1543 lines
42 KiB
C
1543 lines
42 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 blasint logical;
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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]/df(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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#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 {
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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 integer c__1 = 1;
|
|
|
|
/* > \brief \b DSYTF2_RK computes the factorization of a real symmetric indefinite matrix using the bounded Bu
|
|
nch-Kaufman (rook) diagonal pivoting method (BLAS2 unblocked algorithm). */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DSYTF2_RK + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytf2_
|
|
rk.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytf2_
|
|
rk.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytf2_
|
|
rk.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DSYTF2_RK( UPLO, N, A, LDA, E, IPIV, INFO ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER INFO, LDA, N */
|
|
/* INTEGER IPIV( * ) */
|
|
/* DOUBLE PRECISION A( LDA, * ), E ( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > DSYTF2_RK computes the factorization of a real symmetric matrix A */
|
|
/* > using the bounded Bunch-Kaufman (rook) diagonal pivoting method: */
|
|
/* > */
|
|
/* > A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), */
|
|
/* > */
|
|
/* > where U (or L) is unit upper (or lower) triangular matrix, */
|
|
/* > U**T (or L**T) is the transpose of U (or L), P is a permutation */
|
|
/* > matrix, P**T is the transpose of P, and D is symmetric and block */
|
|
/* > diagonal with 1-by-1 and 2-by-2 diagonal blocks. */
|
|
/* > */
|
|
/* > This is the unblocked version of the algorithm, calling Level 2 BLAS. */
|
|
/* > For more information see Further Details section. */
|
|
/* > \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 DOUBLE PRECISION 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, contains: */
|
|
/* > a) ONLY diagonal elements of the symmetric block diagonal */
|
|
/* > matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); */
|
|
/* > (superdiagonal (or subdiagonal) elements of D */
|
|
/* > are stored on exit in array E), and */
|
|
/* > b) If UPLO = 'U': factor U in the superdiagonal part of A. */
|
|
/* > If UPLO = 'L': factor L in the subdiagonal part of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On exit, contains the superdiagonal (or subdiagonal) */
|
|
/* > elements of the symmetric block diagonal matrix D */
|
|
/* > with 1-by-1 or 2-by-2 diagonal blocks, where */
|
|
/* > If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0; */
|
|
/* > If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0. */
|
|
/* > */
|
|
/* > NOTE: For 1-by-1 diagonal block D(k), where */
|
|
/* > 1 <= k <= N, the element E(k) is set to 0 in both */
|
|
/* > UPLO = 'U' or UPLO = 'L' cases. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (N) */
|
|
/* > IPIV describes the permutation matrix P in the factorization */
|
|
/* > of matrix A as follows. The absolute value of IPIV(k) */
|
|
/* > represents the index of row and column that were */
|
|
/* > interchanged with the k-th row and column. The value of UPLO */
|
|
/* > describes the order in which the interchanges were applied. */
|
|
/* > Also, the sign of IPIV represents the block structure of */
|
|
/* > the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 */
|
|
/* > diagonal blocks which correspond to 1 or 2 interchanges */
|
|
/* > at each factorization step. For more info see Further */
|
|
/* > Details section. */
|
|
/* > */
|
|
/* > If UPLO = 'U', */
|
|
/* > ( in factorization order, k decreases from N to 1 ): */
|
|
/* > a) A single positive entry IPIV(k) > 0 means: */
|
|
/* > D(k,k) is a 1-by-1 diagonal block. */
|
|
/* > If IPIV(k) != k, rows and columns k and IPIV(k) were */
|
|
/* > interchanged in the matrix A(1:N,1:N); */
|
|
/* > If IPIV(k) = k, no interchange occurred. */
|
|
/* > */
|
|
/* > b) A pair of consecutive negative entries */
|
|
/* > IPIV(k) < 0 and IPIV(k-1) < 0 means: */
|
|
/* > D(k-1:k,k-1:k) is a 2-by-2 diagonal block. */
|
|
/* > (NOTE: negative entries in IPIV appear ONLY in pairs). */
|
|
/* > 1) If -IPIV(k) != k, rows and columns */
|
|
/* > k and -IPIV(k) were interchanged */
|
|
/* > in the matrix A(1:N,1:N). */
|
|
/* > If -IPIV(k) = k, no interchange occurred. */
|
|
/* > 2) If -IPIV(k-1) != k-1, rows and columns */
|
|
/* > k-1 and -IPIV(k-1) were interchanged */
|
|
/* > in the matrix A(1:N,1:N). */
|
|
/* > If -IPIV(k-1) = k-1, no interchange occurred. */
|
|
/* > */
|
|
/* > c) In both cases a) and b), always ABS( IPIV(k) ) <= k. */
|
|
/* > */
|
|
/* > d) NOTE: Any entry IPIV(k) is always NONZERO on output. */
|
|
/* > */
|
|
/* > If UPLO = 'L', */
|
|
/* > ( in factorization order, k increases from 1 to N ): */
|
|
/* > a) A single positive entry IPIV(k) > 0 means: */
|
|
/* > D(k,k) is a 1-by-1 diagonal block. */
|
|
/* > If IPIV(k) != k, rows and columns k and IPIV(k) were */
|
|
/* > interchanged in the matrix A(1:N,1:N). */
|
|
/* > If IPIV(k) = k, no interchange occurred. */
|
|
/* > */
|
|
/* > b) A pair of consecutive negative entries */
|
|
/* > IPIV(k) < 0 and IPIV(k+1) < 0 means: */
|
|
/* > D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
|
|
/* > (NOTE: negative entries in IPIV appear ONLY in pairs). */
|
|
/* > 1) If -IPIV(k) != k, rows and columns */
|
|
/* > k and -IPIV(k) were interchanged */
|
|
/* > in the matrix A(1:N,1:N). */
|
|
/* > If -IPIV(k) = k, no interchange occurred. */
|
|
/* > 2) If -IPIV(k+1) != k+1, rows and columns */
|
|
/* > k-1 and -IPIV(k-1) were interchanged */
|
|
/* > in the matrix A(1:N,1:N). */
|
|
/* > If -IPIV(k+1) = k+1, no interchange occurred. */
|
|
/* > */
|
|
/* > c) In both cases a) and b), always ABS( IPIV(k) ) >= k. */
|
|
/* > */
|
|
/* > d) NOTE: Any entry IPIV(k) is always NONZERO on output. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > */
|
|
/* > < 0: If INFO = -k, the k-th argument had an illegal value */
|
|
/* > */
|
|
/* > > 0: If INFO = k, the matrix A is singular, because: */
|
|
/* > If UPLO = 'U': column k in the upper */
|
|
/* > triangular part of A contains all zeros. */
|
|
/* > If UPLO = 'L': column k in the lower */
|
|
/* > triangular part of A contains all zeros. */
|
|
/* > */
|
|
/* > Therefore D(k,k) is exactly zero, and superdiagonal */
|
|
/* > elements of column k of U (or subdiagonal elements of */
|
|
/* > column k of L ) are all zeros. The factorization has */
|
|
/* > been completed, but the block diagonal matrix D is */
|
|
/* > exactly singular, and division by zero will occur if */
|
|
/* > it is used to solve a system of equations. */
|
|
/* > */
|
|
/* > NOTE: INFO only stores the first occurrence of */
|
|
/* > a singularity, any subsequent occurrence of singularity */
|
|
/* > is not stored in INFO even though the factorization */
|
|
/* > always completes. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleSYcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > TODO: put further details */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > December 2016, Igor Kozachenko, */
|
|
/* > Computer Science Division, */
|
|
/* > University of California, Berkeley */
|
|
/* > */
|
|
/* > September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, */
|
|
/* > School of Mathematics, */
|
|
/* > University of Manchester */
|
|
/* > */
|
|
/* > 01-01-96 - Based on modifications by */
|
|
/* > J. Lewis, Boeing Computer Services Company */
|
|
/* > A. Petitet, Computer Science Dept., */
|
|
/* > Univ. of Tenn., Knoxville abd , USA */
|
|
/* > \endverbatim */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dsytf2_rk_(char *uplo, integer *n, doublereal *a,
|
|
integer *lda, doublereal *e, integer *ipiv, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2;
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
logical done;
|
|
integer imax, jmax;
|
|
extern /* Subroutine */ void dsyr_(char *, integer *, doublereal *,
|
|
doublereal *, integer *, doublereal *, integer *);
|
|
integer i__, j, k, p;
|
|
doublereal t, alpha;
|
|
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
|
|
integer *);
|
|
extern logical lsame_(char *, char *);
|
|
doublereal dtemp, sfmin;
|
|
integer itemp;
|
|
extern /* Subroutine */ void dswap_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *);
|
|
integer kstep;
|
|
logical upper;
|
|
doublereal d11, d12, d21, d22;
|
|
integer ii, kk;
|
|
extern doublereal dlamch_(char *);
|
|
integer kp;
|
|
doublereal absakk, wk;
|
|
extern integer idamax_(integer *, doublereal *, integer *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
doublereal colmax, rowmax, wkm1, wkp1;
|
|
|
|
|
|
/* -- 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 */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--e;
|
|
--ipiv;
|
|
|
|
/* 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_("DSYTF2_RK", &i__1, (ftnlen)9);
|
|
return;
|
|
}
|
|
|
|
/* Initialize ALPHA for use in choosing pivot block size. */
|
|
|
|
alpha = (sqrt(17.) + 1.) / 8.;
|
|
|
|
/* Compute machine safe minimum */
|
|
|
|
sfmin = dlamch_("S");
|
|
|
|
if (upper) {
|
|
|
|
/* Factorize A as U*D*U**T using the upper triangle of A */
|
|
|
|
/* Initialize the first entry of array E, where superdiagonal */
|
|
/* elements of D are stored */
|
|
|
|
e[1] = 0.;
|
|
|
|
/* K is the main loop index, decreasing from N to 1 in steps of */
|
|
/* 1 or 2 */
|
|
|
|
k = *n;
|
|
L10:
|
|
|
|
/* If K < 1, exit from loop */
|
|
|
|
if (k < 1) {
|
|
goto L34;
|
|
}
|
|
kstep = 1;
|
|
p = k;
|
|
|
|
/* Determine rows and columns to be interchanged and whether */
|
|
/* a 1-by-1 or 2-by-2 pivot block will be used */
|
|
|
|
absakk = (d__1 = a[k + k * a_dim1], abs(d__1));
|
|
|
|
/* IMAX is the row-index of the largest off-diagonal element in */
|
|
/* column K, and COLMAX is its absolute value. */
|
|
/* Determine both COLMAX and IMAX. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
imax = idamax_(&i__1, &a[k * a_dim1 + 1], &c__1);
|
|
colmax = (d__1 = a[imax + k * a_dim1], abs(d__1));
|
|
} else {
|
|
colmax = 0.;
|
|
}
|
|
|
|
if (f2cmax(absakk,colmax) == 0.) {
|
|
|
|
/* Column K is zero or underflow: set INFO and continue */
|
|
|
|
if (*info == 0) {
|
|
*info = k;
|
|
}
|
|
kp = k;
|
|
|
|
/* Set E( K ) to zero */
|
|
|
|
if (k > 1) {
|
|
e[k] = 0.;
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Test for interchange */
|
|
|
|
/* Equivalent to testing for (used to handle NaN and Inf) */
|
|
/* ABSAKK.GE.ALPHA*COLMAX */
|
|
|
|
if (! (absakk < alpha * colmax)) {
|
|
|
|
/* no interchange, */
|
|
/* use 1-by-1 pivot block */
|
|
|
|
kp = k;
|
|
} else {
|
|
|
|
done = FALSE_;
|
|
|
|
/* Loop until pivot found */
|
|
|
|
L12:
|
|
|
|
/* Begin pivot search loop body */
|
|
|
|
/* JMAX is the column-index of the largest off-diagonal */
|
|
/* element in row IMAX, and ROWMAX is its absolute value. */
|
|
/* Determine both ROWMAX and JMAX. */
|
|
|
|
if (imax != k) {
|
|
i__1 = k - imax;
|
|
jmax = imax + idamax_(&i__1, &a[imax + (imax + 1) *
|
|
a_dim1], lda);
|
|
rowmax = (d__1 = a[imax + jmax * a_dim1], abs(d__1));
|
|
} else {
|
|
rowmax = 0.;
|
|
}
|
|
|
|
if (imax > 1) {
|
|
i__1 = imax - 1;
|
|
itemp = idamax_(&i__1, &a[imax * a_dim1 + 1], &c__1);
|
|
dtemp = (d__1 = a[itemp + imax * a_dim1], abs(d__1));
|
|
if (dtemp > rowmax) {
|
|
rowmax = dtemp;
|
|
jmax = itemp;
|
|
}
|
|
}
|
|
|
|
/* Equivalent to testing for (used to handle NaN and Inf) */
|
|
/* ABS( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX */
|
|
|
|
if (! ((d__1 = a[imax + imax * a_dim1], abs(d__1)) < alpha *
|
|
rowmax)) {
|
|
|
|
/* interchange rows and columns K and IMAX, */
|
|
/* use 1-by-1 pivot block */
|
|
|
|
kp = imax;
|
|
done = TRUE_;
|
|
|
|
/* Equivalent to testing for ROWMAX .EQ. COLMAX, */
|
|
/* used to handle NaN and Inf */
|
|
|
|
} else if (p == jmax || rowmax <= colmax) {
|
|
|
|
/* interchange rows and columns K+1 and IMAX, */
|
|
/* use 2-by-2 pivot block */
|
|
|
|
kp = imax;
|
|
kstep = 2;
|
|
done = TRUE_;
|
|
} else {
|
|
|
|
/* Pivot NOT found, set variables and repeat */
|
|
|
|
p = imax;
|
|
colmax = rowmax;
|
|
imax = jmax;
|
|
}
|
|
|
|
/* End pivot search loop body */
|
|
|
|
if (! done) {
|
|
goto L12;
|
|
}
|
|
|
|
}
|
|
|
|
/* Swap TWO rows and TWO columns */
|
|
|
|
/* First swap */
|
|
|
|
if (kstep == 2 && p != k) {
|
|
|
|
/* Interchange rows and column K and P in the leading */
|
|
/* submatrix A(1:k,1:k) if we have a 2-by-2 pivot */
|
|
|
|
if (p > 1) {
|
|
i__1 = p - 1;
|
|
dswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 +
|
|
1], &c__1);
|
|
}
|
|
if (p < k - 1) {
|
|
i__1 = k - p - 1;
|
|
dswap_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p +
|
|
1) * a_dim1], lda);
|
|
}
|
|
t = a[k + k * a_dim1];
|
|
a[k + k * a_dim1] = a[p + p * a_dim1];
|
|
a[p + p * a_dim1] = t;
|
|
|
|
/* Convert upper triangle of A into U form by applying */
|
|
/* the interchanges in columns k+1:N. */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
dswap_(&i__1, &a[k + (k + 1) * a_dim1], lda, &a[p + (k +
|
|
1) * a_dim1], lda);
|
|
}
|
|
|
|
}
|
|
|
|
/* Second swap */
|
|
|
|
kk = k - kstep + 1;
|
|
if (kp != kk) {
|
|
|
|
/* Interchange rows and columns KK and KP in the leading */
|
|
/* submatrix A(1:k,1:k) */
|
|
|
|
if (kp > 1) {
|
|
i__1 = kp - 1;
|
|
dswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
|
|
+ 1], &c__1);
|
|
}
|
|
if (kk > 1 && kp < kk - 1) {
|
|
i__1 = kk - kp - 1;
|
|
dswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (
|
|
kp + 1) * a_dim1], lda);
|
|
}
|
|
t = a[kk + kk * a_dim1];
|
|
a[kk + kk * a_dim1] = a[kp + kp * a_dim1];
|
|
a[kp + kp * a_dim1] = t;
|
|
if (kstep == 2) {
|
|
t = a[k - 1 + k * a_dim1];
|
|
a[k - 1 + k * a_dim1] = a[kp + k * a_dim1];
|
|
a[kp + k * a_dim1] = t;
|
|
}
|
|
|
|
/* Convert upper triangle of A into U form by applying */
|
|
/* the interchanges in columns k+1:N. */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
dswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
|
|
+ 1) * a_dim1], lda);
|
|
}
|
|
|
|
}
|
|
|
|
/* Update the leading submatrix */
|
|
|
|
if (kstep == 1) {
|
|
|
|
/* 1-by-1 pivot block D(k): column k now holds */
|
|
|
|
/* W(k) = U(k)*D(k) */
|
|
|
|
/* where U(k) is the k-th column of U */
|
|
|
|
if (k > 1) {
|
|
|
|
/* Perform a rank-1 update of A(1:k-1,1:k-1) and */
|
|
/* store U(k) in column k */
|
|
|
|
if ((d__1 = a[k + k * a_dim1], abs(d__1)) >= sfmin) {
|
|
|
|
/* Perform a rank-1 update of A(1:k-1,1:k-1) as */
|
|
/* A := A - U(k)*D(k)*U(k)**T */
|
|
/* = A - W(k)*1/D(k)*W(k)**T */
|
|
|
|
d11 = 1. / a[k + k * a_dim1];
|
|
i__1 = k - 1;
|
|
d__1 = -d11;
|
|
dsyr_(uplo, &i__1, &d__1, &a[k * a_dim1 + 1], &c__1, &
|
|
a[a_offset], lda);
|
|
|
|
/* Store U(k) in column k */
|
|
|
|
i__1 = k - 1;
|
|
dscal_(&i__1, &d11, &a[k * a_dim1 + 1], &c__1);
|
|
} else {
|
|
|
|
/* Store L(k) in column K */
|
|
|
|
d11 = a[k + k * a_dim1];
|
|
i__1 = k - 1;
|
|
for (ii = 1; ii <= i__1; ++ii) {
|
|
a[ii + k * a_dim1] /= d11;
|
|
/* L16: */
|
|
}
|
|
|
|
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */
|
|
/* A := A - U(k)*D(k)*U(k)**T */
|
|
/* = A - W(k)*(1/D(k))*W(k)**T */
|
|
/* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T */
|
|
|
|
i__1 = k - 1;
|
|
d__1 = -d11;
|
|
dsyr_(uplo, &i__1, &d__1, &a[k * a_dim1 + 1], &c__1, &
|
|
a[a_offset], lda);
|
|
}
|
|
|
|
/* Store the superdiagonal element of D in array E */
|
|
|
|
e[k] = 0.;
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* 2-by-2 pivot block D(k): columns k and k-1 now hold */
|
|
|
|
/* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) */
|
|
|
|
/* where U(k) and U(k-1) are the k-th and (k-1)-th columns */
|
|
/* of U */
|
|
|
|
/* Perform a rank-2 update of A(1:k-2,1:k-2) as */
|
|
|
|
/* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T */
|
|
/* = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T */
|
|
|
|
/* and store L(k) and L(k+1) in columns k and k+1 */
|
|
|
|
if (k > 2) {
|
|
|
|
d12 = a[k - 1 + k * a_dim1];
|
|
d22 = a[k - 1 + (k - 1) * a_dim1] / d12;
|
|
d11 = a[k + k * a_dim1] / d12;
|
|
t = 1. / (d11 * d22 - 1.);
|
|
|
|
for (j = k - 2; j >= 1; --j) {
|
|
|
|
wkm1 = t * (d11 * a[j + (k - 1) * a_dim1] - a[j + k *
|
|
a_dim1]);
|
|
wk = t * (d22 * a[j + k * a_dim1] - a[j + (k - 1) *
|
|
a_dim1]);
|
|
|
|
for (i__ = j; i__ >= 1; --i__) {
|
|
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] - a[i__
|
|
+ k * a_dim1] / d12 * wk - a[i__ + (k - 1)
|
|
* a_dim1] / d12 * wkm1;
|
|
/* L20: */
|
|
}
|
|
|
|
/* Store U(k) and U(k-1) in cols k and k-1 for row J */
|
|
|
|
a[j + k * a_dim1] = wk / d12;
|
|
a[j + (k - 1) * a_dim1] = wkm1 / d12;
|
|
|
|
/* L30: */
|
|
}
|
|
|
|
}
|
|
|
|
/* Copy superdiagonal elements of D(K) to E(K) and */
|
|
/* ZERO out superdiagonal entry of A */
|
|
|
|
e[k] = a[k - 1 + k * a_dim1];
|
|
e[k - 1] = 0.;
|
|
a[k - 1 + k * a_dim1] = 0.;
|
|
|
|
}
|
|
|
|
/* End column K is nonsingular */
|
|
|
|
}
|
|
|
|
/* Store details of the interchanges in IPIV */
|
|
|
|
if (kstep == 1) {
|
|
ipiv[k] = kp;
|
|
} else {
|
|
ipiv[k] = -p;
|
|
ipiv[k - 1] = -kp;
|
|
}
|
|
|
|
/* Decrease K and return to the start of the main loop */
|
|
|
|
k -= kstep;
|
|
goto L10;
|
|
|
|
L34:
|
|
|
|
;
|
|
} else {
|
|
|
|
/* Factorize A as L*D*L**T using the lower triangle of A */
|
|
|
|
/* Initialize the unused last entry of the subdiagonal array E. */
|
|
|
|
e[*n] = 0.;
|
|
|
|
/* K is the main loop index, increasing from 1 to N in steps of */
|
|
/* 1 or 2 */
|
|
|
|
k = 1;
|
|
L40:
|
|
|
|
/* If K > N, exit from loop */
|
|
|
|
if (k > *n) {
|
|
goto L64;
|
|
}
|
|
kstep = 1;
|
|
p = k;
|
|
|
|
/* Determine rows and columns to be interchanged and whether */
|
|
/* a 1-by-1 or 2-by-2 pivot block will be used */
|
|
|
|
absakk = (d__1 = a[k + k * a_dim1], abs(d__1));
|
|
|
|
/* IMAX is the row-index of the largest off-diagonal element in */
|
|
/* column K, and COLMAX is its absolute value. */
|
|
/* Determine both COLMAX and IMAX. */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
imax = k + idamax_(&i__1, &a[k + 1 + k * a_dim1], &c__1);
|
|
colmax = (d__1 = a[imax + k * a_dim1], abs(d__1));
|
|
} else {
|
|
colmax = 0.;
|
|
}
|
|
|
|
if (f2cmax(absakk,colmax) == 0.) {
|
|
|
|
/* Column K is zero or underflow: set INFO and continue */
|
|
|
|
if (*info == 0) {
|
|
*info = k;
|
|
}
|
|
kp = k;
|
|
|
|
/* Set E( K ) to zero */
|
|
|
|
if (k < *n) {
|
|
e[k] = 0.;
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Test for interchange */
|
|
|
|
/* Equivalent to testing for (used to handle NaN and Inf) */
|
|
/* ABSAKK.GE.ALPHA*COLMAX */
|
|
|
|
if (! (absakk < alpha * colmax)) {
|
|
|
|
/* no interchange, use 1-by-1 pivot block */
|
|
|
|
kp = k;
|
|
|
|
} else {
|
|
|
|
done = FALSE_;
|
|
|
|
/* Loop until pivot found */
|
|
|
|
L42:
|
|
|
|
/* Begin pivot search loop body */
|
|
|
|
/* JMAX is the column-index of the largest off-diagonal */
|
|
/* element in row IMAX, and ROWMAX is its absolute value. */
|
|
/* Determine both ROWMAX and JMAX. */
|
|
|
|
if (imax != k) {
|
|
i__1 = imax - k;
|
|
jmax = k - 1 + idamax_(&i__1, &a[imax + k * a_dim1], lda);
|
|
rowmax = (d__1 = a[imax + jmax * a_dim1], abs(d__1));
|
|
} else {
|
|
rowmax = 0.;
|
|
}
|
|
|
|
if (imax < *n) {
|
|
i__1 = *n - imax;
|
|
itemp = imax + idamax_(&i__1, &a[imax + 1 + imax * a_dim1]
|
|
, &c__1);
|
|
dtemp = (d__1 = a[itemp + imax * a_dim1], abs(d__1));
|
|
if (dtemp > rowmax) {
|
|
rowmax = dtemp;
|
|
jmax = itemp;
|
|
}
|
|
}
|
|
|
|
/* Equivalent to testing for (used to handle NaN and Inf) */
|
|
/* ABS( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX */
|
|
|
|
if (! ((d__1 = a[imax + imax * a_dim1], abs(d__1)) < alpha *
|
|
rowmax)) {
|
|
|
|
/* interchange rows and columns K and IMAX, */
|
|
/* use 1-by-1 pivot block */
|
|
|
|
kp = imax;
|
|
done = TRUE_;
|
|
|
|
/* Equivalent to testing for ROWMAX .EQ. COLMAX, */
|
|
/* used to handle NaN and Inf */
|
|
|
|
} else if (p == jmax || rowmax <= colmax) {
|
|
|
|
/* interchange rows and columns K+1 and IMAX, */
|
|
/* use 2-by-2 pivot block */
|
|
|
|
kp = imax;
|
|
kstep = 2;
|
|
done = TRUE_;
|
|
} else {
|
|
|
|
/* Pivot NOT found, set variables and repeat */
|
|
|
|
p = imax;
|
|
colmax = rowmax;
|
|
imax = jmax;
|
|
}
|
|
|
|
/* End pivot search loop body */
|
|
|
|
if (! done) {
|
|
goto L42;
|
|
}
|
|
|
|
}
|
|
|
|
/* Swap TWO rows and TWO columns */
|
|
|
|
/* First swap */
|
|
|
|
if (kstep == 2 && p != k) {
|
|
|
|
/* Interchange rows and column K and P in the trailing */
|
|
/* submatrix A(k:n,k:n) if we have a 2-by-2 pivot */
|
|
|
|
if (p < *n) {
|
|
i__1 = *n - p;
|
|
dswap_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + 1 + p
|
|
* a_dim1], &c__1);
|
|
}
|
|
if (p > k + 1) {
|
|
i__1 = p - k - 1;
|
|
dswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[p + (k +
|
|
1) * a_dim1], lda);
|
|
}
|
|
t = a[k + k * a_dim1];
|
|
a[k + k * a_dim1] = a[p + p * a_dim1];
|
|
a[p + p * a_dim1] = t;
|
|
|
|
/* Convert lower triangle of A into L form by applying */
|
|
/* the interchanges in columns 1:k-1. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
dswap_(&i__1, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
|
|
}
|
|
|
|
}
|
|
|
|
/* Second swap */
|
|
|
|
kk = k + kstep - 1;
|
|
if (kp != kk) {
|
|
|
|
/* Interchange rows and columns KK and KP in the trailing */
|
|
/* submatrix A(k:n,k:n) */
|
|
|
|
if (kp < *n) {
|
|
i__1 = *n - kp;
|
|
dswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
|
|
+ kp * a_dim1], &c__1);
|
|
}
|
|
if (kk < *n && kp > kk + 1) {
|
|
i__1 = kp - kk - 1;
|
|
dswap_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (
|
|
kk + 1) * a_dim1], lda);
|
|
}
|
|
t = a[kk + kk * a_dim1];
|
|
a[kk + kk * a_dim1] = a[kp + kp * a_dim1];
|
|
a[kp + kp * a_dim1] = t;
|
|
if (kstep == 2) {
|
|
t = a[k + 1 + k * a_dim1];
|
|
a[k + 1 + k * a_dim1] = a[kp + k * a_dim1];
|
|
a[kp + k * a_dim1] = t;
|
|
}
|
|
|
|
/* Convert lower triangle of A into L form by applying */
|
|
/* the interchanges in columns 1:k-1. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
dswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
|
|
}
|
|
|
|
}
|
|
|
|
/* Update the trailing submatrix */
|
|
|
|
if (kstep == 1) {
|
|
|
|
/* 1-by-1 pivot block D(k): column k now holds */
|
|
|
|
/* W(k) = L(k)*D(k) */
|
|
|
|
/* where L(k) is the k-th column of L */
|
|
|
|
if (k < *n) {
|
|
|
|
/* Perform a rank-1 update of A(k+1:n,k+1:n) and */
|
|
/* store L(k) in column k */
|
|
|
|
if ((d__1 = a[k + k * a_dim1], abs(d__1)) >= sfmin) {
|
|
|
|
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */
|
|
/* A := A - L(k)*D(k)*L(k)**T */
|
|
/* = A - W(k)*(1/D(k))*W(k)**T */
|
|
|
|
d11 = 1. / a[k + k * a_dim1];
|
|
i__1 = *n - k;
|
|
d__1 = -d11;
|
|
dsyr_(uplo, &i__1, &d__1, &a[k + 1 + k * a_dim1], &
|
|
c__1, &a[k + 1 + (k + 1) * a_dim1], lda);
|
|
|
|
/* Store L(k) in column k */
|
|
|
|
i__1 = *n - k;
|
|
dscal_(&i__1, &d11, &a[k + 1 + k * a_dim1], &c__1);
|
|
} else {
|
|
|
|
/* Store L(k) in column k */
|
|
|
|
d11 = a[k + k * a_dim1];
|
|
i__1 = *n;
|
|
for (ii = k + 1; ii <= i__1; ++ii) {
|
|
a[ii + k * a_dim1] /= d11;
|
|
/* L46: */
|
|
}
|
|
|
|
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */
|
|
/* A := A - L(k)*D(k)*L(k)**T */
|
|
/* = A - W(k)*(1/D(k))*W(k)**T */
|
|
/* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T */
|
|
|
|
i__1 = *n - k;
|
|
d__1 = -d11;
|
|
dsyr_(uplo, &i__1, &d__1, &a[k + 1 + k * a_dim1], &
|
|
c__1, &a[k + 1 + (k + 1) * a_dim1], lda);
|
|
}
|
|
|
|
/* Store the subdiagonal element of D in array E */
|
|
|
|
e[k] = 0.;
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* 2-by-2 pivot block D(k): columns k and k+1 now hold */
|
|
|
|
/* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) */
|
|
|
|
/* where L(k) and L(k+1) are the k-th and (k+1)-th columns */
|
|
/* of L */
|
|
|
|
|
|
/* Perform a rank-2 update of A(k+2:n,k+2:n) as */
|
|
|
|
/* A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T */
|
|
/* = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T */
|
|
|
|
/* and store L(k) and L(k+1) in columns k and k+1 */
|
|
|
|
if (k < *n - 1) {
|
|
|
|
d21 = a[k + 1 + k * a_dim1];
|
|
d11 = a[k + 1 + (k + 1) * a_dim1] / d21;
|
|
d22 = a[k + k * a_dim1] / d21;
|
|
t = 1. / (d11 * d22 - 1.);
|
|
|
|
i__1 = *n;
|
|
for (j = k + 2; j <= i__1; ++j) {
|
|
|
|
/* Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J */
|
|
|
|
wk = t * (d11 * a[j + k * a_dim1] - a[j + (k + 1) *
|
|
a_dim1]);
|
|
wkp1 = t * (d22 * a[j + (k + 1) * a_dim1] - a[j + k *
|
|
a_dim1]);
|
|
|
|
/* Perform a rank-2 update of A(k+2:n,k+2:n) */
|
|
|
|
i__2 = *n;
|
|
for (i__ = j; i__ <= i__2; ++i__) {
|
|
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] - a[i__
|
|
+ k * a_dim1] / d21 * wk - a[i__ + (k + 1)
|
|
* a_dim1] / d21 * wkp1;
|
|
/* L50: */
|
|
}
|
|
|
|
/* Store L(k) and L(k+1) in cols k and k+1 for row J */
|
|
|
|
a[j + k * a_dim1] = wk / d21;
|
|
a[j + (k + 1) * a_dim1] = wkp1 / d21;
|
|
|
|
/* L60: */
|
|
}
|
|
|
|
}
|
|
|
|
/* Copy subdiagonal elements of D(K) to E(K) and */
|
|
/* ZERO out subdiagonal entry of A */
|
|
|
|
e[k] = a[k + 1 + k * a_dim1];
|
|
e[k + 1] = 0.;
|
|
a[k + 1 + k * a_dim1] = 0.;
|
|
|
|
}
|
|
|
|
/* End column K is nonsingular */
|
|
|
|
}
|
|
|
|
/* Store details of the interchanges in IPIV */
|
|
|
|
if (kstep == 1) {
|
|
ipiv[k] = kp;
|
|
} else {
|
|
ipiv[k] = -p;
|
|
ipiv[k + 1] = -kp;
|
|
}
|
|
|
|
/* Increase K and return to the start of the main loop */
|
|
|
|
k += kstep;
|
|
goto L40;
|
|
|
|
L64:
|
|
|
|
;
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DSYTF2_RK */
|
|
|
|
} /* dsytf2_rk__ */
|
|
|