912 lines
26 KiB
C
912 lines
26 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/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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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static doublereal c_b22 = 1.;
|
|
static doublereal c_b23 = 0.;
|
|
|
|
/* > \brief \b DLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Us
|
|
ed when the original matrix is tridiagonal. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLAED3 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed3.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed3.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed3.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, */
|
|
/* CTOT, W, S, INFO ) */
|
|
|
|
/* INTEGER INFO, K, LDQ, N, N1 */
|
|
/* DOUBLE PRECISION RHO */
|
|
/* INTEGER CTOT( * ), INDX( * ) */
|
|
/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), */
|
|
/* $ S( * ), W( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLAED3 finds the roots of the secular equation, as defined by the */
|
|
/* > values in D, W, and RHO, between 1 and K. It makes the */
|
|
/* > appropriate calls to DLAED4 and then updates the eigenvectors by */
|
|
/* > multiplying the matrix of eigenvectors of the pair of eigensystems */
|
|
/* > being combined by the matrix of eigenvectors of the K-by-K system */
|
|
/* > which is solved here. */
|
|
/* > */
|
|
/* > This code makes very mild assumptions about floating point */
|
|
/* > arithmetic. It will work on machines with a guard digit in */
|
|
/* > add/subtract, or on those binary machines without guard digits */
|
|
/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
|
|
/* > It could conceivably fail on hexadecimal or decimal machines */
|
|
/* > without guard digits, but we know of none. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > The number of terms in the rational function to be solved by */
|
|
/* > DLAED4. K >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of rows and columns in the Q matrix. */
|
|
/* > N >= K (deflation may result in N>K). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N1 */
|
|
/* > \verbatim */
|
|
/* > N1 is INTEGER */
|
|
/* > The location of the last eigenvalue in the leading submatrix. */
|
|
/* > f2cmin(1,N) <= N1 <= N/2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > D(I) contains the updated eigenvalues for */
|
|
/* > 1 <= I <= K. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
|
|
/* > Initially the first K columns are used as workspace. */
|
|
/* > On output the columns 1 to K contain */
|
|
/* > the updated eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. LDQ >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RHO */
|
|
/* > \verbatim */
|
|
/* > RHO is DOUBLE PRECISION */
|
|
/* > The value of the parameter in the rank one update equation. */
|
|
/* > RHO >= 0 required. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] DLAMDA */
|
|
/* > \verbatim */
|
|
/* > DLAMDA is DOUBLE PRECISION array, dimension (K) */
|
|
/* > The first K elements of this array contain the old roots */
|
|
/* > of the deflated updating problem. These are the poles */
|
|
/* > of the secular equation. May be changed on output by */
|
|
/* > having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */
|
|
/* > Cray-2, or Cray C-90, as described above. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Q2 */
|
|
/* > \verbatim */
|
|
/* > Q2 is DOUBLE PRECISION array, dimension (LDQ2*N) */
|
|
/* > The first K columns of this matrix contain the non-deflated */
|
|
/* > eigenvectors for the split problem. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] INDX */
|
|
/* > \verbatim */
|
|
/* > INDX is INTEGER array, dimension (N) */
|
|
/* > The permutation used to arrange the columns of the deflated */
|
|
/* > Q matrix into three groups (see DLAED2). */
|
|
/* > The rows of the eigenvectors found by DLAED4 must be likewise */
|
|
/* > permuted before the matrix multiply can take place. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CTOT */
|
|
/* > \verbatim */
|
|
/* > CTOT is INTEGER array, dimension (4) */
|
|
/* > A count of the total number of the various types of columns */
|
|
/* > in Q, as described in INDX. The fourth column type is any */
|
|
/* > column which has been deflated. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] W */
|
|
/* > \verbatim */
|
|
/* > W is DOUBLE PRECISION array, dimension (K) */
|
|
/* > The first K elements of this array contain the components */
|
|
/* > of the deflation-adjusted updating vector. Destroyed on */
|
|
/* > output. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION array, dimension (N1 + 1)*K */
|
|
/* > Will contain the eigenvectors of the repaired matrix which */
|
|
/* > will be multiplied by the previously accumulated eigenvectors */
|
|
/* > to update the system. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: if INFO = 1, an eigenvalue did not converge */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2017 */
|
|
|
|
/* > \ingroup auxOTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Jeff Rutter, Computer Science Division, University of California */
|
|
/* > at Berkeley, USA \n */
|
|
/* > Modified by Francoise Tisseur, University of Tennessee */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlaed3_(integer *k, integer *n, integer *n1, doublereal *
|
|
d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda,
|
|
doublereal *q2, integer *indx, integer *ctot, doublereal *w,
|
|
doublereal *s, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer q_dim1, q_offset, i__1, i__2;
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
doublereal temp;
|
|
extern doublereal dnrm2_(integer *, doublereal *, integer *);
|
|
integer i__, j;
|
|
extern /* Subroutine */ void dgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, integer *),
|
|
dcopy_(integer *, doublereal *, integer *, doublereal *, integer
|
|
*), dlaed4_(integer *, integer *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, integer *);
|
|
integer n2;
|
|
extern doublereal dlamc3_(doublereal *, doublereal *);
|
|
integer n12, ii, n23;
|
|
extern /* Subroutine */ void dlacpy_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *),
|
|
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
|
|
doublereal *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
integer iq2;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
--d__;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
--dlamda;
|
|
--q2;
|
|
--indx;
|
|
--ctot;
|
|
--w;
|
|
--s;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
if (*k < 0) {
|
|
*info = -1;
|
|
} else if (*n < *k) {
|
|
*info = -2;
|
|
} else if (*ldq < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DLAED3", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*k == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
|
|
/* be computed with high relative accuracy (barring over/underflow). */
|
|
/* This is a problem on machines without a guard digit in */
|
|
/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
|
|
/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
|
|
/* which on any of these machines zeros out the bottommost */
|
|
/* bit of DLAMDA(I) if it is 1; this makes the subsequent */
|
|
/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
|
|
/* occurs. On binary machines with a guard digit (almost all */
|
|
/* machines) it does not change DLAMDA(I) at all. On hexadecimal */
|
|
/* and decimal machines with a guard digit, it slightly */
|
|
/* changes the bottommost bits of DLAMDA(I). It does not account */
|
|
/* for hexadecimal or decimal machines without guard digits */
|
|
/* (we know of none). We use a subroutine call to compute */
|
|
/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
|
|
/* this code. */
|
|
|
|
i__1 = *k;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
|
|
/* L10: */
|
|
}
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j],
|
|
info);
|
|
|
|
/* If the zero finder fails, the computation is terminated. */
|
|
|
|
if (*info != 0) {
|
|
goto L120;
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
if (*k == 1) {
|
|
goto L110;
|
|
}
|
|
if (*k == 2) {
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
w[1] = q[j * q_dim1 + 1];
|
|
w[2] = q[j * q_dim1 + 2];
|
|
ii = indx[1];
|
|
q[j * q_dim1 + 1] = w[ii];
|
|
ii = indx[2];
|
|
q[j * q_dim1 + 2] = w[ii];
|
|
/* L30: */
|
|
}
|
|
goto L110;
|
|
}
|
|
|
|
/* Compute updated W. */
|
|
|
|
dcopy_(k, &w[1], &c__1, &s[1], &c__1);
|
|
|
|
/* Initialize W(I) = Q(I,I) */
|
|
|
|
i__1 = *ldq + 1;
|
|
dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
|
|
/* L40: */
|
|
}
|
|
i__2 = *k;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
i__1 = *k;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
d__1 = sqrt(-w[i__]);
|
|
w[i__] = d_sign(&d__1, &s[i__]);
|
|
/* L70: */
|
|
}
|
|
|
|
/* Compute eigenvectors of the modified rank-1 modification. */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *k;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
s[i__] = w[i__] / q[i__ + j * q_dim1];
|
|
/* L80: */
|
|
}
|
|
temp = dnrm2_(k, &s[1], &c__1);
|
|
i__2 = *k;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
ii = indx[i__];
|
|
q[i__ + j * q_dim1] = s[ii] / temp;
|
|
/* L90: */
|
|
}
|
|
/* L100: */
|
|
}
|
|
|
|
/* Compute the updated eigenvectors. */
|
|
|
|
L110:
|
|
|
|
n2 = *n - *n1;
|
|
n12 = ctot[1] + ctot[2];
|
|
n23 = ctot[2] + ctot[3];
|
|
|
|
dlacpy_("A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23);
|
|
iq2 = *n1 * n12 + 1;
|
|
if (n23 != 0) {
|
|
dgemm_("N", "N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, &
|
|
c_b23, &q[*n1 + 1 + q_dim1], ldq);
|
|
} else {
|
|
dlaset_("A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq);
|
|
}
|
|
|
|
dlacpy_("A", &n12, k, &q[q_offset], ldq, &s[1], &n12);
|
|
if (n12 != 0) {
|
|
dgemm_("N", "N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23,
|
|
&q[q_offset], ldq);
|
|
} else {
|
|
dlaset_("A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq);
|
|
}
|
|
|
|
|
|
L120:
|
|
return;
|
|
|
|
/* End of DLAED3 */
|
|
|
|
} /* dlaed3_ */
|
|
|