 d__ = t * (ak * akp1 - 1.);
1041 work[k - 1 + invd * work_dim1] = akp1 / d__;
1042 work[k + invd * work_dim1] = ak / d__;
1043 work[k + (invd + 1) * work_dim1] = -akkp1 / d__;
1044 work[k - 1 + (invd + 1) * work_dim1] = work[k + (invd + 1) *
1051 /* inv(L**T) = (inv(L))**T */
1053 /* inv(L**T) * inv(D) * inv(L) */
1058 if (cut + nnb > *n) {
1062 /* count negative elements, */
1064 for (i__ = cut + 1; i__ <= i__1; ++i__) {
1065 if (ipiv[i__] < 0) {
1069 /* need a even number for a clear cut */
1070 if (icount % 2 == 1) {
1077 i__1 = *n - cut - nnb;
1078 for (i__ = 1; i__ <= i__1; ++i__) {
1080 for (j = 1; j <= i__2; ++j) {
1081 work[i__ + j * work_dim1] = a[cut + nnb + i__ + (cut + j)
1089 for (i__ = 1; i__ <= i__1; ++i__) {
1090 work[u11 + i__ + i__ * work_dim1] = 1.;
1092 for (j = i__ + 1; j <= i__2; ++j) {
1093 work[u11 + i__ + j * work_dim1] = 0.;
1096 for (j = 1; j <= i__2; ++j) {
1097 work[u11 + i__ + j * work_dim1] = a[cut + i__ + (cut + j)
1104 i__ = *n - cut - nnb;
1106 if (ipiv[cut + nnb + i__] > 0) {
1108 for (j = 1; j <= i__1; ++j) {
1109 work[i__ + j * work_dim1] = work[cut + nnb + i__ +
1110 invd * work_dim1] * work[i__ + j * work_dim1];
1114 for (j = 1; j <= i__1; ++j) {
1115 u01_i_j__ = work[i__ + j * work_dim1];
1116 u01_ip1_j__ = work[i__ - 1 + j * work_dim1];
1117 work[i__ + j * work_dim1] = work[cut + nnb + i__ +
1118 invd * work_dim1] * u01_i_j__ + work[cut +
1119 nnb + i__ + (invd + 1) * work_dim1] *
1121 work[i__ - 1 + j * work_dim1] = work[cut + nnb + i__
1122 - 1 + (invd + 1) * work_dim1] * u01_i_j__ +
1123 work[cut + nnb + i__ - 1 + invd * work_dim1] *
1135 if (ipiv[cut + i__] > 0) {
1137 for (j = 1; j <= i__1; ++j) {
1138 work[u11 + i__ + j * work_dim1] = work[cut + i__ +
1139 invd * work_dim1] * work[u11 + i__ + j *
1144 for (j = 1; j <= i__1; ++j) {
1145 u11_i_j__ = work[u11 + i__ + j * work_dim1];
1146 u11_ip1_j__ = work[u11 + i__ - 1 + j * work_dim1];
1147 work[u11 + i__ + j * work_dim1] = work[cut + i__ +
1148 invd * work_dim1] * work[u11 + i__ + j *
1149 work_dim1] + work[cut + i__ + (invd + 1) *
1150 work_dim1] * u11_ip1_j__;
1151 work[u11 + i__ - 1 + j * work_dim1] = work[cut + i__
1152 - 1 + (invd + 1) * work_dim1] * u11_i_j__ +
1153 work[cut + i__ - 1 + invd * work_dim1] *
1161 /* L11**T * invD1 * L11 -> L11 */
1163 i__1 = *n + *nb + 1;
1164 dtrmm_("L", uplo, "T", "U", &nnb, &nnb, &c_b10, &a[cut + 1 + (cut
1165 + 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
1168 for (i__ = 1; i__ <= i__1; ++i__) {
1170 for (j = 1; j <= i__2; ++j) {
1171 a[cut + i__ + (cut + j) * a_dim1] = work[u11 + i__ + j *
1176 if (cut + nnb < *n) {
1178 /* L21**T * invD2*L21 -> A( CUT+I, CUT+J ) */
1180 i__1 = *n - nnb - cut;
1181 i__2 = *n + *nb + 1;
1182 i__3 = *n + *nb + 1;
1183 dgemm_("T", "N", &nnb, &nnb, &i__1, &c_b10, &a[cut + nnb + 1
1184 + (cut + 1) * a_dim1], lda, &work[work_offset], &i__2,
1185 &c_b14, &work[u11 + 1 + work_dim1], &i__3);
1187 /* L11 = L11**T * invD1 * L11 + U01**T * invD * U01 */
1190 for (i__ = 1; i__ <= i__1; ++i__) {
1192 for (j = 1; j <= i__2; ++j) {
1193 a[cut + i__ + (cut + j) * a_dim1] += work[u11 + i__ +
1198 /* L01 = L22**T * invD2 * L21 */
1200 i__1 = *n - nnb - cut;
1201 i__2 = *n + *nb + 1;
1202 dtrmm_("L", uplo, "T", "U", &i__1, &nnb, &c_b10, &a[cut + nnb
1203 + 1 + (cut + nnb + 1) * a_dim1], lda, &work[
1204 work_offset], &i__2);
1208 i__1 = *n - cut - nnb;
1209 for (i__ = 1; i__ <= i__1; ++i__) {
1211 for (j = 1; j <= i__2; ++j) {
1212 a[cut + nnb + i__ + (cut + j) * a_dim1] = work[i__ +
1219 /* L11 = L11**T * invD1 * L11 */
1222 for (i__ = 1; i__ <= i__1; ++i__) {
1224 for (j = 1; j <= i__2; ++j) {
1225 a[cut + i__ + (cut + j) * a_dim1] = work[u11 + i__ +
1237 /* Apply PERMUTATIONS P and P**T: */
1238 /* P * inv(L**T) * inv(D) * inv(L) * P**T. */
1239 /* Interchange rows and columns I and IPIV(I) in reverse order */
1240 /* from the formation order of IPIV vector for Lower case. */
1242 /* ( We can use a loop over IPIV with increment -1, */
1243 /* since the ABS value of IPIV(I) represents the row (column) */
1244 /* index of the interchange with row (column) i in both 1x1 */
1245 /* and 2x2 pivot cases, i.e. we don't need separate code branches */
1246 /* for 1x1 and 2x2 pivot cases ) */
1248 for (i__ = *n; i__ >= 1; --i__) {
1249 ip = (i__1 = ipiv[i__], abs(i__1));
1252 dsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
1255 dsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
1264 /* End of DSYTRI_3X */