882 lines
23 KiB
C
882 lines
23 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) */
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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;
|
|
static doublereal c_b5 = 1.;
|
|
|
|
/* > \brief \b DLAIC1 applies one step of incremental condition estimation. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLAIC1 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaic1.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaic1.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaic1.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C ) */
|
|
|
|
/* INTEGER J, JOB */
|
|
/* DOUBLE PRECISION C, GAMMA, S, SEST, SESTPR */
|
|
/* DOUBLE PRECISION W( J ), X( J ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLAIC1 applies one step of incremental condition estimation in */
|
|
/* > its simplest version: */
|
|
/* > */
|
|
/* > Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j */
|
|
/* > lower triangular matrix L, such that */
|
|
/* > twonorm(L*x) = sest */
|
|
/* > Then DLAIC1 computes sestpr, s, c such that */
|
|
/* > the vector */
|
|
/* > [ s*x ] */
|
|
/* > xhat = [ c ] */
|
|
/* > is an approximate singular vector of */
|
|
/* > [ L 0 ] */
|
|
/* > Lhat = [ w**T gamma ] */
|
|
/* > in the sense that */
|
|
/* > twonorm(Lhat*xhat) = sestpr. */
|
|
/* > */
|
|
/* > Depending on JOB, an estimate for the largest or smallest singular */
|
|
/* > value is computed. */
|
|
/* > */
|
|
/* > Note that [s c]**T and sestpr**2 is an eigenpair of the system */
|
|
/* > */
|
|
/* > diag(sest*sest, 0) + [alpha gamma] * [ alpha ] */
|
|
/* > [ gamma ] */
|
|
/* > */
|
|
/* > where alpha = x**T*w. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOB */
|
|
/* > \verbatim */
|
|
/* > JOB is INTEGER */
|
|
/* > = 1: an estimate for the largest singular value is computed. */
|
|
/* > = 2: an estimate for the smallest singular value is computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] J */
|
|
/* > \verbatim */
|
|
/* > J is INTEGER */
|
|
/* > Length of X and W */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] X */
|
|
/* > \verbatim */
|
|
/* > X is DOUBLE PRECISION array, dimension (J) */
|
|
/* > The j-vector x. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SEST */
|
|
/* > \verbatim */
|
|
/* > SEST is DOUBLE PRECISION */
|
|
/* > Estimated singular value of j by j matrix L */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] W */
|
|
/* > \verbatim */
|
|
/* > W is DOUBLE PRECISION array, dimension (J) */
|
|
/* > The j-vector w. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GAMMA */
|
|
/* > \verbatim */
|
|
/* > GAMMA is DOUBLE PRECISION */
|
|
/* > The diagonal element gamma. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SESTPR */
|
|
/* > \verbatim */
|
|
/* > SESTPR is DOUBLE PRECISION */
|
|
/* > Estimated singular value of (j+1) by (j+1) matrix Lhat. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION */
|
|
/* > Sine needed in forming xhat. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] C */
|
|
/* > \verbatim */
|
|
/* > C is DOUBLE PRECISION */
|
|
/* > Cosine needed in forming xhat. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleOTHERauxiliary */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlaic1_(integer *job, integer *j, doublereal *x,
|
|
doublereal *sest, doublereal *w, doublereal *gamma, doublereal *
|
|
sestpr, doublereal *s, doublereal *c__)
|
|
{
|
|
/* System generated locals */
|
|
doublereal d__1, d__2, d__3, d__4;
|
|
|
|
/* Local variables */
|
|
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
|
|
integer *);
|
|
doublereal sine, test, zeta1, zeta2, b, t, alpha, norma, s1, s2;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal absgam, absalp, cosine, absest, eps, tmp;
|
|
|
|
|
|
/* -- 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
--w;
|
|
--x;
|
|
|
|
/* Function Body */
|
|
eps = dlamch_("Epsilon");
|
|
alpha = ddot_(j, &x[1], &c__1, &w[1], &c__1);
|
|
|
|
absalp = abs(alpha);
|
|
absgam = abs(*gamma);
|
|
absest = abs(*sest);
|
|
|
|
if (*job == 1) {
|
|
|
|
/* Estimating largest singular value */
|
|
|
|
/* special cases */
|
|
|
|
if (*sest == 0.) {
|
|
s1 = f2cmax(absgam,absalp);
|
|
if (s1 == 0.) {
|
|
*s = 0.;
|
|
*c__ = 1.;
|
|
*sestpr = 0.;
|
|
} else {
|
|
*s = alpha / s1;
|
|
*c__ = *gamma / s1;
|
|
tmp = sqrt(*s * *s + *c__ * *c__);
|
|
*s /= tmp;
|
|
*c__ /= tmp;
|
|
*sestpr = s1 * tmp;
|
|
}
|
|
return;
|
|
} else if (absgam <= eps * absest) {
|
|
*s = 1.;
|
|
*c__ = 0.;
|
|
tmp = f2cmax(absest,absalp);
|
|
s1 = absest / tmp;
|
|
s2 = absalp / tmp;
|
|
*sestpr = tmp * sqrt(s1 * s1 + s2 * s2);
|
|
return;
|
|
} else if (absalp <= eps * absest) {
|
|
s1 = absgam;
|
|
s2 = absest;
|
|
if (s1 <= s2) {
|
|
*s = 1.;
|
|
*c__ = 0.;
|
|
*sestpr = s2;
|
|
} else {
|
|
*s = 0.;
|
|
*c__ = 1.;
|
|
*sestpr = s1;
|
|
}
|
|
return;
|
|
} else if (absest <= eps * absalp || absest <= eps * absgam) {
|
|
s1 = absgam;
|
|
s2 = absalp;
|
|
if (s1 <= s2) {
|
|
tmp = s1 / s2;
|
|
*s = sqrt(tmp * tmp + 1.);
|
|
*sestpr = s2 * *s;
|
|
*c__ = *gamma / s2 / *s;
|
|
*s = d_sign(&c_b5, &alpha) / *s;
|
|
} else {
|
|
tmp = s2 / s1;
|
|
*c__ = sqrt(tmp * tmp + 1.);
|
|
*sestpr = s1 * *c__;
|
|
*s = alpha / s1 / *c__;
|
|
*c__ = d_sign(&c_b5, gamma) / *c__;
|
|
}
|
|
return;
|
|
} else {
|
|
|
|
/* normal case */
|
|
|
|
zeta1 = alpha / absest;
|
|
zeta2 = *gamma / absest;
|
|
|
|
b = (1. - zeta1 * zeta1 - zeta2 * zeta2) * .5;
|
|
*c__ = zeta1 * zeta1;
|
|
if (b > 0.) {
|
|
t = *c__ / (b + sqrt(b * b + *c__));
|
|
} else {
|
|
t = sqrt(b * b + *c__) - b;
|
|
}
|
|
|
|
sine = -zeta1 / t;
|
|
cosine = -zeta2 / (t + 1.);
|
|
tmp = sqrt(sine * sine + cosine * cosine);
|
|
*s = sine / tmp;
|
|
*c__ = cosine / tmp;
|
|
*sestpr = sqrt(t + 1.) * absest;
|
|
return;
|
|
}
|
|
|
|
} else if (*job == 2) {
|
|
|
|
/* Estimating smallest singular value */
|
|
|
|
/* special cases */
|
|
|
|
if (*sest == 0.) {
|
|
*sestpr = 0.;
|
|
if (f2cmax(absgam,absalp) == 0.) {
|
|
sine = 1.;
|
|
cosine = 0.;
|
|
} else {
|
|
sine = -(*gamma);
|
|
cosine = alpha;
|
|
}
|
|
/* Computing MAX */
|
|
d__1 = abs(sine), d__2 = abs(cosine);
|
|
s1 = f2cmax(d__1,d__2);
|
|
*s = sine / s1;
|
|
*c__ = cosine / s1;
|
|
tmp = sqrt(*s * *s + *c__ * *c__);
|
|
*s /= tmp;
|
|
*c__ /= tmp;
|
|
return;
|
|
} else if (absgam <= eps * absest) {
|
|
*s = 0.;
|
|
*c__ = 1.;
|
|
*sestpr = absgam;
|
|
return;
|
|
} else if (absalp <= eps * absest) {
|
|
s1 = absgam;
|
|
s2 = absest;
|
|
if (s1 <= s2) {
|
|
*s = 0.;
|
|
*c__ = 1.;
|
|
*sestpr = s1;
|
|
} else {
|
|
*s = 1.;
|
|
*c__ = 0.;
|
|
*sestpr = s2;
|
|
}
|
|
return;
|
|
} else if (absest <= eps * absalp || absest <= eps * absgam) {
|
|
s1 = absgam;
|
|
s2 = absalp;
|
|
if (s1 <= s2) {
|
|
tmp = s1 / s2;
|
|
*c__ = sqrt(tmp * tmp + 1.);
|
|
*sestpr = absest * (tmp / *c__);
|
|
*s = -(*gamma / s2) / *c__;
|
|
*c__ = d_sign(&c_b5, &alpha) / *c__;
|
|
} else {
|
|
tmp = s2 / s1;
|
|
*s = sqrt(tmp * tmp + 1.);
|
|
*sestpr = absest / *s;
|
|
*c__ = alpha / s1 / *s;
|
|
*s = -d_sign(&c_b5, gamma) / *s;
|
|
}
|
|
return;
|
|
} else {
|
|
|
|
/* normal case */
|
|
|
|
zeta1 = alpha / absest;
|
|
zeta2 = *gamma / absest;
|
|
|
|
/* Computing MAX */
|
|
d__3 = zeta1 * zeta1 + 1. + (d__1 = zeta1 * zeta2, abs(d__1)),
|
|
d__4 = (d__2 = zeta1 * zeta2, abs(d__2)) + zeta2 * zeta2;
|
|
norma = f2cmax(d__3,d__4);
|
|
|
|
/* See if root is closer to zero or to ONE */
|
|
|
|
test = (zeta1 - zeta2) * 2. * (zeta1 + zeta2) + 1.;
|
|
if (test >= 0.) {
|
|
|
|
/* root is close to zero, compute directly */
|
|
|
|
b = (zeta1 * zeta1 + zeta2 * zeta2 + 1.) * .5;
|
|
*c__ = zeta2 * zeta2;
|
|
t = *c__ / (b + sqrt((d__1 = b * b - *c__, abs(d__1))));
|
|
sine = zeta1 / (1. - t);
|
|
cosine = -zeta2 / t;
|
|
*sestpr = sqrt(t + eps * 4. * eps * norma) * absest;
|
|
} else {
|
|
|
|
/* root is closer to ONE, shift by that amount */
|
|
|
|
b = (zeta2 * zeta2 + zeta1 * zeta1 - 1.) * .5;
|
|
*c__ = zeta1 * zeta1;
|
|
if (b >= 0.) {
|
|
t = -(*c__) / (b + sqrt(b * b + *c__));
|
|
} else {
|
|
t = b - sqrt(b * b + *c__);
|
|
}
|
|
sine = -zeta1 / t;
|
|
cosine = -zeta2 / (t + 1.);
|
|
*sestpr = sqrt(t + 1. + eps * 4. * eps * norma) * absest;
|
|
}
|
|
tmp = sqrt(sine * sine + cosine * cosine);
|
|
*s = sine / tmp;
|
|
*c__ = cosine / tmp;
|
|
return;
|
|
|
|
}
|
|
}
|
|
return;
|
|
|
|
/* End of DLAIC1 */
|
|
|
|
} /* dlaic1_ */
|
|
|