1670 lines
42 KiB
C
1670 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)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* > \brief \b DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one
|
|
modification to a positive diagonal matrix. Used by dbdsdc. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLASD4 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd4.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd4.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd4.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO ) */
|
|
|
|
/* INTEGER I, INFO, N */
|
|
/* DOUBLE PRECISION RHO, SIGMA */
|
|
/* DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > This subroutine computes the square root of the I-th updated */
|
|
/* > eigenvalue of a positive symmetric rank-one modification to */
|
|
/* > a positive diagonal matrix whose entries are given as the squares */
|
|
/* > of the corresponding entries in the array d, and that */
|
|
/* > */
|
|
/* > 0 <= D(i) < D(j) for i < j */
|
|
/* > */
|
|
/* > and that RHO > 0. This is arranged by the calling routine, and is */
|
|
/* > no loss in generality. The rank-one modified system is thus */
|
|
/* > */
|
|
/* > diag( D ) * diag( D ) + RHO * Z * Z_transpose. */
|
|
/* > */
|
|
/* > where we assume the Euclidean norm of Z is 1. */
|
|
/* > */
|
|
/* > The method consists of approximating the rational functions in the */
|
|
/* > secular equation by simpler interpolating rational functions. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The length of all arrays. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] I */
|
|
/* > \verbatim */
|
|
/* > I is INTEGER */
|
|
/* > The index of the eigenvalue to be computed. 1 <= I <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension ( N ) */
|
|
/* > The original eigenvalues. It is assumed that they are in */
|
|
/* > order, 0 <= D(I) < D(J) for I < J. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Z */
|
|
/* > \verbatim */
|
|
/* > Z is DOUBLE PRECISION array, dimension ( N ) */
|
|
/* > The components of the updating vector. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DELTA */
|
|
/* > \verbatim */
|
|
/* > DELTA is DOUBLE PRECISION array, dimension ( N ) */
|
|
/* > If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th */
|
|
/* > component. If N = 1, then DELTA(1) = 1. The vector DELTA */
|
|
/* > contains the information necessary to construct the */
|
|
/* > (singular) eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RHO */
|
|
/* > \verbatim */
|
|
/* > RHO is DOUBLE PRECISION */
|
|
/* > The scalar in the symmetric updating formula. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SIGMA */
|
|
/* > \verbatim */
|
|
/* > SIGMA is DOUBLE PRECISION */
|
|
/* > The computed sigma_I, the I-th updated eigenvalue. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension ( N ) */
|
|
/* > If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th */
|
|
/* > component. If N = 1, then WORK( 1 ) = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > > 0: if INFO = 1, the updating process failed. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Internal Parameters: */
|
|
/* ========================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > Logical variable ORGATI (origin-at-i?) is used for distinguishing */
|
|
/* > whether D(i) or D(i+1) is treated as the origin. */
|
|
/* > */
|
|
/* > ORGATI = .true. origin at i */
|
|
/* > ORGATI = .false. origin at i+1 */
|
|
/* > */
|
|
/* > Logical variable SWTCH3 (switch-for-3-poles?) is for noting */
|
|
/* > if we are working with THREE poles! */
|
|
/* > */
|
|
/* > MAXIT is the maximum number of iterations allowed for each */
|
|
/* > eigenvalue. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup OTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ren-Cang Li, Computer Science Division, University of California */
|
|
/* > at Berkeley, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlasd4_(integer *n, integer *i__, doublereal *d__,
|
|
doublereal *z__, doublereal *delta, doublereal *rho, doublereal *
|
|
sigma, doublereal *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1;
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
doublereal dphi, sglb, dpsi, sgub;
|
|
integer iter;
|
|
doublereal temp, prew, temp1, temp2, a, b, c__;
|
|
integer j;
|
|
doublereal w, dtiim, delsq, dtiip;
|
|
integer niter;
|
|
doublereal dtisq;
|
|
logical swtch;
|
|
doublereal dtnsq;
|
|
extern /* Subroutine */ void dlaed6_(integer *, logical *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *, integer *)
|
|
, dlasd5_(integer *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *);
|
|
doublereal delsq2, dd[3], dtnsq1;
|
|
logical swtch3;
|
|
integer ii;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal dw, zz[3];
|
|
logical orgati;
|
|
doublereal erretm, dtipsq, rhoinv;
|
|
integer ip1;
|
|
doublereal sq2, eta, phi, eps, tau, psi;
|
|
logical geomavg;
|
|
integer iim1, iip1;
|
|
doublereal tau2;
|
|
|
|
|
|
/* -- LAPACK auxiliary 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Since this routine is called in an inner loop, we do no argument */
|
|
/* checking. */
|
|
|
|
/* Quick return for N=1 and 2. */
|
|
|
|
/* Parameter adjustments */
|
|
--work;
|
|
--delta;
|
|
--z__;
|
|
--d__;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
if (*n == 1) {
|
|
|
|
/* Presumably, I=1 upon entry */
|
|
|
|
*sigma = sqrt(d__[1] * d__[1] + *rho * z__[1] * z__[1]);
|
|
delta[1] = 1.;
|
|
work[1] = 1.;
|
|
return;
|
|
}
|
|
if (*n == 2) {
|
|
dlasd5_(i__, &d__[1], &z__[1], &delta[1], rho, sigma, &work[1]);
|
|
return;
|
|
}
|
|
|
|
/* Compute machine epsilon */
|
|
|
|
eps = dlamch_("Epsilon");
|
|
rhoinv = 1. / *rho;
|
|
tau2 = 0.;
|
|
|
|
/* The case I = N */
|
|
|
|
if (*i__ == *n) {
|
|
|
|
/* Initialize some basic variables */
|
|
|
|
ii = *n - 1;
|
|
niter = 1;
|
|
|
|
/* Calculate initial guess */
|
|
|
|
temp = *rho / 2.;
|
|
|
|
/* If ||Z||_2 is not one, then TEMP should be set to */
|
|
/* RHO * ||Z||_2^2 / TWO */
|
|
|
|
temp1 = temp / (d__[*n] + sqrt(d__[*n] * d__[*n] + temp));
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
work[j] = d__[j] + d__[*n] + temp1;
|
|
delta[j] = d__[j] - d__[*n] - temp1;
|
|
/* L10: */
|
|
}
|
|
|
|
psi = 0.;
|
|
i__1 = *n - 2;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
psi += z__[j] * z__[j] / (delta[j] * work[j]);
|
|
/* L20: */
|
|
}
|
|
|
|
c__ = rhoinv + psi;
|
|
w = c__ + z__[ii] * z__[ii] / (delta[ii] * work[ii]) + z__[*n] * z__[*
|
|
n] / (delta[*n] * work[*n]);
|
|
|
|
if (w <= 0.) {
|
|
temp1 = sqrt(d__[*n] * d__[*n] + *rho);
|
|
temp = z__[*n - 1] * z__[*n - 1] / ((d__[*n - 1] + temp1) * (d__[*
|
|
n] - d__[*n - 1] + *rho / (d__[*n] + temp1))) + z__[*n] *
|
|
z__[*n] / *rho;
|
|
|
|
/* The following TAU2 is to approximate */
|
|
/* SIGMA_n^2 - D( N )*D( N ) */
|
|
|
|
if (c__ <= temp) {
|
|
tau = *rho;
|
|
} else {
|
|
delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]);
|
|
a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*
|
|
n];
|
|
b = z__[*n] * z__[*n] * delsq;
|
|
if (a < 0.) {
|
|
tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a);
|
|
} else {
|
|
tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.);
|
|
}
|
|
tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2));
|
|
}
|
|
|
|
/* It can be proved that */
|
|
/* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU2 <= D(N)^2+RHO */
|
|
|
|
} else {
|
|
delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]);
|
|
a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n];
|
|
b = z__[*n] * z__[*n] * delsq;
|
|
|
|
/* The following TAU2 is to approximate */
|
|
/* SIGMA_n^2 - D( N )*D( N ) */
|
|
|
|
if (a < 0.) {
|
|
tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a);
|
|
} else {
|
|
tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.);
|
|
}
|
|
tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2));
|
|
|
|
/* It can be proved that */
|
|
/* D(N)^2 < D(N)^2+TAU2 < SIGMA(N)^2 < D(N)^2+RHO/2 */
|
|
|
|
}
|
|
|
|
/* The following TAU is to approximate SIGMA_n - D( N ) */
|
|
|
|
/* TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) ) */
|
|
|
|
*sigma = d__[*n] + tau;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] = d__[j] - d__[*n] - tau;
|
|
work[j] = d__[j] + d__[*n] + tau;
|
|
/* L30: */
|
|
}
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.;
|
|
psi = 0.;
|
|
erretm = 0.;
|
|
i__1 = ii;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / (delta[j] * work[j]);
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L40: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
temp = z__[*n] / (delta[*n] * work[*n]);
|
|
phi = z__[*n] * temp;
|
|
dphi = temp * temp;
|
|
erretm = (-phi - psi) * 8. + erretm - phi + rhoinv;
|
|
/* $ + ABS( TAU2 )*( DPSI+DPHI ) */
|
|
|
|
w = rhoinv + phi + psi;
|
|
|
|
/* Test for convergence */
|
|
|
|
if (abs(w) <= eps * erretm) {
|
|
goto L240;
|
|
}
|
|
|
|
/* Calculate the new step */
|
|
|
|
++niter;
|
|
dtnsq1 = work[*n - 1] * delta[*n - 1];
|
|
dtnsq = work[*n] * delta[*n];
|
|
c__ = w - dtnsq1 * dpsi - dtnsq * dphi;
|
|
a = (dtnsq + dtnsq1) * w - dtnsq * dtnsq1 * (dpsi + dphi);
|
|
b = dtnsq * dtnsq1 * w;
|
|
if (c__ < 0.) {
|
|
c__ = abs(c__);
|
|
}
|
|
if (c__ == 0.) {
|
|
eta = *rho - *sigma * *sigma;
|
|
} else if (a >= 0.) {
|
|
eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__
|
|
* 2.);
|
|
} else {
|
|
eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))
|
|
);
|
|
}
|
|
|
|
/* Note, eta should be positive if w is negative, and */
|
|
/* eta should be negative otherwise. However, */
|
|
/* if for some reason caused by roundoff, eta*w > 0, */
|
|
/* we simply use one Newton step instead. This way */
|
|
/* will guarantee eta*w < 0. */
|
|
|
|
if (w * eta > 0.) {
|
|
eta = -w / (dpsi + dphi);
|
|
}
|
|
temp = eta - dtnsq;
|
|
if (temp > *rho) {
|
|
eta = *rho + dtnsq;
|
|
}
|
|
|
|
eta /= *sigma + sqrt(eta + *sigma * *sigma);
|
|
tau += eta;
|
|
*sigma += eta;
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] -= eta;
|
|
work[j] += eta;
|
|
/* L50: */
|
|
}
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.;
|
|
psi = 0.;
|
|
erretm = 0.;
|
|
i__1 = ii;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / (work[j] * delta[j]);
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L60: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
tau2 = work[*n] * delta[*n];
|
|
temp = z__[*n] / tau2;
|
|
phi = z__[*n] * temp;
|
|
dphi = temp * temp;
|
|
erretm = (-phi - psi) * 8. + erretm - phi + rhoinv;
|
|
/* $ + ABS( TAU2 )*( DPSI+DPHI ) */
|
|
|
|
w = rhoinv + phi + psi;
|
|
|
|
/* Main loop to update the values of the array DELTA */
|
|
|
|
iter = niter + 1;
|
|
|
|
for (niter = iter; niter <= 400; ++niter) {
|
|
|
|
/* Test for convergence */
|
|
|
|
if (abs(w) <= eps * erretm) {
|
|
goto L240;
|
|
}
|
|
|
|
/* Calculate the new step */
|
|
|
|
dtnsq1 = work[*n - 1] * delta[*n - 1];
|
|
dtnsq = work[*n] * delta[*n];
|
|
c__ = w - dtnsq1 * dpsi - dtnsq * dphi;
|
|
a = (dtnsq + dtnsq1) * w - dtnsq1 * dtnsq * (dpsi + dphi);
|
|
b = dtnsq1 * dtnsq * w;
|
|
if (a >= 0.) {
|
|
eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (
|
|
c__ * 2.);
|
|
} else {
|
|
eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(
|
|
d__1))));
|
|
}
|
|
|
|
/* Note, eta should be positive if w is negative, and */
|
|
/* eta should be negative otherwise. However, */
|
|
/* if for some reason caused by roundoff, eta*w > 0, */
|
|
/* we simply use one Newton step instead. This way */
|
|
/* will guarantee eta*w < 0. */
|
|
|
|
if (w * eta > 0.) {
|
|
eta = -w / (dpsi + dphi);
|
|
}
|
|
temp = eta - dtnsq;
|
|
if (temp <= 0.) {
|
|
eta /= 2.;
|
|
}
|
|
|
|
eta /= *sigma + sqrt(eta + *sigma * *sigma);
|
|
tau += eta;
|
|
*sigma += eta;
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] -= eta;
|
|
work[j] += eta;
|
|
/* L70: */
|
|
}
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.;
|
|
psi = 0.;
|
|
erretm = 0.;
|
|
i__1 = ii;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / (work[j] * delta[j]);
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L80: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
tau2 = work[*n] * delta[*n];
|
|
temp = z__[*n] / tau2;
|
|
phi = z__[*n] * temp;
|
|
dphi = temp * temp;
|
|
erretm = (-phi - psi) * 8. + erretm - phi + rhoinv;
|
|
/* $ + ABS( TAU2 )*( DPSI+DPHI ) */
|
|
|
|
w = rhoinv + phi + psi;
|
|
/* L90: */
|
|
}
|
|
|
|
/* Return with INFO = 1, NITER = MAXIT and not converged */
|
|
|
|
*info = 1;
|
|
goto L240;
|
|
|
|
/* End for the case I = N */
|
|
|
|
} else {
|
|
|
|
/* The case for I < N */
|
|
|
|
niter = 1;
|
|
ip1 = *i__ + 1;
|
|
|
|
/* Calculate initial guess */
|
|
|
|
delsq = (d__[ip1] - d__[*i__]) * (d__[ip1] + d__[*i__]);
|
|
delsq2 = delsq / 2.;
|
|
sq2 = sqrt((d__[*i__] * d__[*i__] + d__[ip1] * d__[ip1]) / 2.);
|
|
temp = delsq2 / (d__[*i__] + sq2);
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
work[j] = d__[j] + d__[*i__] + temp;
|
|
delta[j] = d__[j] - d__[*i__] - temp;
|
|
/* L100: */
|
|
}
|
|
|
|
psi = 0.;
|
|
i__1 = *i__ - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
psi += z__[j] * z__[j] / (work[j] * delta[j]);
|
|
/* L110: */
|
|
}
|
|
|
|
phi = 0.;
|
|
i__1 = *i__ + 2;
|
|
for (j = *n; j >= i__1; --j) {
|
|
phi += z__[j] * z__[j] / (work[j] * delta[j]);
|
|
/* L120: */
|
|
}
|
|
c__ = rhoinv + psi + phi;
|
|
w = c__ + z__[*i__] * z__[*i__] / (work[*i__] * delta[*i__]) + z__[
|
|
ip1] * z__[ip1] / (work[ip1] * delta[ip1]);
|
|
|
|
geomavg = FALSE_;
|
|
if (w > 0.) {
|
|
|
|
/* d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2 */
|
|
|
|
/* We choose d(i) as origin. */
|
|
|
|
orgati = TRUE_;
|
|
ii = *i__;
|
|
sglb = 0.;
|
|
sgub = delsq2 / (d__[*i__] + sq2);
|
|
a = c__ * delsq + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1];
|
|
b = z__[*i__] * z__[*i__] * delsq;
|
|
if (a > 0.) {
|
|
tau2 = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(
|
|
d__1))));
|
|
} else {
|
|
tau2 = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) /
|
|
(c__ * 2.);
|
|
}
|
|
|
|
/* TAU2 now is an estimation of SIGMA^2 - D( I )^2. The */
|
|
/* following, however, is the corresponding estimation of */
|
|
/* SIGMA - D( I ). */
|
|
|
|
tau = tau2 / (d__[*i__] + sqrt(d__[*i__] * d__[*i__] + tau2));
|
|
temp = sqrt(eps);
|
|
if (d__[*i__] <= temp * d__[ip1] && (d__1 = z__[*i__], abs(d__1))
|
|
<= temp && d__[*i__] > 0.) {
|
|
/* Computing MIN */
|
|
d__1 = d__[*i__] * 10.;
|
|
tau = f2cmin(d__1,sgub);
|
|
geomavg = TRUE_;
|
|
}
|
|
} else {
|
|
|
|
/* (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2 */
|
|
|
|
/* We choose d(i+1) as origin. */
|
|
|
|
orgati = FALSE_;
|
|
ii = ip1;
|
|
sglb = -delsq2 / (d__[ii] + sq2);
|
|
sgub = 0.;
|
|
a = c__ * delsq - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1];
|
|
b = z__[ip1] * z__[ip1] * delsq;
|
|
if (a < 0.) {
|
|
tau2 = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs(
|
|
d__1))));
|
|
} else {
|
|
tau2 = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) /
|
|
(c__ * 2.);
|
|
}
|
|
|
|
/* TAU2 now is an estimation of SIGMA^2 - D( IP1 )^2. The */
|
|
/* following, however, is the corresponding estimation of */
|
|
/* SIGMA - D( IP1 ). */
|
|
|
|
tau = tau2 / (d__[ip1] + sqrt((d__1 = d__[ip1] * d__[ip1] + tau2,
|
|
abs(d__1))));
|
|
}
|
|
|
|
*sigma = d__[ii] + tau;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
work[j] = d__[j] + d__[ii] + tau;
|
|
delta[j] = d__[j] - d__[ii] - tau;
|
|
/* L130: */
|
|
}
|
|
iim1 = ii - 1;
|
|
iip1 = ii + 1;
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.;
|
|
psi = 0.;
|
|
erretm = 0.;
|
|
i__1 = iim1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / (work[j] * delta[j]);
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L150: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
dphi = 0.;
|
|
phi = 0.;
|
|
i__1 = iip1;
|
|
for (j = *n; j >= i__1; --j) {
|
|
temp = z__[j] / (work[j] * delta[j]);
|
|
phi += z__[j] * temp;
|
|
dphi += temp * temp;
|
|
erretm += phi;
|
|
/* L160: */
|
|
}
|
|
|
|
w = rhoinv + phi + psi;
|
|
|
|
/* W is the value of the secular function with */
|
|
/* its ii-th element removed. */
|
|
|
|
swtch3 = FALSE_;
|
|
if (orgati) {
|
|
if (w < 0.) {
|
|
swtch3 = TRUE_;
|
|
}
|
|
} else {
|
|
if (w > 0.) {
|
|
swtch3 = TRUE_;
|
|
}
|
|
}
|
|
if (ii == 1 || ii == *n) {
|
|
swtch3 = FALSE_;
|
|
}
|
|
|
|
temp = z__[ii] / (work[ii] * delta[ii]);
|
|
dw = dpsi + dphi + temp * temp;
|
|
temp = z__[ii] * temp;
|
|
w += temp;
|
|
erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.;
|
|
/* $ + ABS( TAU2 )*DW */
|
|
|
|
/* Test for convergence */
|
|
|
|
if (abs(w) <= eps * erretm) {
|
|
goto L240;
|
|
}
|
|
|
|
if (w <= 0.) {
|
|
sglb = f2cmax(sglb,tau);
|
|
} else {
|
|
sgub = f2cmin(sgub,tau);
|
|
}
|
|
|
|
/* Calculate the new step */
|
|
|
|
++niter;
|
|
if (! swtch3) {
|
|
dtipsq = work[ip1] * delta[ip1];
|
|
dtisq = work[*i__] * delta[*i__];
|
|
if (orgati) {
|
|
/* Computing 2nd power */
|
|
d__1 = z__[*i__] / dtisq;
|
|
c__ = w - dtipsq * dw + delsq * (d__1 * d__1);
|
|
} else {
|
|
/* Computing 2nd power */
|
|
d__1 = z__[ip1] / dtipsq;
|
|
c__ = w - dtisq * dw - delsq * (d__1 * d__1);
|
|
}
|
|
a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw;
|
|
b = dtipsq * dtisq * w;
|
|
if (c__ == 0.) {
|
|
if (a == 0.) {
|
|
if (orgati) {
|
|
a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi +
|
|
dphi);
|
|
} else {
|
|
a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi +
|
|
dphi);
|
|
}
|
|
}
|
|
eta = b / a;
|
|
} else if (a <= 0.) {
|
|
eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (
|
|
c__ * 2.);
|
|
} else {
|
|
eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(
|
|
d__1))));
|
|
}
|
|
} else {
|
|
|
|
/* Interpolation using THREE most relevant poles */
|
|
|
|
dtiim = work[iim1] * delta[iim1];
|
|
dtiip = work[iip1] * delta[iip1];
|
|
temp = rhoinv + psi + phi;
|
|
if (orgati) {
|
|
temp1 = z__[iim1] / dtiim;
|
|
temp1 *= temp1;
|
|
c__ = temp - dtiip * (dpsi + dphi) - (d__[iim1] - d__[iip1]) *
|
|
(d__[iim1] + d__[iip1]) * temp1;
|
|
zz[0] = z__[iim1] * z__[iim1];
|
|
if (dpsi < temp1) {
|
|
zz[2] = dtiip * dtiip * dphi;
|
|
} else {
|
|
zz[2] = dtiip * dtiip * (dpsi - temp1 + dphi);
|
|
}
|
|
} else {
|
|
temp1 = z__[iip1] / dtiip;
|
|
temp1 *= temp1;
|
|
c__ = temp - dtiim * (dpsi + dphi) - (d__[iip1] - d__[iim1]) *
|
|
(d__[iim1] + d__[iip1]) * temp1;
|
|
if (dphi < temp1) {
|
|
zz[0] = dtiim * dtiim * dpsi;
|
|
} else {
|
|
zz[0] = dtiim * dtiim * (dpsi + (dphi - temp1));
|
|
}
|
|
zz[2] = z__[iip1] * z__[iip1];
|
|
}
|
|
zz[1] = z__[ii] * z__[ii];
|
|
dd[0] = dtiim;
|
|
dd[1] = delta[ii] * work[ii];
|
|
dd[2] = dtiip;
|
|
dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info);
|
|
|
|
if (*info != 0) {
|
|
|
|
/* If INFO is not 0, i.e., DLAED6 failed, switch back */
|
|
/* to 2 pole interpolation. */
|
|
|
|
swtch3 = FALSE_;
|
|
*info = 0;
|
|
dtipsq = work[ip1] * delta[ip1];
|
|
dtisq = work[*i__] * delta[*i__];
|
|
if (orgati) {
|
|
/* Computing 2nd power */
|
|
d__1 = z__[*i__] / dtisq;
|
|
c__ = w - dtipsq * dw + delsq * (d__1 * d__1);
|
|
} else {
|
|
/* Computing 2nd power */
|
|
d__1 = z__[ip1] / dtipsq;
|
|
c__ = w - dtisq * dw - delsq * (d__1 * d__1);
|
|
}
|
|
a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw;
|
|
b = dtipsq * dtisq * w;
|
|
if (c__ == 0.) {
|
|
if (a == 0.) {
|
|
if (orgati) {
|
|
a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (
|
|
dpsi + dphi);
|
|
} else {
|
|
a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi +
|
|
dphi);
|
|
}
|
|
}
|
|
eta = b / a;
|
|
} else if (a <= 0.) {
|
|
eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))))
|
|
/ (c__ * 2.);
|
|
} else {
|
|
eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__,
|
|
abs(d__1))));
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Note, eta should be positive if w is negative, and */
|
|
/* eta should be negative otherwise. However, */
|
|
/* if for some reason caused by roundoff, eta*w > 0, */
|
|
/* we simply use one Newton step instead. This way */
|
|
/* will guarantee eta*w < 0. */
|
|
|
|
if (w * eta >= 0.) {
|
|
eta = -w / dw;
|
|
}
|
|
|
|
eta /= *sigma + sqrt(*sigma * *sigma + eta);
|
|
temp = tau + eta;
|
|
if (temp > sgub || temp < sglb) {
|
|
if (w < 0.) {
|
|
eta = (sgub - tau) / 2.;
|
|
} else {
|
|
eta = (sglb - tau) / 2.;
|
|
}
|
|
if (geomavg) {
|
|
if (w < 0.) {
|
|
if (tau > 0.) {
|
|
eta = sqrt(sgub * tau) - tau;
|
|
}
|
|
} else {
|
|
if (sglb > 0.) {
|
|
eta = sqrt(sglb * tau) - tau;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
prew = w;
|
|
|
|
tau += eta;
|
|
*sigma += eta;
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
work[j] += eta;
|
|
delta[j] -= eta;
|
|
/* L170: */
|
|
}
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.;
|
|
psi = 0.;
|
|
erretm = 0.;
|
|
i__1 = iim1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / (work[j] * delta[j]);
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L180: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
dphi = 0.;
|
|
phi = 0.;
|
|
i__1 = iip1;
|
|
for (j = *n; j >= i__1; --j) {
|
|
temp = z__[j] / (work[j] * delta[j]);
|
|
phi += z__[j] * temp;
|
|
dphi += temp * temp;
|
|
erretm += phi;
|
|
/* L190: */
|
|
}
|
|
|
|
tau2 = work[ii] * delta[ii];
|
|
temp = z__[ii] / tau2;
|
|
dw = dpsi + dphi + temp * temp;
|
|
temp = z__[ii] * temp;
|
|
w = rhoinv + phi + psi + temp;
|
|
erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.;
|
|
/* $ + ABS( TAU2 )*DW */
|
|
|
|
swtch = FALSE_;
|
|
if (orgati) {
|
|
if (-w > abs(prew) / 10.) {
|
|
swtch = TRUE_;
|
|
}
|
|
} else {
|
|
if (w > abs(prew) / 10.) {
|
|
swtch = TRUE_;
|
|
}
|
|
}
|
|
|
|
/* Main loop to update the values of the array DELTA and WORK */
|
|
|
|
iter = niter + 1;
|
|
|
|
for (niter = iter; niter <= 400; ++niter) {
|
|
|
|
/* Test for convergence */
|
|
|
|
if (abs(w) <= eps * erretm) {
|
|
/* $ .OR. (SGUB-SGLB).LE.EIGHT*ABS(SGUB+SGLB) ) THEN */
|
|
goto L240;
|
|
}
|
|
|
|
if (w <= 0.) {
|
|
sglb = f2cmax(sglb,tau);
|
|
} else {
|
|
sgub = f2cmin(sgub,tau);
|
|
}
|
|
|
|
/* Calculate the new step */
|
|
|
|
if (! swtch3) {
|
|
dtipsq = work[ip1] * delta[ip1];
|
|
dtisq = work[*i__] * delta[*i__];
|
|
if (! swtch) {
|
|
if (orgati) {
|
|
/* Computing 2nd power */
|
|
d__1 = z__[*i__] / dtisq;
|
|
c__ = w - dtipsq * dw + delsq * (d__1 * d__1);
|
|
} else {
|
|
/* Computing 2nd power */
|
|
d__1 = z__[ip1] / dtipsq;
|
|
c__ = w - dtisq * dw - delsq * (d__1 * d__1);
|
|
}
|
|
} else {
|
|
temp = z__[ii] / (work[ii] * delta[ii]);
|
|
if (orgati) {
|
|
dpsi += temp * temp;
|
|
} else {
|
|
dphi += temp * temp;
|
|
}
|
|
c__ = w - dtisq * dpsi - dtipsq * dphi;
|
|
}
|
|
a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw;
|
|
b = dtipsq * dtisq * w;
|
|
if (c__ == 0.) {
|
|
if (a == 0.) {
|
|
if (! swtch) {
|
|
if (orgati) {
|
|
a = z__[*i__] * z__[*i__] + dtipsq * dtipsq *
|
|
(dpsi + dphi);
|
|
} else {
|
|
a = z__[ip1] * z__[ip1] + dtisq * dtisq * (
|
|
dpsi + dphi);
|
|
}
|
|
} else {
|
|
a = dtisq * dtisq * dpsi + dtipsq * dtipsq * dphi;
|
|
}
|
|
}
|
|
eta = b / a;
|
|
} else if (a <= 0.) {
|
|
eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))))
|
|
/ (c__ * 2.);
|
|
} else {
|
|
eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__,
|
|
abs(d__1))));
|
|
}
|
|
} else {
|
|
|
|
/* Interpolation using THREE most relevant poles */
|
|
|
|
dtiim = work[iim1] * delta[iim1];
|
|
dtiip = work[iip1] * delta[iip1];
|
|
temp = rhoinv + psi + phi;
|
|
if (swtch) {
|
|
c__ = temp - dtiim * dpsi - dtiip * dphi;
|
|
zz[0] = dtiim * dtiim * dpsi;
|
|
zz[2] = dtiip * dtiip * dphi;
|
|
} else {
|
|
if (orgati) {
|
|
temp1 = z__[iim1] / dtiim;
|
|
temp1 *= temp1;
|
|
temp2 = (d__[iim1] - d__[iip1]) * (d__[iim1] + d__[
|
|
iip1]) * temp1;
|
|
c__ = temp - dtiip * (dpsi + dphi) - temp2;
|
|
zz[0] = z__[iim1] * z__[iim1];
|
|
if (dpsi < temp1) {
|
|
zz[2] = dtiip * dtiip * dphi;
|
|
} else {
|
|
zz[2] = dtiip * dtiip * (dpsi - temp1 + dphi);
|
|
}
|
|
} else {
|
|
temp1 = z__[iip1] / dtiip;
|
|
temp1 *= temp1;
|
|
temp2 = (d__[iip1] - d__[iim1]) * (d__[iim1] + d__[
|
|
iip1]) * temp1;
|
|
c__ = temp - dtiim * (dpsi + dphi) - temp2;
|
|
if (dphi < temp1) {
|
|
zz[0] = dtiim * dtiim * dpsi;
|
|
} else {
|
|
zz[0] = dtiim * dtiim * (dpsi + (dphi - temp1));
|
|
}
|
|
zz[2] = z__[iip1] * z__[iip1];
|
|
}
|
|
}
|
|
dd[0] = dtiim;
|
|
dd[1] = delta[ii] * work[ii];
|
|
dd[2] = dtiip;
|
|
dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info);
|
|
|
|
if (*info != 0) {
|
|
|
|
/* If INFO is not 0, i.e., DLAED6 failed, switch */
|
|
/* back to two pole interpolation */
|
|
|
|
swtch3 = FALSE_;
|
|
*info = 0;
|
|
dtipsq = work[ip1] * delta[ip1];
|
|
dtisq = work[*i__] * delta[*i__];
|
|
if (! swtch) {
|
|
if (orgati) {
|
|
/* Computing 2nd power */
|
|
d__1 = z__[*i__] / dtisq;
|
|
c__ = w - dtipsq * dw + delsq * (d__1 * d__1);
|
|
} else {
|
|
/* Computing 2nd power */
|
|
d__1 = z__[ip1] / dtipsq;
|
|
c__ = w - dtisq * dw - delsq * (d__1 * d__1);
|
|
}
|
|
} else {
|
|
temp = z__[ii] / (work[ii] * delta[ii]);
|
|
if (orgati) {
|
|
dpsi += temp * temp;
|
|
} else {
|
|
dphi += temp * temp;
|
|
}
|
|
c__ = w - dtisq * dpsi - dtipsq * dphi;
|
|
}
|
|
a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw;
|
|
b = dtipsq * dtisq * w;
|
|
if (c__ == 0.) {
|
|
if (a == 0.) {
|
|
if (! swtch) {
|
|
if (orgati) {
|
|
a = z__[*i__] * z__[*i__] + dtipsq *
|
|
dtipsq * (dpsi + dphi);
|
|
} else {
|
|
a = z__[ip1] * z__[ip1] + dtisq * dtisq *
|
|
(dpsi + dphi);
|
|
}
|
|
} else {
|
|
a = dtisq * dtisq * dpsi + dtipsq * dtipsq *
|
|
dphi;
|
|
}
|
|
}
|
|
eta = b / a;
|
|
} else if (a <= 0.) {
|
|
eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(
|
|
d__1)))) / (c__ * 2.);
|
|
} else {
|
|
eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__,
|
|
abs(d__1))));
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Note, eta should be positive if w is negative, and */
|
|
/* eta should be negative otherwise. However, */
|
|
/* if for some reason caused by roundoff, eta*w > 0, */
|
|
/* we simply use one Newton step instead. This way */
|
|
/* will guarantee eta*w < 0. */
|
|
|
|
if (w * eta >= 0.) {
|
|
eta = -w / dw;
|
|
}
|
|
|
|
eta /= *sigma + sqrt(*sigma * *sigma + eta);
|
|
temp = tau + eta;
|
|
if (temp > sgub || temp < sglb) {
|
|
if (w < 0.) {
|
|
eta = (sgub - tau) / 2.;
|
|
} else {
|
|
eta = (sglb - tau) / 2.;
|
|
}
|
|
if (geomavg) {
|
|
if (w < 0.) {
|
|
if (tau > 0.) {
|
|
eta = sqrt(sgub * tau) - tau;
|
|
}
|
|
} else {
|
|
if (sglb > 0.) {
|
|
eta = sqrt(sglb * tau) - tau;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
prew = w;
|
|
|
|
tau += eta;
|
|
*sigma += eta;
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
work[j] += eta;
|
|
delta[j] -= eta;
|
|
/* L200: */
|
|
}
|
|
|
|
/* Evaluate PSI and the derivative DPSI */
|
|
|
|
dpsi = 0.;
|
|
psi = 0.;
|
|
erretm = 0.;
|
|
i__1 = iim1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / (work[j] * delta[j]);
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
/* L210: */
|
|
}
|
|
erretm = abs(erretm);
|
|
|
|
/* Evaluate PHI and the derivative DPHI */
|
|
|
|
dphi = 0.;
|
|
phi = 0.;
|
|
i__1 = iip1;
|
|
for (j = *n; j >= i__1; --j) {
|
|
temp = z__[j] / (work[j] * delta[j]);
|
|
phi += z__[j] * temp;
|
|
dphi += temp * temp;
|
|
erretm += phi;
|
|
/* L220: */
|
|
}
|
|
|
|
tau2 = work[ii] * delta[ii];
|
|
temp = z__[ii] / tau2;
|
|
dw = dpsi + dphi + temp * temp;
|
|
temp = z__[ii] * temp;
|
|
w = rhoinv + phi + psi + temp;
|
|
erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.;
|
|
/* $ + ABS( TAU2 )*DW */
|
|
|
|
if (w * prew > 0. && abs(w) > abs(prew) / 10.) {
|
|
swtch = ! swtch;
|
|
}
|
|
|
|
/* L230: */
|
|
}
|
|
|
|
/* Return with INFO = 1, NITER = MAXIT and not converged */
|
|
|
|
*info = 1;
|
|
|
|
}
|
|
|
|
L240:
|
|
return;
|
|
|
|
/* End of DLASD4 */
|
|
|
|
} /* dlasd4_ */
|
|
|