#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #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]);} #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]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #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++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #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]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle_() continue; #define myceiling_(w) {ceil(w)} #define myhuge_(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc_(w,s,e,n) dmaxloc_(w,*(s),*(e),n) /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b ZPSTRF computes the Cholesky factorization with complete pivoting of a complex Hermitian positi ve semidefinite matrix. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZPSTRF + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) */ /* DOUBLE PRECISION TOL */ /* INTEGER INFO, LDA, N, RANK */ /* CHARACTER UPLO */ /* COMPLEX*16 A( LDA, * ) */ /* DOUBLE PRECISION WORK( 2*N ) */ /* INTEGER PIV( N ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZPSTRF computes the Cholesky factorization with complete */ /* > pivoting of a complex Hermitian positive semidefinite matrix A. */ /* > */ /* > The factorization has the form */ /* > P**T * A * P = U**H * U , if UPLO = 'U', */ /* > P**T * A * P = L * L**H, if UPLO = 'L', */ /* > where U is an upper triangular matrix and L is lower triangular, and */ /* > P is stored as vector PIV. */ /* > */ /* > This algorithm does not attempt to check that A is positive */ /* > semidefinite. This version of the algorithm calls level 3 BLAS. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is CHARACTER*1 */ /* > Specifies whether the upper or lower triangular part of the */ /* > symmetric matrix A is stored. */ /* > = 'U': Upper triangular */ /* > = 'L': Lower triangular */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension (LDA,N) */ /* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ /* > n by n upper triangular part of A contains the upper */ /* > triangular part of the matrix A, and the strictly lower */ /* > triangular part of A is not referenced. If UPLO = 'L', the */ /* > leading n by n lower triangular part of A contains the lower */ /* > triangular part of the matrix A, and the strictly upper */ /* > triangular part of A is not referenced. */ /* > */ /* > On exit, if INFO = 0, the factor U or L from the Cholesky */ /* > factorization as above. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] PIV */ /* > \verbatim */ /* > PIV is INTEGER array, dimension (N) */ /* > PIV is such that the nonzero entries are P( PIV(K), K ) = 1. */ /* > \endverbatim */ /* > */ /* > \param[out] RANK */ /* > \verbatim */ /* > RANK is INTEGER */ /* > The rank of A given by the number of steps the algorithm */ /* > completed. */ /* > \endverbatim */ /* > */ /* > \param[in] TOL */ /* > \verbatim */ /* > TOL is DOUBLE PRECISION */ /* > User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) */ /* > will be used. The algorithm terminates at the (K-1)st step */ /* > if the pivot <= TOL. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (2*N) */ /* > Work space. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > < 0: If INFO = -K, the K-th argument had an illegal value, */ /* > = 0: algorithm completed successfully, and */ /* > > 0: the matrix A is either rank deficient with computed rank */ /* > as returned in RANK, or is not positive semidefinite. See */ /* > Section 7 of LAPACK Working Note #161 for further */ /* > information. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ /* Subroutine */ int zpstrf_(char *uplo, integer *n, doublecomplex *a, integer *lda, integer *piv, integer *rank, doublereal *tol, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1; doublecomplex z__1, z__2; /* Local variables */ integer i__, j, k; extern logical lsame_(char *, char *); doublereal dtemp; integer itemp; extern /* Subroutine */ int zherk_(char *, char *, integer *, integer *, doublereal *, doublecomplex *, integer *, doublereal *, doublecomplex *, integer *), zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); doublereal dstop; logical upper; doublecomplex ztemp; extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); integer jb, nb; extern doublereal dlamch_(char *); extern /* Subroutine */ int zpstf2_(char *, integer *, doublecomplex *, integer *, integer *, integer *, doublereal *, doublereal *, integer *); extern logical disnan_(doublereal *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int zdscal_(integer *, doublereal *, doublecomplex *, integer *), zlacgv_(integer *, doublecomplex *, integer *); doublereal ajj; integer pvt; /* -- LAPACK computational routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ --work; --piv; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < f2cmax(1,*n)) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPSTRF", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Get block size */ nb = ilaenv_(&c__1, "ZPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); if (nb <= 1 || nb >= *n) { /* Use unblocked code */ zpstf2_(uplo, n, &a[a_dim1 + 1], lda, &piv[1], rank, tol, &work[1], info); goto L230; } else { /* Initialize PIV */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { piv[i__] = i__; /* L100: */ } /* Compute stopping value */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + i__ * a_dim1; work[i__] = a[i__2].r; /* L110: */ } pvt = mymaxloc_(&work[1], &c__1, n, &c__1); i__1 = pvt + pvt * a_dim1; ajj = a[i__1].r; if (ajj <= 0. || disnan_(&ajj)) { *rank = 0; *info = 1; goto L230; } /* Compute stopping value if not supplied */ if (*tol < 0.) { dstop = *n * dlamch_("Epsilon") * ajj; } else { dstop = *tol; } if (upper) { /* Compute the Cholesky factorization P**T * A * P = U**H * U */ i__1 = *n; i__2 = nb; for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { /* Account for last block not being NB wide */ /* Computing MIN */ i__3 = nb, i__4 = *n - k + 1; jb = f2cmin(i__3,i__4); /* Set relevant part of first half of WORK to zero, */ /* holds dot products */ i__3 = *n; for (i__ = k; i__ <= i__3; ++i__) { work[i__] = 0.; /* L120: */ } i__3 = k + jb - 1; for (j = k; j <= i__3; ++j) { /* Find pivot, test for exit, else swap rows and columns */ /* Update dot products, compute possible pivots which are */ /* stored in the second half of WORK */ i__4 = *n; for (i__ = j; i__ <= i__4; ++i__) { if (j > k) { d_cnjg(&z__2, &a[j - 1 + i__ * a_dim1]); i__5 = j - 1 + i__ * a_dim1; z__1.r = z__2.r * a[i__5].r - z__2.i * a[i__5].i, z__1.i = z__2.r * a[i__5].i + z__2.i * a[ i__5].r; work[i__] += z__1.r; } i__5 = i__ + i__ * a_dim1; work[*n + i__] = a[i__5].r - work[i__]; /* L130: */ } if (j > 1) { i__4 = *n + j; i__5 = *n << 1; itemp = mymaxloc_(&work[1], &i__4, &i__5, &c__1); pvt = itemp + j - 1; ajj = work[*n + pvt]; if (ajj <= dstop || disnan_(&ajj)) { i__4 = j + j * a_dim1; a[i__4].r = ajj, a[i__4].i = 0.; goto L220; } } if (j != pvt) { /* Pivot OK, so can now swap pivot rows and columns */ i__4 = pvt + pvt * a_dim1; i__5 = j + j * a_dim1; a[i__4].r = a[i__5].r, a[i__4].i = a[i__5].i; i__4 = j - 1; zswap_(&i__4, &a[j * a_dim1 + 1], &c__1, &a[pvt * a_dim1 + 1], &c__1); if (pvt < *n) { i__4 = *n - pvt; zswap_(&i__4, &a[j + (pvt + 1) * a_dim1], lda, &a[ pvt + (pvt + 1) * a_dim1], lda); } i__4 = pvt - 1; for (i__ = j + 1; i__ <= i__4; ++i__) { d_cnjg(&z__1, &a[j + i__ * a_dim1]); ztemp.r = z__1.r, ztemp.i = z__1.i; i__5 = j + i__ * a_dim1; d_cnjg(&z__1, &a[i__ + pvt * a_dim1]); a[i__5].r = z__1.r, a[i__5].i = z__1.i; i__5 = i__ + pvt * a_dim1; a[i__5].r = ztemp.r, a[i__5].i = ztemp.i; /* L140: */ } i__4 = j + pvt * a_dim1; d_cnjg(&z__1, &a[j + pvt * a_dim1]); a[i__4].r = z__1.r, a[i__4].i = z__1.i; /* Swap dot products and PIV */ dtemp = work[j]; work[j] = work[pvt]; work[pvt] = dtemp; itemp = piv[pvt]; piv[pvt] = piv[j]; piv[j] = itemp; } ajj = sqrt(ajj); i__4 = j + j * a_dim1; a[i__4].r = ajj, a[i__4].i = 0.; /* Compute elements J+1:N of row J. */ if (j < *n) { i__4 = j - 1; zlacgv_(&i__4, &a[j * a_dim1 + 1], &c__1); i__4 = j - k; i__5 = *n - j; z__1.r = -1., z__1.i = 0.; zgemv_("Trans", &i__4, &i__5, &z__1, &a[k + (j + 1) * a_dim1], lda, &a[k + j * a_dim1], &c__1, & c_b1, &a[j + (j + 1) * a_dim1], lda); i__4 = j - 1; zlacgv_(&i__4, &a[j * a_dim1 + 1], &c__1); i__4 = *n - j; d__1 = 1. / ajj; zdscal_(&i__4, &d__1, &a[j + (j + 1) * a_dim1], lda); } /* L150: */ } /* Update trailing matrix, J already incremented */ if (k + jb <= *n) { i__3 = *n - j + 1; zherk_("Upper", "Conj Trans", &i__3, &jb, &c_b32, &a[k + j * a_dim1], lda, &c_b33, &a[j + j * a_dim1], lda); } /* L160: */ } } else { /* Compute the Cholesky factorization P**T * A * P = L * L**H */ i__2 = *n; i__1 = nb; for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { /* Account for last block not being NB wide */ /* Computing MIN */ i__3 = nb, i__4 = *n - k + 1; jb = f2cmin(i__3,i__4); /* Set relevant part of first half of WORK to zero, */ /* holds dot products */ i__3 = *n; for (i__ = k; i__ <= i__3; ++i__) { work[i__] = 0.; /* L170: */ } i__3 = k + jb - 1; for (j = k; j <= i__3; ++j) { /* Find pivot, test for exit, else swap rows and columns */ /* Update dot products, compute possible pivots which are */ /* stored in the second half of WORK */ i__4 = *n; for (i__ = j; i__ <= i__4; ++i__) { if (j > k) { d_cnjg(&z__2, &a[i__ + (j - 1) * a_dim1]); i__5 = i__ + (j - 1) * a_dim1; z__1.r = z__2.r * a[i__5].r - z__2.i * a[i__5].i, z__1.i = z__2.r * a[i__5].i + z__2.i * a[ i__5].r; work[i__] += z__1.r; } i__5 = i__ + i__ * a_dim1; work[*n + i__] = a[i__5].r - work[i__]; /* L180: */ } if (j > 1) { i__4 = *n + j; i__5 = *n << 1; itemp = mymaxloc_(&work[1], &i__4, &i__5, &c__1); pvt = itemp + j - 1; ajj = work[*n + pvt]; if (ajj <= dstop || disnan_(&ajj)) { i__4 = j + j * a_dim1; a[i__4].r = ajj, a[i__4].i = 0.; goto L220; } } if (j != pvt) { /* Pivot OK, so can now swap pivot rows and columns */ i__4 = pvt + pvt * a_dim1; i__5 = j + j * a_dim1; a[i__4].r = a[i__5].r, a[i__4].i = a[i__5].i; i__4 = j - 1; zswap_(&i__4, &a[j + a_dim1], lda, &a[pvt + a_dim1], lda); if (pvt < *n) { i__4 = *n - pvt; zswap_(&i__4, &a[pvt + 1 + j * a_dim1], &c__1, &a[ pvt + 1 + pvt * a_dim1], &c__1); } i__4 = pvt - 1; for (i__ = j + 1; i__ <= i__4; ++i__) { d_cnjg(&z__1, &a[i__ + j * a_dim1]); ztemp.r = z__1.r, ztemp.i = z__1.i; i__5 = i__ + j * a_dim1; d_cnjg(&z__1, &a[pvt + i__ * a_dim1]); a[i__5].r = z__1.r, a[i__5].i = z__1.i; i__5 = pvt + i__ * a_dim1; a[i__5].r = ztemp.r, a[i__5].i = ztemp.i; /* L190: */ } i__4 = pvt + j * a_dim1; d_cnjg(&z__1, &a[pvt + j * a_dim1]); a[i__4].r = z__1.r, a[i__4].i = z__1.i; /* Swap dot products and PIV */ dtemp = work[j]; work[j] = work[pvt]; work[pvt] = dtemp; itemp = piv[pvt]; piv[pvt] = piv[j]; piv[j] = itemp; } ajj = sqrt(ajj); i__4 = j + j * a_dim1; a[i__4].r = ajj, a[i__4].i = 0.; /* Compute elements J+1:N of column J. */ if (j < *n) { i__4 = j - 1; zlacgv_(&i__4, &a[j + a_dim1], lda); i__4 = *n - j; i__5 = j - k; z__1.r = -1., z__1.i = 0.; zgemv_("No Trans", &i__4, &i__5, &z__1, &a[j + 1 + k * a_dim1], lda, &a[j + k * a_dim1], lda, &c_b1, &a[j + 1 + j * a_dim1], &c__1); i__4 = j - 1; zlacgv_(&i__4, &a[j + a_dim1], lda); i__4 = *n - j; d__1 = 1. / ajj; zdscal_(&i__4, &d__1, &a[j + 1 + j * a_dim1], &c__1); } /* L200: */ } /* Update trailing matrix, J already incremented */ if (k + jb <= *n) { i__3 = *n - j + 1; zherk_("Lower", "No Trans", &i__3, &jb, &c_b32, &a[j + k * a_dim1], lda, &c_b33, &a[j + j * a_dim1], lda); } /* L210: */ } } } /* Ran to completion, A has full rank */ *rank = *n; goto L230; L220: /* Rank is the number of steps completed. Set INFO = 1 to signal */ /* that the factorization cannot be used to solve a system. */ *rank = j - 1; *info = 1; L230: return 0; /* End of ZPSTRF */ } /* zpstrf_ */