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 DSYTF2_ROOK computes the factorization of a real symmetric indefinite matrix using the bounded
518 Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm). */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download DSYTF2_ROOK + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytf2_
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytf2_
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytf2_
541 /* SUBROUTINE DSYTF2_ROOK( UPLO, N, A, LDA, IPIV, INFO ) */
544 /* INTEGER INFO, LDA, N */
545 /* INTEGER IPIV( * ) */
546 /* DOUBLE PRECISION A( LDA, * ) */
549 /* > \par Purpose: */
554 /* > DSYTF2_ROOK computes the factorization of a real symmetric matrix A */
555 /* > using the bounded Bunch-Kaufman ("rook") diagonal pivoting method: */
557 /* > A = U*D*U**T or A = L*D*L**T */
559 /* > where U (or L) is a product of permutation and unit upper (lower) */
560 /* > triangular matrices, U**T is the transpose of U, and D is symmetric and */
561 /* > block diagonal with 1-by-1 and 2-by-2 diagonal blocks. */
563 /* > This is the unblocked version of the algorithm, calling Level 2 BLAS. */
569 /* > \param[in] UPLO */
571 /* > UPLO is CHARACTER*1 */
572 /* > Specifies whether the upper or lower triangular part of the */
573 /* > symmetric matrix A is stored: */
574 /* > = 'U': Upper triangular */
575 /* > = 'L': Lower triangular */
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, the symmetric matrix A. If UPLO = 'U', the leading */
588 /* > n-by-n upper triangular part of A contains the upper */
589 /* > triangular part of the matrix A, and the strictly lower */
590 /* > triangular part of A is not referenced. If UPLO = 'L', the */
591 /* > leading n-by-n lower triangular part of A contains the lower */
592 /* > triangular part of the matrix A, and the strictly upper */
593 /* > triangular part of A is not referenced. */
595 /* > On exit, the block diagonal matrix D and the multipliers used */
596 /* > to obtain the factor U or L (see below for further details). */
599 /* > \param[in] LDA */
601 /* > LDA is INTEGER */
602 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
605 /* > \param[out] IPIV */
607 /* > IPIV is INTEGER array, dimension (N) */
608 /* > Details of the interchanges and the block structure of D. */
610 /* > If UPLO = 'U': */
611 /* > If IPIV(k) > 0, then rows and columns k and IPIV(k) */
612 /* > were interchanged and D(k,k) is a 1-by-1 diagonal block. */
614 /* > If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and */
615 /* > columns k and -IPIV(k) were interchanged and rows and */
616 /* > columns k-1 and -IPIV(k-1) were inerchaged, */
617 /* > D(k-1:k,k-1:k) is a 2-by-2 diagonal block. */
619 /* > If UPLO = 'L': */
620 /* > If IPIV(k) > 0, then rows and columns k and IPIV(k) */
621 /* > were interchanged and D(k,k) is a 1-by-1 diagonal block. */
623 /* > If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and */
624 /* > columns k and -IPIV(k) were interchanged and rows and */
625 /* > columns k+1 and -IPIV(k+1) were inerchaged, */
626 /* > D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
629 /* > \param[out] INFO */
631 /* > INFO is INTEGER */
632 /* > = 0: successful exit */
633 /* > < 0: if INFO = -k, the k-th argument had an illegal value */
634 /* > > 0: if INFO = k, D(k,k) is exactly zero. The factorization */
635 /* > has been completed, but the block diagonal matrix D is */
636 /* > exactly singular, and division by zero will occur if it */
637 /* > is used to solve a system of equations. */
643 /* > \author Univ. of Tennessee */
644 /* > \author Univ. of California Berkeley */
645 /* > \author Univ. of Colorado Denver */
646 /* > \author NAG Ltd. */
648 /* > \date November 2013 */
650 /* > \ingroup doubleSYcomputational */
652 /* > \par Further Details: */
653 /* ===================== */
657 /* > If UPLO = 'U', then A = U*D*U**T, where */
658 /* > U = P(n)*U(n)* ... *P(k)U(k)* ..., */
659 /* > i.e., U is a product of terms P(k)*U(k), where k decreases from n to */
660 /* > 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
661 /* > and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */
662 /* > defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */
663 /* > that if the diagonal block D(k) is of order s (s = 1 or 2), then */
665 /* > ( I v 0 ) k-s */
666 /* > U(k) = ( 0 I 0 ) s */
667 /* > ( 0 0 I ) n-k */
670 /* > If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */
671 /* > If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */
672 /* > and A(k,k), and v overwrites A(1:k-2,k-1:k). */
674 /* > If UPLO = 'L', then A = L*D*L**T, where */
675 /* > L = P(1)*L(1)* ... *P(k)*L(k)* ..., */
676 /* > i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */
677 /* > n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
678 /* > and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */
679 /* > defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */
680 /* > that if the diagonal block D(k) is of order s (s = 1 or 2), then */
682 /* > ( I 0 0 ) k-1 */
683 /* > L(k) = ( 0 I 0 ) s */
684 /* > ( 0 v I ) n-k-s+1 */
685 /* > k-1 s n-k-s+1 */
687 /* > If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */
688 /* > If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */
689 /* > and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */
692 /* > \par Contributors: */
693 /* ================== */
697 /* > November 2013, Igor Kozachenko, */
698 /* > Computer Science Division, */
699 /* > University of California, Berkeley */
701 /* > September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, */
702 /* > School of Mathematics, */
703 /* > University of Manchester */
705 /* > 01-01-96 - Based on modifications by */
706 /* > J. Lewis, Boeing Computer Services Company */
707 /* > A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville abd , USA */
710 /* ===================================================================== */
711 /* Subroutine */ int dsytf2_rook_(char *uplo, integer *n, doublereal *a,
712 integer *lda, integer *ipiv, integer *info)
714 /* System generated locals */
715 integer a_dim1, a_offset, i__1, i__2;
718 /* Local variables */
721 extern /* Subroutine */ int dsyr_(char *, integer *, doublereal *,
722 doublereal *, integer *, doublereal *, integer *);
723 integer i__, j, k, p;
725 extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
727 extern logical lsame_(char *, char *);
728 doublereal dtemp, sfmin;
730 extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
731 doublereal *, integer *);
734 doublereal d11, d12, d21, d22;
736 extern doublereal dlamch_(char *);
738 doublereal absakk, wk;
739 extern integer idamax_(integer *, doublereal *, integer *);
740 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
741 doublereal colmax, rowmax, wkm1, wkp1;
744 /* -- LAPACK computational routine (version 3.5.0) -- */
745 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
746 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
750 /* ===================================================================== */
753 /* Test the input parameters. */
755 /* Parameter adjustments */
757 a_offset = 1 + a_dim1 * 1;
763 upper = lsame_(uplo, "U");
764 if (! upper && ! lsame_(uplo, "L")) {
768 } else if (*lda < f2cmax(1,*n)) {
773 xerbla_("DSYTF2_ROOK", &i__1, (ftnlen)11);
777 /* Initialize ALPHA for use in choosing pivot block size. */
779 alpha = (sqrt(17.) + 1.) / 8.;
781 /* Compute machine safe minimum */
783 sfmin = dlamch_("S");
787 /* Factorize A as U*D*U**T using the upper triangle of A */
789 /* K is the main loop index, decreasing from N to 1 in steps of */
795 /* If K < 1, exit from loop */
803 /* Determine rows and columns to be interchanged and whether */
804 /* a 1-by-1 or 2-by-2 pivot block will be used */
806 absakk = (d__1 = a[k + k * a_dim1], abs(d__1));
808 /* IMAX is the row-index of the largest off-diagonal element in */
809 /* column K, and COLMAX is its absolute value. */
810 /* Determine both COLMAX and IMAX. */
814 imax = idamax_(&i__1, &a[k * a_dim1 + 1], &c__1);
815 colmax = (d__1 = a[imax + k * a_dim1], abs(d__1));
820 if (f2cmax(absakk,colmax) == 0.) {
822 /* Column K is zero or underflow: set INFO and continue */
830 /* Test for interchange */
832 /* Equivalent to testing for (used to handle NaN and Inf) */
833 /* ABSAKK.GE.ALPHA*COLMAX */
835 if (! (absakk < alpha * colmax)) {
837 /* no interchange, */
838 /* use 1-by-1 pivot block */
845 /* Loop until pivot found */
849 /* Begin pivot search loop body */
851 /* JMAX is the column-index of the largest off-diagonal */
852 /* element in row IMAX, and ROWMAX is its absolute value. */
853 /* Determine both ROWMAX and JMAX. */
857 jmax = imax + idamax_(&i__1, &a[imax + (imax + 1) *
859 rowmax = (d__1 = a[imax + jmax * a_dim1], abs(d__1));
866 itemp = idamax_(&i__1, &a[imax * a_dim1 + 1], &c__1);
867 dtemp = (d__1 = a[itemp + imax * a_dim1], abs(d__1));
868 if (dtemp > rowmax) {
874 /* Equivalent to testing for (used to handle NaN and Inf) */
875 /* ABS( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX */
877 if (! ((d__1 = a[imax + imax * a_dim1], abs(d__1)) < alpha *
880 /* interchange rows and columns K and IMAX, */
881 /* use 1-by-1 pivot block */
886 /* Equivalent to testing for ROWMAX .EQ. COLMAX, */
887 /* used to handle NaN and Inf */
889 } else if (p == jmax || rowmax <= colmax) {
891 /* interchange rows and columns K+1 and IMAX, */
892 /* use 2-by-2 pivot block */
899 /* Pivot NOT found, set variables and repeat */
906 /* End pivot search loop body */
914 /* Swap TWO rows and TWO columns */
918 if (kstep == 2 && p != k) {
920 /* Interchange rows and column K and P in the leading */
921 /* submatrix A(1:k,1:k) if we have a 2-by-2 pivot */
925 dswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 +
930 dswap_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p +
933 t = a[k + k * a_dim1];
934 a[k + k * a_dim1] = a[p + p * a_dim1];
935 a[p + p * a_dim1] = t;
943 /* Interchange rows and columns KK and KP in the leading */
944 /* submatrix A(1:k,1:k) */
948 dswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
951 if (kk > 1 && kp < kk - 1) {
953 dswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (
954 kp + 1) * a_dim1], lda);
956 t = a[kk + kk * a_dim1];
957 a[kk + kk * a_dim1] = a[kp + kp * a_dim1];
958 a[kp + kp * a_dim1] = t;
960 t = a[k - 1 + k * a_dim1];
961 a[k - 1 + k * a_dim1] = a[kp + k * a_dim1];
962 a[kp + k * a_dim1] = t;
966 /* Update the leading submatrix */
970 /* 1-by-1 pivot block D(k): column k now holds */
972 /* W(k) = U(k)*D(k) */
974 /* where U(k) is the k-th column of U */
978 /* Perform a rank-1 update of A(1:k-1,1:k-1) and */
979 /* store U(k) in column k */
981 if ((d__1 = a[k + k * a_dim1], abs(d__1)) >= sfmin) {
983 /* Perform a rank-1 update of A(1:k-1,1:k-1) as */
984 /* A := A - U(k)*D(k)*U(k)**T */
985 /* = A - W(k)*1/D(k)*W(k)**T */
987 d11 = 1. / a[k + k * a_dim1];
990 dsyr_(uplo, &i__1, &d__1, &a[k * a_dim1 + 1], &c__1, &
993 /* Store U(k) in column k */
996 dscal_(&i__1, &d11, &a[k * a_dim1 + 1], &c__1);
999 /* Store L(k) in column K */
1001 d11 = a[k + k * a_dim1];
1003 for (ii = 1; ii <= i__1; ++ii) {
1004 a[ii + k * a_dim1] /= d11;
1008 /* Perform a rank-1 update of A(k+1:n,k+1:n) as */
1009 /* A := A - U(k)*D(k)*U(k)**T */
1010 /* = A - W(k)*(1/D(k))*W(k)**T */
1011 /* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T */
1015 dsyr_(uplo, &i__1, &d__1, &a[k * a_dim1 + 1], &c__1, &
1022 /* 2-by-2 pivot block D(k): columns k and k-1 now hold */
1024 /* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) */
1026 /* where U(k) and U(k-1) are the k-th and (k-1)-th columns */
1029 /* Perform a rank-2 update of A(1:k-2,1:k-2) as */
1031 /* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T */
1032 /* = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T */
1034 /* and store L(k) and L(k+1) in columns k and k+1 */
1038 d12 = a[k - 1 + k * a_dim1];
1039 d22 = a[k - 1 + (k - 1) * a_dim1] / d12;
1040 d11 = a[k + k * a_dim1] / d12;
1041 t = 1. / (d11 * d22 - 1.);
1043 for (j = k - 2; j >= 1; --j) {
1045 wkm1 = t * (d11 * a[j + (k - 1) * a_dim1] - a[j + k *
1047 wk = t * (d22 * a[j + k * a_dim1] - a[j + (k - 1) *
1050 for (i__ = j; i__ >= 1; --i__) {
1051 a[i__ + j * a_dim1] = a[i__ + j * a_dim1] - a[i__
1052 + k * a_dim1] / d12 * wk - a[i__ + (k - 1)
1053 * a_dim1] / d12 * wkm1;
1057 /* Store U(k) and U(k-1) in cols k and k-1 for row J */
1059 a[j + k * a_dim1] = wk / d12;
1060 a[j + (k - 1) * a_dim1] = wkm1 / d12;
1070 /* Store details of the interchanges in IPIV */
1079 /* Decrease K and return to the start of the main loop */
1086 /* Factorize A as L*D*L**T using the lower triangle of A */
1088 /* K is the main loop index, increasing from 1 to N in steps of */
1094 /* If K > N, exit from loop */
1102 /* Determine rows and columns to be interchanged and whether */
1103 /* a 1-by-1 or 2-by-2 pivot block will be used */
1105 absakk = (d__1 = a[k + k * a_dim1], abs(d__1));
1107 /* IMAX is the row-index of the largest off-diagonal element in */
1108 /* column K, and COLMAX is its absolute value. */
1109 /* Determine both COLMAX and IMAX. */
1113 imax = k + idamax_(&i__1, &a[k + 1 + k * a_dim1], &c__1);
1114 colmax = (d__1 = a[imax + k * a_dim1], abs(d__1));
1119 if (f2cmax(absakk,colmax) == 0.) {
1121 /* Column K is zero or underflow: set INFO and continue */
1129 /* Test for interchange */
1131 /* Equivalent to testing for (used to handle NaN and Inf) */
1132 /* ABSAKK.GE.ALPHA*COLMAX */
1134 if (! (absakk < alpha * colmax)) {
1136 /* no interchange, use 1-by-1 pivot block */
1143 /* Loop until pivot found */
1147 /* Begin pivot search loop body */
1149 /* JMAX is the column-index of the largest off-diagonal */
1150 /* element in row IMAX, and ROWMAX is its absolute value. */
1151 /* Determine both ROWMAX and JMAX. */
1155 jmax = k - 1 + idamax_(&i__1, &a[imax + k * a_dim1], lda);
1156 rowmax = (d__1 = a[imax + jmax * a_dim1], abs(d__1));
1163 itemp = imax + idamax_(&i__1, &a[imax + 1 + imax * a_dim1]
1165 dtemp = (d__1 = a[itemp + imax * a_dim1], abs(d__1));
1166 if (dtemp > rowmax) {
1172 /* Equivalent to testing for (used to handle NaN and Inf) */
1173 /* ABS( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX */
1175 if (! ((d__1 = a[imax + imax * a_dim1], abs(d__1)) < alpha *
1178 /* interchange rows and columns K and IMAX, */
1179 /* use 1-by-1 pivot block */
1184 /* Equivalent to testing for ROWMAX .EQ. COLMAX, */
1185 /* used to handle NaN and Inf */
1187 } else if (p == jmax || rowmax <= colmax) {
1189 /* interchange rows and columns K+1 and IMAX, */
1190 /* use 2-by-2 pivot block */
1197 /* Pivot NOT found, set variables and repeat */
1204 /* End pivot search loop body */
1212 /* Swap TWO rows and TWO columns */
1216 if (kstep == 2 && p != k) {
1218 /* Interchange rows and column K and P in the trailing */
1219 /* submatrix A(k:n,k:n) if we have a 2-by-2 pivot */
1223 dswap_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + 1 + p
1228 dswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[p + (k +
1231 t = a[k + k * a_dim1];
1232 a[k + k * a_dim1] = a[p + p * a_dim1];
1233 a[p + p * a_dim1] = t;
1241 /* Interchange rows and columns KK and KP in the trailing */
1242 /* submatrix A(k:n,k:n) */
1246 dswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
1247 + kp * a_dim1], &c__1);
1249 if (kk < *n && kp > kk + 1) {
1251 dswap_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (
1252 kk + 1) * a_dim1], lda);
1254 t = a[kk + kk * a_dim1];
1255 a[kk + kk * a_dim1] = a[kp + kp * a_dim1];
1256 a[kp + kp * a_dim1] = t;
1258 t = a[k + 1 + k * a_dim1];
1259 a[k + 1 + k * a_dim1] = a[kp + k * a_dim1];
1260 a[kp + k * a_dim1] = t;
1264 /* Update the trailing submatrix */
1268 /* 1-by-1 pivot block D(k): column k now holds */
1270 /* W(k) = L(k)*D(k) */
1272 /* where L(k) is the k-th column of L */
1276 /* Perform a rank-1 update of A(k+1:n,k+1:n) and */
1277 /* store L(k) in column k */
1279 if ((d__1 = a[k + k * a_dim1], abs(d__1)) >= sfmin) {
1281 /* Perform a rank-1 update of A(k+1:n,k+1:n) as */
1282 /* A := A - L(k)*D(k)*L(k)**T */
1283 /* = A - W(k)*(1/D(k))*W(k)**T */
1285 d11 = 1. / a[k + k * a_dim1];
1288 dsyr_(uplo, &i__1, &d__1, &a[k + 1 + k * a_dim1], &
1289 c__1, &a[k + 1 + (k + 1) * a_dim1], lda);
1291 /* Store L(k) in column k */
1294 dscal_(&i__1, &d11, &a[k + 1 + k * a_dim1], &c__1);
1297 /* Store L(k) in column k */
1299 d11 = a[k + k * a_dim1];
1301 for (ii = k + 1; ii <= i__1; ++ii) {
1302 a[ii + k * a_dim1] /= d11;
1306 /* Perform a rank-1 update of A(k+1:n,k+1:n) as */
1307 /* A := A - L(k)*D(k)*L(k)**T */
1308 /* = A - W(k)*(1/D(k))*W(k)**T */
1309 /* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T */
1313 dsyr_(uplo, &i__1, &d__1, &a[k + 1 + k * a_dim1], &
1314 c__1, &a[k + 1 + (k + 1) * a_dim1], lda);
1320 /* 2-by-2 pivot block D(k): columns k and k+1 now hold */
1322 /* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) */
1324 /* where L(k) and L(k+1) are the k-th and (k+1)-th columns */
1328 /* Perform a rank-2 update of A(k+2:n,k+2:n) as */
1330 /* A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T */
1331 /* = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T */
1333 /* and store L(k) and L(k+1) in columns k and k+1 */
1337 d21 = a[k + 1 + k * a_dim1];
1338 d11 = a[k + 1 + (k + 1) * a_dim1] / d21;
1339 d22 = a[k + k * a_dim1] / d21;
1340 t = 1. / (d11 * d22 - 1.);
1343 for (j = k + 2; j <= i__1; ++j) {
1345 /* Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J */
1347 wk = t * (d11 * a[j + k * a_dim1] - a[j + (k + 1) *
1349 wkp1 = t * (d22 * a[j + (k + 1) * a_dim1] - a[j + k *
1352 /* Perform a rank-2 update of A(k+2:n,k+2:n) */
1355 for (i__ = j; i__ <= i__2; ++i__) {
1356 a[i__ + j * a_dim1] = a[i__ + j * a_dim1] - a[i__
1357 + k * a_dim1] / d21 * wk - a[i__ + (k + 1)
1358 * a_dim1] / d21 * wkp1;
1362 /* Store L(k) and L(k+1) in cols k and k+1 for row J */
1364 a[j + k * a_dim1] = wk / d21;
1365 a[j + (k + 1) * a_dim1] = wkp1 / d21;
1375 /* Store details of the interchanges in IPIV */
1384 /* Increase K and return to the start of the main loop */
1395 /* End of DSYTF2_ROOK */
1397 } /* dsytf2_rook__ */