1040 lines
29 KiB
C
1040 lines
29 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef 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 DLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn
|
|
of the tridiagonal matrix LDLT - λI. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLAR1V + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlar1v.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlar1v.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlar1v.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD, */
|
|
/* PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, */
|
|
/* R, ISUPPZ, NRMINV, RESID, RQCORR, WORK ) */
|
|
|
|
/* LOGICAL WANTNC */
|
|
/* INTEGER B1, BN, N, NEGCNT, R */
|
|
/* DOUBLE PRECISION GAPTOL, LAMBDA, MINGMA, NRMINV, PIVMIN, RESID, */
|
|
/* $ RQCORR, ZTZ */
|
|
/* INTEGER ISUPPZ( * ) */
|
|
/* DOUBLE PRECISION D( * ), L( * ), LD( * ), LLD( * ), */
|
|
/* $ WORK( * ) */
|
|
/* DOUBLE PRECISION Z( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLAR1V computes the (scaled) r-th column of the inverse of */
|
|
/* > the sumbmatrix in rows B1 through BN of the tridiagonal matrix */
|
|
/* > L D L**T - sigma I. When sigma is close to an eigenvalue, the */
|
|
/* > computed vector is an accurate eigenvector. Usually, r corresponds */
|
|
/* > to the index where the eigenvector is largest in magnitude. */
|
|
/* > The following steps accomplish this computation : */
|
|
/* > (a) Stationary qd transform, L D L**T - sigma I = L(+) D(+) L(+)**T, */
|
|
/* > (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T, */
|
|
/* > (c) Computation of the diagonal elements of the inverse of */
|
|
/* > L D L**T - sigma I by combining the above transforms, and choosing */
|
|
/* > r as the index where the diagonal of the inverse is (one of the) */
|
|
/* > largest in magnitude. */
|
|
/* > (d) Computation of the (scaled) r-th column of the inverse using the */
|
|
/* > twisted factorization obtained by combining the top part of the */
|
|
/* > the stationary and the bottom part of the progressive transform. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix L D L**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B1 */
|
|
/* > \verbatim */
|
|
/* > B1 is INTEGER */
|
|
/* > First index of the submatrix of L D L**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] BN */
|
|
/* > \verbatim */
|
|
/* > BN is INTEGER */
|
|
/* > Last index of the submatrix of L D L**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LAMBDA */
|
|
/* > \verbatim */
|
|
/* > LAMBDA is DOUBLE PRECISION */
|
|
/* > The shift. In order to compute an accurate eigenvector, */
|
|
/* > LAMBDA should be a good approximation to an eigenvalue */
|
|
/* > of L D L**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] L */
|
|
/* > \verbatim */
|
|
/* > L is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The (n-1) subdiagonal elements of the unit bidiagonal matrix */
|
|
/* > L, in elements 1 to N-1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The n diagonal elements of the diagonal matrix D. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LD */
|
|
/* > \verbatim */
|
|
/* > LD is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The n-1 elements L(i)*D(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LLD */
|
|
/* > \verbatim */
|
|
/* > LLD is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The n-1 elements L(i)*L(i)*D(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] PIVMIN */
|
|
/* > \verbatim */
|
|
/* > PIVMIN is DOUBLE PRECISION */
|
|
/* > The minimum pivot in the Sturm sequence. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GAPTOL */
|
|
/* > \verbatim */
|
|
/* > GAPTOL is DOUBLE PRECISION */
|
|
/* > Tolerance that indicates when eigenvector entries are negligible */
|
|
/* > w.r.t. their contribution to the residual. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On input, all entries of Z must be set to 0. */
|
|
/* > On output, Z contains the (scaled) r-th column of the */
|
|
/* > inverse. The scaling is such that Z(R) equals 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WANTNC */
|
|
/* > \verbatim */
|
|
/* > WANTNC is LOGICAL */
|
|
/* > Specifies whether NEGCNT has to be computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] NEGCNT */
|
|
/* > \verbatim */
|
|
/* > NEGCNT is INTEGER */
|
|
/* > If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin */
|
|
/* > in the matrix factorization L D L**T, and NEGCNT = -1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ZTZ */
|
|
/* > \verbatim */
|
|
/* > ZTZ is DOUBLE PRECISION */
|
|
/* > The square of the 2-norm of Z. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] MINGMA */
|
|
/* > \verbatim */
|
|
/* > MINGMA is DOUBLE PRECISION */
|
|
/* > The reciprocal of the largest (in magnitude) diagonal */
|
|
/* > element of the inverse of L D L**T - sigma I. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] R */
|
|
/* > \verbatim */
|
|
/* > R is INTEGER */
|
|
/* > The twist index for the twisted factorization used to */
|
|
/* > compute Z. */
|
|
/* > On input, 0 <= R <= N. If R is input as 0, R is set to */
|
|
/* > the index where (L D L**T - sigma I)^{-1} is largest */
|
|
/* > in magnitude. If 1 <= R <= N, R is unchanged. */
|
|
/* > On output, R contains the twist index used to compute Z. */
|
|
/* > Ideally, R designates the position of the maximum entry in the */
|
|
/* > eigenvector. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ISUPPZ */
|
|
/* > \verbatim */
|
|
/* > ISUPPZ is INTEGER array, dimension (2) */
|
|
/* > The support of the vector in Z, i.e., the vector Z is */
|
|
/* > nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] NRMINV */
|
|
/* > \verbatim */
|
|
/* > NRMINV is DOUBLE PRECISION */
|
|
/* > NRMINV = 1/SQRT( ZTZ ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RESID */
|
|
/* > \verbatim */
|
|
/* > RESID is DOUBLE PRECISION */
|
|
/* > The residual of the FP vector. */
|
|
/* > RESID = ABS( MINGMA )/SQRT( ZTZ ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RQCORR */
|
|
/* > \verbatim */
|
|
/* > RQCORR is DOUBLE PRECISION */
|
|
/* > The Rayleigh Quotient correction to LAMBDA. */
|
|
/* > RQCORR = MINGMA*TMP */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (4*N) */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleOTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Beresford Parlett, University of California, Berkeley, USA \n */
|
|
/* > Jim Demmel, University of California, Berkeley, USA \n */
|
|
/* > Inderjit Dhillon, University of Texas, Austin, USA \n */
|
|
/* > Osni Marques, LBNL/NERSC, USA \n */
|
|
/* > Christof Voemel, University of California, Berkeley, USA */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlar1v_(integer *n, integer *b1, integer *bn, doublereal
|
|
*lambda, doublereal *d__, doublereal *l, doublereal *ld, doublereal *
|
|
lld, doublereal *pivmin, doublereal *gaptol, doublereal *z__, logical
|
|
*wantnc, integer *negcnt, doublereal *ztz, doublereal *mingma,
|
|
integer *r__, integer *isuppz, doublereal *nrminv, doublereal *resid,
|
|
doublereal *rqcorr, doublereal *work)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1;
|
|
doublereal d__1, d__2, d__3;
|
|
|
|
/* Local variables */
|
|
integer indp, inds, i__;
|
|
doublereal s, dplus;
|
|
integer r1, r2;
|
|
extern doublereal dlamch_(char *);
|
|
extern logical disnan_(doublereal *);
|
|
integer indlpl, indumn;
|
|
doublereal dminus;
|
|
logical sawnan1, sawnan2;
|
|
doublereal eps, tmp;
|
|
integer neg1, neg2;
|
|
|
|
|
|
/* -- 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 */
|
|
--work;
|
|
--isuppz;
|
|
--z__;
|
|
--lld;
|
|
--ld;
|
|
--l;
|
|
--d__;
|
|
|
|
/* Function Body */
|
|
eps = dlamch_("Precision");
|
|
if (*r__ == 0) {
|
|
r1 = *b1;
|
|
r2 = *bn;
|
|
} else {
|
|
r1 = *r__;
|
|
r2 = *r__;
|
|
}
|
|
/* Storage for LPLUS */
|
|
indlpl = 0;
|
|
/* Storage for UMINUS */
|
|
indumn = *n;
|
|
inds = (*n << 1) + 1;
|
|
indp = *n * 3 + 1;
|
|
if (*b1 == 1) {
|
|
work[inds] = 0.;
|
|
} else {
|
|
work[inds + *b1 - 1] = lld[*b1 - 1];
|
|
}
|
|
|
|
/* Compute the stationary transform (using the differential form) */
|
|
/* until the index R2. */
|
|
|
|
sawnan1 = FALSE_;
|
|
neg1 = 0;
|
|
s = work[inds + *b1 - 1] - *lambda;
|
|
i__1 = r1 - 1;
|
|
for (i__ = *b1; i__ <= i__1; ++i__) {
|
|
dplus = d__[i__] + s;
|
|
work[indlpl + i__] = ld[i__] / dplus;
|
|
if (dplus < 0.) {
|
|
++neg1;
|
|
}
|
|
work[inds + i__] = s * work[indlpl + i__] * l[i__];
|
|
s = work[inds + i__] - *lambda;
|
|
/* L50: */
|
|
}
|
|
sawnan1 = disnan_(&s);
|
|
if (sawnan1) {
|
|
goto L60;
|
|
}
|
|
i__1 = r2 - 1;
|
|
for (i__ = r1; i__ <= i__1; ++i__) {
|
|
dplus = d__[i__] + s;
|
|
work[indlpl + i__] = ld[i__] / dplus;
|
|
work[inds + i__] = s * work[indlpl + i__] * l[i__];
|
|
s = work[inds + i__] - *lambda;
|
|
/* L51: */
|
|
}
|
|
sawnan1 = disnan_(&s);
|
|
|
|
L60:
|
|
if (sawnan1) {
|
|
/* Runs a slower version of the above loop if a NaN is detected */
|
|
neg1 = 0;
|
|
s = work[inds + *b1 - 1] - *lambda;
|
|
i__1 = r1 - 1;
|
|
for (i__ = *b1; i__ <= i__1; ++i__) {
|
|
dplus = d__[i__] + s;
|
|
if (abs(dplus) < *pivmin) {
|
|
dplus = -(*pivmin);
|
|
}
|
|
work[indlpl + i__] = ld[i__] / dplus;
|
|
if (dplus < 0.) {
|
|
++neg1;
|
|
}
|
|
work[inds + i__] = s * work[indlpl + i__] * l[i__];
|
|
if (work[indlpl + i__] == 0.) {
|
|
work[inds + i__] = lld[i__];
|
|
}
|
|
s = work[inds + i__] - *lambda;
|
|
/* L70: */
|
|
}
|
|
i__1 = r2 - 1;
|
|
for (i__ = r1; i__ <= i__1; ++i__) {
|
|
dplus = d__[i__] + s;
|
|
if (abs(dplus) < *pivmin) {
|
|
dplus = -(*pivmin);
|
|
}
|
|
work[indlpl + i__] = ld[i__] / dplus;
|
|
work[inds + i__] = s * work[indlpl + i__] * l[i__];
|
|
if (work[indlpl + i__] == 0.) {
|
|
work[inds + i__] = lld[i__];
|
|
}
|
|
s = work[inds + i__] - *lambda;
|
|
/* L71: */
|
|
}
|
|
}
|
|
|
|
/* Compute the progressive transform (using the differential form) */
|
|
/* until the index R1 */
|
|
|
|
sawnan2 = FALSE_;
|
|
neg2 = 0;
|
|
work[indp + *bn - 1] = d__[*bn] - *lambda;
|
|
i__1 = r1;
|
|
for (i__ = *bn - 1; i__ >= i__1; --i__) {
|
|
dminus = lld[i__] + work[indp + i__];
|
|
tmp = d__[i__] / dminus;
|
|
if (dminus < 0.) {
|
|
++neg2;
|
|
}
|
|
work[indumn + i__] = l[i__] * tmp;
|
|
work[indp + i__ - 1] = work[indp + i__] * tmp - *lambda;
|
|
/* L80: */
|
|
}
|
|
tmp = work[indp + r1 - 1];
|
|
sawnan2 = disnan_(&tmp);
|
|
if (sawnan2) {
|
|
/* Runs a slower version of the above loop if a NaN is detected */
|
|
neg2 = 0;
|
|
i__1 = r1;
|
|
for (i__ = *bn - 1; i__ >= i__1; --i__) {
|
|
dminus = lld[i__] + work[indp + i__];
|
|
if (abs(dminus) < *pivmin) {
|
|
dminus = -(*pivmin);
|
|
}
|
|
tmp = d__[i__] / dminus;
|
|
if (dminus < 0.) {
|
|
++neg2;
|
|
}
|
|
work[indumn + i__] = l[i__] * tmp;
|
|
work[indp + i__ - 1] = work[indp + i__] * tmp - *lambda;
|
|
if (tmp == 0.) {
|
|
work[indp + i__ - 1] = d__[i__] - *lambda;
|
|
}
|
|
/* L100: */
|
|
}
|
|
}
|
|
|
|
/* Find the index (from R1 to R2) of the largest (in magnitude) */
|
|
/* diagonal element of the inverse */
|
|
|
|
*mingma = work[inds + r1 - 1] + work[indp + r1 - 1];
|
|
if (*mingma < 0.) {
|
|
++neg1;
|
|
}
|
|
if (*wantnc) {
|
|
*negcnt = neg1 + neg2;
|
|
} else {
|
|
*negcnt = -1;
|
|
}
|
|
if (abs(*mingma) == 0.) {
|
|
*mingma = eps * work[inds + r1 - 1];
|
|
}
|
|
*r__ = r1;
|
|
i__1 = r2 - 1;
|
|
for (i__ = r1; i__ <= i__1; ++i__) {
|
|
tmp = work[inds + i__] + work[indp + i__];
|
|
if (tmp == 0.) {
|
|
tmp = eps * work[inds + i__];
|
|
}
|
|
if (abs(tmp) <= abs(*mingma)) {
|
|
*mingma = tmp;
|
|
*r__ = i__ + 1;
|
|
}
|
|
/* L110: */
|
|
}
|
|
|
|
/* Compute the FP vector: solve N^T v = e_r */
|
|
|
|
isuppz[1] = *b1;
|
|
isuppz[2] = *bn;
|
|
z__[*r__] = 1.;
|
|
*ztz = 1.;
|
|
|
|
/* Compute the FP vector upwards from R */
|
|
|
|
if (! sawnan1 && ! sawnan2) {
|
|
i__1 = *b1;
|
|
for (i__ = *r__ - 1; i__ >= i__1; --i__) {
|
|
z__[i__] = -(work[indlpl + i__] * z__[i__ + 1]);
|
|
if (((d__1 = z__[i__], abs(d__1)) + (d__2 = z__[i__ + 1], abs(
|
|
d__2))) * (d__3 = ld[i__], abs(d__3)) < *gaptol) {
|
|
z__[i__] = 0.;
|
|
isuppz[1] = i__ + 1;
|
|
goto L220;
|
|
}
|
|
*ztz += z__[i__] * z__[i__];
|
|
/* L210: */
|
|
}
|
|
L220:
|
|
;
|
|
} else {
|
|
/* Run slower loop if NaN occurred. */
|
|
i__1 = *b1;
|
|
for (i__ = *r__ - 1; i__ >= i__1; --i__) {
|
|
if (z__[i__ + 1] == 0.) {
|
|
z__[i__] = -(ld[i__ + 1] / ld[i__]) * z__[i__ + 2];
|
|
} else {
|
|
z__[i__] = -(work[indlpl + i__] * z__[i__ + 1]);
|
|
}
|
|
if (((d__1 = z__[i__], abs(d__1)) + (d__2 = z__[i__ + 1], abs(
|
|
d__2))) * (d__3 = ld[i__], abs(d__3)) < *gaptol) {
|
|
z__[i__] = 0.;
|
|
isuppz[1] = i__ + 1;
|
|
goto L240;
|
|
}
|
|
*ztz += z__[i__] * z__[i__];
|
|
/* L230: */
|
|
}
|
|
L240:
|
|
;
|
|
}
|
|
/* Compute the FP vector downwards from R in blocks of size BLKSIZ */
|
|
if (! sawnan1 && ! sawnan2) {
|
|
i__1 = *bn - 1;
|
|
for (i__ = *r__; i__ <= i__1; ++i__) {
|
|
z__[i__ + 1] = -(work[indumn + i__] * z__[i__]);
|
|
if (((d__1 = z__[i__], abs(d__1)) + (d__2 = z__[i__ + 1], abs(
|
|
d__2))) * (d__3 = ld[i__], abs(d__3)) < *gaptol) {
|
|
z__[i__ + 1] = 0.;
|
|
isuppz[2] = i__;
|
|
goto L260;
|
|
}
|
|
*ztz += z__[i__ + 1] * z__[i__ + 1];
|
|
/* L250: */
|
|
}
|
|
L260:
|
|
;
|
|
} else {
|
|
/* Run slower loop if NaN occurred. */
|
|
i__1 = *bn - 1;
|
|
for (i__ = *r__; i__ <= i__1; ++i__) {
|
|
if (z__[i__] == 0.) {
|
|
z__[i__ + 1] = -(ld[i__ - 1] / ld[i__]) * z__[i__ - 1];
|
|
} else {
|
|
z__[i__ + 1] = -(work[indumn + i__] * z__[i__]);
|
|
}
|
|
if (((d__1 = z__[i__], abs(d__1)) + (d__2 = z__[i__ + 1], abs(
|
|
d__2))) * (d__3 = ld[i__], abs(d__3)) < *gaptol) {
|
|
z__[i__ + 1] = 0.;
|
|
isuppz[2] = i__;
|
|
goto L280;
|
|
}
|
|
*ztz += z__[i__ + 1] * z__[i__ + 1];
|
|
/* L270: */
|
|
}
|
|
L280:
|
|
;
|
|
}
|
|
|
|
/* Compute quantities for convergence test */
|
|
|
|
tmp = 1. / *ztz;
|
|
*nrminv = sqrt(tmp);
|
|
*resid = abs(*mingma) * *nrminv;
|
|
*rqcorr = *mingma * tmp;
|
|
|
|
|
|
return;
|
|
|
|
/* End of DLAR1V */
|
|
|
|
} /* dlar1v_ */
|
|
|