14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* Table of constant values */
515 static integer c__1 = 1;
516 static doublereal c_b9 = -1.;
518 /* > \brief \b ZPBSTF */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download ZPBSTF + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpbstf.
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpbstf.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpbstf.
541 /* SUBROUTINE ZPBSTF( UPLO, N, KD, AB, LDAB, INFO ) */
544 /* INTEGER INFO, KD, LDAB, N */
545 /* COMPLEX*16 AB( LDAB, * ) */
548 /* > \par Purpose: */
553 /* > ZPBSTF computes a split Cholesky factorization of a complex */
554 /* > Hermitian positive definite band matrix A. */
556 /* > This routine is designed to be used in conjunction with ZHBGST. */
558 /* > The factorization has the form A = S**H*S where S is a band matrix */
559 /* > of the same bandwidth as A and the following structure: */
564 /* > where U is upper triangular of order m = (n+kd)/2, and L is lower */
565 /* > triangular of order n-m. */
571 /* > \param[in] UPLO */
573 /* > UPLO is CHARACTER*1 */
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] KD */
586 /* > KD is INTEGER */
587 /* > The number of superdiagonals of the matrix A if UPLO = 'U', */
588 /* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
591 /* > \param[in,out] AB */
593 /* > AB is COMPLEX*16 array, dimension (LDAB,N) */
594 /* > On entry, the upper or lower triangle of the Hermitian band */
595 /* > matrix A, stored in the first kd+1 rows of the array. The */
596 /* > j-th column of A is stored in the j-th column of the array AB */
598 /* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
599 /* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
601 /* > On exit, if INFO = 0, the factor S from the split Cholesky */
602 /* > factorization A = S**H*S. See Further Details. */
605 /* > \param[in] LDAB */
607 /* > LDAB is INTEGER */
608 /* > The leading dimension of the array AB. LDAB >= KD+1. */
611 /* > \param[out] INFO */
613 /* > INFO is INTEGER */
614 /* > = 0: successful exit */
615 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
616 /* > > 0: if INFO = i, the factorization could not be completed, */
617 /* > because the updated element a(i,i) was negative; the */
618 /* > matrix A is not positive definite. */
624 /* > \author Univ. of Tennessee */
625 /* > \author Univ. of California Berkeley */
626 /* > \author Univ. of Colorado Denver */
627 /* > \author NAG Ltd. */
629 /* > \date December 2016 */
631 /* > \ingroup complex16OTHERcomputational */
633 /* > \par Further Details: */
634 /* ===================== */
638 /* > The band storage scheme is illustrated by the following example, when */
639 /* > N = 7, KD = 2: */
641 /* > S = ( s11 s12 s13 ) */
642 /* > ( s22 s23 s24 ) */
645 /* > ( s53 s54 s55 ) */
646 /* > ( s64 s65 s66 ) */
647 /* > ( s75 s76 s77 ) */
649 /* > If UPLO = 'U', the array AB holds: */
651 /* > on entry: on exit: */
653 /* > * * a13 a24 a35 a46 a57 * * s13 s24 s53**H s64**H s75**H */
654 /* > * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54**H s65**H s76**H */
655 /* > a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 */
657 /* > If UPLO = 'L', the array AB holds: */
659 /* > on entry: on exit: */
661 /* > a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 */
662 /* > a21 a32 a43 a54 a65 a76 * s12**H s23**H s34**H s54 s65 s76 * */
663 /* > a31 a42 a53 a64 a64 * * s13**H s24**H s53 s64 s75 * * */
665 /* > Array elements marked * are not used by the routine; s12**H denotes */
666 /* > conjg(s12); the diagonal elements of S are real. */
669 /* ===================================================================== */
670 /* Subroutine */ int zpbstf_(char *uplo, integer *n, integer *kd,
671 doublecomplex *ab, integer *ldab, integer *info)
673 /* System generated locals */
674 integer ab_dim1, ab_offset, i__1, i__2, i__3;
677 /* Local variables */
678 extern /* Subroutine */ int zher_(char *, integer *, doublereal *,
679 doublecomplex *, integer *, doublecomplex *, integer *);
681 extern logical lsame_(char *, char *);
684 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zdscal_(
685 integer *, doublereal *, doublecomplex *, integer *), zlacgv_(
686 integer *, doublecomplex *, integer *);
691 /* -- LAPACK computational routine (version 3.7.0) -- */
692 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
693 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
697 /* ===================================================================== */
700 /* Test the input parameters. */
702 /* Parameter adjustments */
704 ab_offset = 1 + ab_dim1 * 1;
709 upper = lsame_(uplo, "U");
710 if (! upper && ! lsame_(uplo, "L")) {
714 } else if (*kd < 0) {
716 } else if (*ldab < *kd + 1) {
721 xerbla_("ZPBSTF", &i__1, (ftnlen)6);
725 /* Quick return if possible */
732 i__1 = 1, i__2 = *ldab - 1;
733 kld = f2cmax(i__1,i__2);
735 /* Set the splitting point m. */
741 /* Factorize A(m+1:n,m+1:n) as L**H*L, and update A(1:m,1:m). */
744 for (j = *n; j >= i__1; --j) {
746 /* Compute s(j,j) and test for non-positive-definiteness. */
748 i__2 = *kd + 1 + j * ab_dim1;
751 i__2 = *kd + 1 + j * ab_dim1;
752 ab[i__2].r = ajj, ab[i__2].i = 0.;
756 i__2 = *kd + 1 + j * ab_dim1;
757 ab[i__2].r = ajj, ab[i__2].i = 0.;
760 km = f2cmin(i__2,*kd);
762 /* Compute elements j-km:j-1 of the j-th column and update the */
763 /* the leading submatrix within the band. */
766 zdscal_(&km, &d__1, &ab[*kd + 1 - km + j * ab_dim1], &c__1);
767 zher_("Upper", &km, &c_b9, &ab[*kd + 1 - km + j * ab_dim1], &c__1,
768 &ab[*kd + 1 + (j - km) * ab_dim1], &kld);
772 /* Factorize the updated submatrix A(1:m,1:m) as U**H*U. */
775 for (j = 1; j <= i__1; ++j) {
777 /* Compute s(j,j) and test for non-positive-definiteness. */
779 i__2 = *kd + 1 + j * ab_dim1;
782 i__2 = *kd + 1 + j * ab_dim1;
783 ab[i__2].r = ajj, ab[i__2].i = 0.;
787 i__2 = *kd + 1 + j * ab_dim1;
788 ab[i__2].r = ajj, ab[i__2].i = 0.;
790 i__2 = *kd, i__3 = m - j;
791 km = f2cmin(i__2,i__3);
793 /* Compute elements j+1:j+km of the j-th row and update the */
794 /* trailing submatrix within the band. */
798 zdscal_(&km, &d__1, &ab[*kd + (j + 1) * ab_dim1], &kld);
799 zlacgv_(&km, &ab[*kd + (j + 1) * ab_dim1], &kld);
800 zher_("Upper", &km, &c_b9, &ab[*kd + (j + 1) * ab_dim1], &kld,
801 &ab[*kd + 1 + (j + 1) * ab_dim1], &kld);
802 zlacgv_(&km, &ab[*kd + (j + 1) * ab_dim1], &kld);
808 /* Factorize A(m+1:n,m+1:n) as L**H*L, and update A(1:m,1:m). */
811 for (j = *n; j >= i__1; --j) {
813 /* Compute s(j,j) and test for non-positive-definiteness. */
815 i__2 = j * ab_dim1 + 1;
818 i__2 = j * ab_dim1 + 1;
819 ab[i__2].r = ajj, ab[i__2].i = 0.;
823 i__2 = j * ab_dim1 + 1;
824 ab[i__2].r = ajj, ab[i__2].i = 0.;
827 km = f2cmin(i__2,*kd);
829 /* Compute elements j-km:j-1 of the j-th row and update the */
830 /* trailing submatrix within the band. */
833 zdscal_(&km, &d__1, &ab[km + 1 + (j - km) * ab_dim1], &kld);
834 zlacgv_(&km, &ab[km + 1 + (j - km) * ab_dim1], &kld);
835 zher_("Lower", &km, &c_b9, &ab[km + 1 + (j - km) * ab_dim1], &kld,
836 &ab[(j - km) * ab_dim1 + 1], &kld);
837 zlacgv_(&km, &ab[km + 1 + (j - km) * ab_dim1], &kld);
841 /* Factorize the updated submatrix A(1:m,1:m) as U**H*U. */
844 for (j = 1; j <= i__1; ++j) {
846 /* Compute s(j,j) and test for non-positive-definiteness. */
848 i__2 = j * ab_dim1 + 1;
851 i__2 = j * ab_dim1 + 1;
852 ab[i__2].r = ajj, ab[i__2].i = 0.;
856 i__2 = j * ab_dim1 + 1;
857 ab[i__2].r = ajj, ab[i__2].i = 0.;
859 i__2 = *kd, i__3 = m - j;
860 km = f2cmin(i__2,i__3);
862 /* Compute elements j+1:j+km of the j-th column and update the */
863 /* trailing submatrix within the band. */
867 zdscal_(&km, &d__1, &ab[j * ab_dim1 + 2], &c__1);
868 zher_("Lower", &km, &c_b9, &ab[j * ab_dim1 + 2], &c__1, &ab[(
869 j + 1) * ab_dim1 + 1], &kld);