1090 lines
29 KiB
C
1090 lines
29 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#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]);}
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#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]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#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++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#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]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle_() continue;
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#define myceiling_(w) {ceil(w)}
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#define myhuge_(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc_(w,s,e,n) dmaxloc_(w,*(s),*(e),n)
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static doublereal c_b32 = -1.;
|
|
static doublereal c_b33 = 1.;
|
|
|
|
/* > \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 */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpstrf.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpstrf.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpstrf.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \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 */ void 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 */ void 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 */ void zswap_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *);
|
|
integer jb, nb;
|
|
extern doublereal dlamch_(char *);
|
|
extern /* Subroutine */ void 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 */ void 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;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* 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;
|
|
|
|
/* End of ZPSTRF */
|
|
|
|
} /* zpstrf_ */
|
|
|