1121 lines
31 KiB
C
1121 lines
31 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublereal c_b3 = -1.;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original
|
|
matrix is tridiagonal. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLAED2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed2.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed2.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed2.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, */
|
|
/* Q2, INDX, INDXC, INDXP, COLTYP, INFO ) */
|
|
|
|
/* INTEGER INFO, K, LDQ, N, N1 */
|
|
/* DOUBLE PRECISION RHO */
|
|
/* INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ), */
|
|
/* $ INDXQ( * ) */
|
|
/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), */
|
|
/* $ W( * ), Z( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLAED2 merges the two sets of eigenvalues together into a single */
|
|
/* > sorted set. Then it tries to deflate the size of the problem. */
|
|
/* > There are two ways in which deflation can occur: when two or more */
|
|
/* > eigenvalues are close together or if there is a tiny entry in the */
|
|
/* > Z vector. For each such occurrence the order of the related secular */
|
|
/* > equation problem is reduced by one. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[out] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > The number of non-deflated eigenvalues, and the order of the */
|
|
/* > related secular equation. 0 <= K <=N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N1 */
|
|
/* > \verbatim */
|
|
/* > N1 is INTEGER */
|
|
/* > The location of the last eigenvalue in the leading sub-matrix. */
|
|
/* > f2cmin(1,N) <= N1 <= N/2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On entry, D contains the eigenvalues of the two submatrices to */
|
|
/* > be combined. */
|
|
/* > On exit, D contains the trailing (N-K) updated eigenvalues */
|
|
/* > (those which were deflated) sorted into increasing order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is DOUBLE PRECISION array, dimension (LDQ, N) */
|
|
/* > On entry, Q contains the eigenvectors of two submatrices in */
|
|
/* > the two square blocks with corners at (1,1), (N1,N1) */
|
|
/* > and (N1+1, N1+1), (N,N). */
|
|
/* > On exit, Q contains the trailing (N-K) updated eigenvectors */
|
|
/* > (those which were deflated) in its last N-K columns. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. LDQ >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] INDXQ */
|
|
/* > \verbatim */
|
|
/* > INDXQ is INTEGER array, dimension (N) */
|
|
/* > The permutation which separately sorts the two sub-problems */
|
|
/* > in D into ascending order. Note that elements in the second */
|
|
/* > half of this permutation must first have N1 added to their */
|
|
/* > values. Destroyed on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] RHO */
|
|
/* > \verbatim */
|
|
/* > RHO is DOUBLE PRECISION */
|
|
/* > On entry, the off-diagonal element associated with the rank-1 */
|
|
/* > cut which originally split the two submatrices which are now */
|
|
/* > being recombined. */
|
|
/* > On exit, RHO has been modified to the value required by */
|
|
/* > DLAED3. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Z */
|
|
/* > \verbatim */
|
|
/* > Z is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On entry, Z contains the updating vector (the last */
|
|
/* > row of the first sub-eigenvector matrix and the first row of */
|
|
/* > the second sub-eigenvector matrix). */
|
|
/* > On exit, the contents of Z have been destroyed by the updating */
|
|
/* > process. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DLAMDA */
|
|
/* > \verbatim */
|
|
/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */
|
|
/* > A copy of the first K eigenvalues which will be used by */
|
|
/* > DLAED3 to form the secular equation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] W */
|
|
/* > \verbatim */
|
|
/* > W is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The first k values of the final deflation-altered z-vector */
|
|
/* > which will be passed to DLAED3. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Q2 */
|
|
/* > \verbatim */
|
|
/* > Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2) */
|
|
/* > A copy of the first K eigenvectors which will be used by */
|
|
/* > DLAED3 in a matrix multiply (DGEMM) to solve for the new */
|
|
/* > eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INDX */
|
|
/* > \verbatim */
|
|
/* > INDX is INTEGER array, dimension (N) */
|
|
/* > The permutation used to sort the contents of DLAMDA into */
|
|
/* > ascending order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INDXC */
|
|
/* > \verbatim */
|
|
/* > INDXC is INTEGER array, dimension (N) */
|
|
/* > The permutation used to arrange the columns of the deflated */
|
|
/* > Q matrix into three groups: the first group contains non-zero */
|
|
/* > elements only at and above N1, the second contains */
|
|
/* > non-zero elements only below N1, and the third is dense. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INDXP */
|
|
/* > \verbatim */
|
|
/* > INDXP is INTEGER array, dimension (N) */
|
|
/* > The permutation used to place deflated values of D at the end */
|
|
/* > of the array. INDXP(1:K) points to the nondeflated D-values */
|
|
/* > and INDXP(K+1:N) points to the deflated eigenvalues. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] COLTYP */
|
|
/* > \verbatim */
|
|
/* > COLTYP is INTEGER array, dimension (N) */
|
|
/* > During execution, a label which will indicate which of the */
|
|
/* > following types a column in the Q2 matrix is: */
|
|
/* > 1 : non-zero in the upper half only; */
|
|
/* > 2 : dense; */
|
|
/* > 3 : non-zero in the lower half only; */
|
|
/* > 4 : deflated. */
|
|
/* > On exit, COLTYP(i) is the number of columns of type i, */
|
|
/* > for i=1 to 4 only. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \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 dlaed2_(integer *k, integer *n, integer *n1, doublereal *
|
|
d__, doublereal *q, integer *ldq, integer *indxq, doublereal *rho,
|
|
doublereal *z__, doublereal *dlamda, doublereal *w, doublereal *q2,
|
|
integer *indx, integer *indxc, integer *indxp, integer *coltyp,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer q_dim1, q_offset, i__1, i__2;
|
|
doublereal d__1, d__2, d__3, d__4;
|
|
|
|
/* Local variables */
|
|
integer imax, jmax;
|
|
extern /* Subroutine */ void drot_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *);
|
|
integer ctot[4];
|
|
doublereal c__;
|
|
integer i__, j;
|
|
doublereal s, t;
|
|
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
|
|
integer *), dcopy_(integer *, doublereal *, integer *, doublereal
|
|
*, integer *);
|
|
integer k2, n2;
|
|
extern doublereal dlapy2_(doublereal *, doublereal *);
|
|
integer ct, nj;
|
|
extern doublereal dlamch_(char *);
|
|
integer pj, js;
|
|
extern integer idamax_(integer *, doublereal *, integer *);
|
|
extern /* Subroutine */ void dlamrg_(integer *, integer *, doublereal *,
|
|
integer *, integer *, integer *), dlacpy_(char *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
integer iq1, iq2, n1p1;
|
|
doublereal eps, tau, tol;
|
|
integer psm[4];
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
--d__;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
--indxq;
|
|
--z__;
|
|
--dlamda;
|
|
--w;
|
|
--q2;
|
|
--indx;
|
|
--indxc;
|
|
--indxp;
|
|
--coltyp;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*ldq < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MIN */
|
|
i__1 = 1, i__2 = *n / 2;
|
|
if (f2cmin(i__1,i__2) > *n1 || *n / 2 < *n1) {
|
|
*info = -3;
|
|
}
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DLAED2", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
n2 = *n - *n1;
|
|
n1p1 = *n1 + 1;
|
|
|
|
if (*rho < 0.) {
|
|
dscal_(&n2, &c_b3, &z__[n1p1], &c__1);
|
|
}
|
|
|
|
/* Normalize z so that norm(z) = 1. Since z is the concatenation of */
|
|
/* two normalized vectors, norm2(z) = sqrt(2). */
|
|
|
|
t = 1. / sqrt(2.);
|
|
dscal_(n, &t, &z__[1], &c__1);
|
|
|
|
/* RHO = ABS( norm(z)**2 * RHO ) */
|
|
|
|
*rho = (d__1 = *rho * 2., abs(d__1));
|
|
|
|
/* Sort the eigenvalues into increasing order */
|
|
|
|
i__1 = *n;
|
|
for (i__ = n1p1; i__ <= i__1; ++i__) {
|
|
indxq[i__] += *n1;
|
|
/* L10: */
|
|
}
|
|
|
|
/* re-integrate the deflated parts from the last pass */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
dlamda[i__] = d__[indxq[i__]];
|
|
/* L20: */
|
|
}
|
|
dlamrg_(n1, &n2, &dlamda[1], &c__1, &c__1, &indxc[1]);
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
indx[i__] = indxq[indxc[i__]];
|
|
/* L30: */
|
|
}
|
|
|
|
/* Calculate the allowable deflation tolerance */
|
|
|
|
imax = idamax_(n, &z__[1], &c__1);
|
|
jmax = idamax_(n, &d__[1], &c__1);
|
|
eps = dlamch_("Epsilon");
|
|
/* Computing MAX */
|
|
d__3 = (d__1 = d__[jmax], abs(d__1)), d__4 = (d__2 = z__[imax], abs(d__2))
|
|
;
|
|
tol = eps * 8. * f2cmax(d__3,d__4);
|
|
|
|
/* If the rank-1 modifier is small enough, no more needs to be done */
|
|
/* except to reorganize Q so that its columns correspond with the */
|
|
/* elements in D. */
|
|
|
|
if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) {
|
|
*k = 0;
|
|
iq2 = 1;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__ = indx[j];
|
|
dcopy_(n, &q[i__ * q_dim1 + 1], &c__1, &q2[iq2], &c__1);
|
|
dlamda[j] = d__[i__];
|
|
iq2 += *n;
|
|
/* L40: */
|
|
}
|
|
dlacpy_("A", n, n, &q2[1], n, &q[q_offset], ldq);
|
|
dcopy_(n, &dlamda[1], &c__1, &d__[1], &c__1);
|
|
goto L190;
|
|
}
|
|
|
|
/* If there are multiple eigenvalues then the problem deflates. Here */
|
|
/* the number of equal eigenvalues are found. As each equal */
|
|
/* eigenvalue is found, an elementary reflector is computed to rotate */
|
|
/* the corresponding eigensubspace so that the corresponding */
|
|
/* components of Z are zero in this new basis. */
|
|
|
|
i__1 = *n1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
coltyp[i__] = 1;
|
|
/* L50: */
|
|
}
|
|
i__1 = *n;
|
|
for (i__ = n1p1; i__ <= i__1; ++i__) {
|
|
coltyp[i__] = 3;
|
|
/* L60: */
|
|
}
|
|
|
|
|
|
*k = 0;
|
|
k2 = *n + 1;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
nj = indx[j];
|
|
if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) {
|
|
|
|
/* Deflate due to small z component. */
|
|
|
|
--k2;
|
|
coltyp[nj] = 4;
|
|
indxp[k2] = nj;
|
|
if (j == *n) {
|
|
goto L100;
|
|
}
|
|
} else {
|
|
pj = nj;
|
|
goto L80;
|
|
}
|
|
/* L70: */
|
|
}
|
|
L80:
|
|
++j;
|
|
nj = indx[j];
|
|
if (j > *n) {
|
|
goto L100;
|
|
}
|
|
if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) {
|
|
|
|
/* Deflate due to small z component. */
|
|
|
|
--k2;
|
|
coltyp[nj] = 4;
|
|
indxp[k2] = nj;
|
|
} else {
|
|
|
|
/* Check if eigenvalues are close enough to allow deflation. */
|
|
|
|
s = z__[pj];
|
|
c__ = z__[nj];
|
|
|
|
/* Find sqrt(a**2+b**2) without overflow or */
|
|
/* destructive underflow. */
|
|
|
|
tau = dlapy2_(&c__, &s);
|
|
t = d__[nj] - d__[pj];
|
|
c__ /= tau;
|
|
s = -s / tau;
|
|
if ((d__1 = t * c__ * s, abs(d__1)) <= tol) {
|
|
|
|
/* Deflation is possible. */
|
|
|
|
z__[nj] = tau;
|
|
z__[pj] = 0.;
|
|
if (coltyp[nj] != coltyp[pj]) {
|
|
coltyp[nj] = 2;
|
|
}
|
|
coltyp[pj] = 4;
|
|
drot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, &
|
|
c__, &s);
|
|
/* Computing 2nd power */
|
|
d__1 = c__;
|
|
/* Computing 2nd power */
|
|
d__2 = s;
|
|
t = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2);
|
|
/* Computing 2nd power */
|
|
d__1 = s;
|
|
/* Computing 2nd power */
|
|
d__2 = c__;
|
|
d__[nj] = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2);
|
|
d__[pj] = t;
|
|
--k2;
|
|
i__ = 1;
|
|
L90:
|
|
if (k2 + i__ <= *n) {
|
|
if (d__[pj] < d__[indxp[k2 + i__]]) {
|
|
indxp[k2 + i__ - 1] = indxp[k2 + i__];
|
|
indxp[k2 + i__] = pj;
|
|
++i__;
|
|
goto L90;
|
|
} else {
|
|
indxp[k2 + i__ - 1] = pj;
|
|
}
|
|
} else {
|
|
indxp[k2 + i__ - 1] = pj;
|
|
}
|
|
pj = nj;
|
|
} else {
|
|
++(*k);
|
|
dlamda[*k] = d__[pj];
|
|
w[*k] = z__[pj];
|
|
indxp[*k] = pj;
|
|
pj = nj;
|
|
}
|
|
}
|
|
goto L80;
|
|
L100:
|
|
|
|
/* Record the last eigenvalue. */
|
|
|
|
++(*k);
|
|
dlamda[*k] = d__[pj];
|
|
w[*k] = z__[pj];
|
|
indxp[*k] = pj;
|
|
|
|
/* Count up the total number of the various types of columns, then */
|
|
/* form a permutation which positions the four column types into */
|
|
/* four uniform groups (although one or more of these groups may be */
|
|
/* empty). */
|
|
|
|
for (j = 1; j <= 4; ++j) {
|
|
ctot[j - 1] = 0;
|
|
/* L110: */
|
|
}
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
ct = coltyp[j];
|
|
++ctot[ct - 1];
|
|
/* L120: */
|
|
}
|
|
|
|
/* PSM(*) = Position in SubMatrix (of types 1 through 4) */
|
|
|
|
psm[0] = 1;
|
|
psm[1] = ctot[0] + 1;
|
|
psm[2] = psm[1] + ctot[1];
|
|
psm[3] = psm[2] + ctot[2];
|
|
*k = *n - ctot[3];
|
|
|
|
/* Fill out the INDXC array so that the permutation which it induces */
|
|
/* will place all type-1 columns first, all type-2 columns next, */
|
|
/* then all type-3's, and finally all type-4's. */
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
js = indxp[j];
|
|
ct = coltyp[js];
|
|
indx[psm[ct - 1]] = js;
|
|
indxc[psm[ct - 1]] = j;
|
|
++psm[ct - 1];
|
|
/* L130: */
|
|
}
|
|
|
|
/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */
|
|
/* and Q2 respectively. The eigenvalues/vectors which were not */
|
|
/* deflated go into the first K slots of DLAMDA and Q2 respectively, */
|
|
/* while those which were deflated go into the last N - K slots. */
|
|
|
|
i__ = 1;
|
|
iq1 = 1;
|
|
iq2 = (ctot[0] + ctot[1]) * *n1 + 1;
|
|
i__1 = ctot[0];
|
|
for (j = 1; j <= i__1; ++j) {
|
|
js = indx[i__];
|
|
dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1);
|
|
z__[i__] = d__[js];
|
|
++i__;
|
|
iq1 += *n1;
|
|
/* L140: */
|
|
}
|
|
|
|
i__1 = ctot[1];
|
|
for (j = 1; j <= i__1; ++j) {
|
|
js = indx[i__];
|
|
dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1);
|
|
dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1);
|
|
z__[i__] = d__[js];
|
|
++i__;
|
|
iq1 += *n1;
|
|
iq2 += n2;
|
|
/* L150: */
|
|
}
|
|
|
|
i__1 = ctot[2];
|
|
for (j = 1; j <= i__1; ++j) {
|
|
js = indx[i__];
|
|
dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1);
|
|
z__[i__] = d__[js];
|
|
++i__;
|
|
iq2 += n2;
|
|
/* L160: */
|
|
}
|
|
|
|
iq1 = iq2;
|
|
i__1 = ctot[3];
|
|
for (j = 1; j <= i__1; ++j) {
|
|
js = indx[i__];
|
|
dcopy_(n, &q[js * q_dim1 + 1], &c__1, &q2[iq2], &c__1);
|
|
iq2 += *n;
|
|
z__[i__] = d__[js];
|
|
++i__;
|
|
/* L170: */
|
|
}
|
|
|
|
/* The deflated eigenvalues and their corresponding vectors go back */
|
|
/* into the last N - K slots of D and Q respectively. */
|
|
|
|
if (*k < *n) {
|
|
dlacpy_("A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq);
|
|
i__1 = *n - *k;
|
|
dcopy_(&i__1, &z__[*k + 1], &c__1, &d__[*k + 1], &c__1);
|
|
}
|
|
|
|
/* Copy CTOT into COLTYP for referencing in DLAED3. */
|
|
|
|
for (j = 1; j <= 4; ++j) {
|
|
coltyp[j] = ctot[j - 1];
|
|
/* L180: */
|
|
}
|
|
|
|
L190:
|
|
return;
|
|
|
|
/* End of DLAED2 */
|
|
|
|
} /* dlaed2_ */
|
|
|