1001 lines
28 KiB
C
1001 lines
28 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__9 = 9;
|
|
static integer c__0 = 0;
|
|
static integer c__2 = 2;
|
|
static real c_b23 = 1.f;
|
|
static real c_b24 = 0.f;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b SLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced
|
|
symmetric tridiagonal matrix using the divide and conquer method. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SLAED0 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaed0.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaed0.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaed0.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, */
|
|
/* WORK, IWORK, INFO ) */
|
|
|
|
/* INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ */
|
|
/* INTEGER IWORK( * ) */
|
|
/* REAL D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), */
|
|
/* $ WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SLAED0 computes all eigenvalues and corresponding eigenvectors of a */
|
|
/* > symmetric tridiagonal matrix using the divide and conquer method. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] ICOMPQ */
|
|
/* > \verbatim */
|
|
/* > ICOMPQ is INTEGER */
|
|
/* > = 0: Compute eigenvalues only. */
|
|
/* > = 1: Compute eigenvectors of original dense symmetric matrix */
|
|
/* > also. On entry, Q contains the orthogonal matrix used */
|
|
/* > to reduce the original matrix to tridiagonal form. */
|
|
/* > = 2: Compute eigenvalues and eigenvectors of tridiagonal */
|
|
/* > matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] QSIZ */
|
|
/* > \verbatim */
|
|
/* > QSIZ is INTEGER */
|
|
/* > The dimension of the orthogonal matrix used to reduce */
|
|
/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is REAL array, dimension (N) */
|
|
/* > On entry, the main diagonal of the tridiagonal matrix. */
|
|
/* > On exit, its eigenvalues. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] E */
|
|
/* > \verbatim */
|
|
/* > E is REAL array, dimension (N-1) */
|
|
/* > The off-diagonal elements of the tridiagonal matrix. */
|
|
/* > On exit, E has been destroyed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is REAL array, dimension (LDQ, N) */
|
|
/* > On entry, Q must contain an N-by-N orthogonal matrix. */
|
|
/* > If ICOMPQ = 0 Q is not referenced. */
|
|
/* > If ICOMPQ = 1 On entry, Q is a subset of the columns of the */
|
|
/* > orthogonal matrix used to reduce the full */
|
|
/* > matrix to tridiagonal form corresponding to */
|
|
/* > the subset of the full matrix which is being */
|
|
/* > decomposed at this time. */
|
|
/* > If ICOMPQ = 2 On entry, Q will be the identity matrix. */
|
|
/* > On exit, Q contains the eigenvectors of the */
|
|
/* > tridiagonal matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. If eigenvectors are */
|
|
/* > desired, then LDQ >= f2cmax(1,N). In any case, LDQ >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] QSTORE */
|
|
/* > \verbatim */
|
|
/* > QSTORE is REAL array, dimension (LDQS, N) */
|
|
/* > Referenced only when ICOMPQ = 1. Used to store parts of */
|
|
/* > the eigenvector matrix when the updating matrix multiplies */
|
|
/* > take place. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQS */
|
|
/* > \verbatim */
|
|
/* > LDQS is INTEGER */
|
|
/* > The leading dimension of the array QSTORE. If ICOMPQ = 1, */
|
|
/* > then LDQS >= f2cmax(1,N). In any case, LDQS >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, */
|
|
/* > If ICOMPQ = 0 or 1, the dimension of WORK must be at least */
|
|
/* > 1 + 3*N + 2*N*lg N + 3*N**2 */
|
|
/* > ( lg( N ) = smallest integer k */
|
|
/* > such that 2^k >= N ) */
|
|
/* > If ICOMPQ = 2, the dimension of WORK must be at least */
|
|
/* > 4*N + N**2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, */
|
|
/* > If ICOMPQ = 0 or 1, the dimension of IWORK must be at least */
|
|
/* > 6 + 6*N + 5*N*lg N. */
|
|
/* > ( lg( N ) = smallest integer k */
|
|
/* > such that 2^k >= N ) */
|
|
/* > If ICOMPQ = 2, the dimension of IWORK must be at least */
|
|
/* > 3 + 5*N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: The algorithm failed to compute an eigenvalue while */
|
|
/* > working on the submatrix lying in rows and columns */
|
|
/* > INFO/(N+1) through mod(INFO,N+1). */
|
|
/* > \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 */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void slaed0_(integer *icompq, integer *qsiz, integer *n, real
|
|
*d__, real *e, real *q, integer *ldq, real *qstore, integer *ldqs,
|
|
real *work, integer *iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2;
|
|
real r__1;
|
|
|
|
/* Local variables */
|
|
real temp;
|
|
integer curr, i__, j, k;
|
|
extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *,
|
|
integer *, real *, real *, integer *, real *, integer *, real *,
|
|
real *, integer *);
|
|
integer iperm, indxq, iwrem;
|
|
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
|
|
integer *);
|
|
integer iqptr, tlvls;
|
|
extern /* Subroutine */ void slaed1_(integer *, real *, real *, integer *,
|
|
integer *, real *, integer *, real *, integer *, integer *),
|
|
slaed7_(integer *, integer *, integer *, integer *, integer *,
|
|
integer *, real *, real *, integer *, integer *, real *, integer *
|
|
, real *, integer *, integer *, integer *, integer *, integer *,
|
|
real *, real *, integer *, integer *);
|
|
integer iq, igivcl;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
integer igivnm, submat;
|
|
extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *,
|
|
integer *, real *, integer *);
|
|
integer curprb, subpbs, igivpt, curlvl, matsiz, iprmpt, smlsiz;
|
|
extern /* Subroutine */ void ssteqr_(char *, integer *, real *, real *,
|
|
real *, integer *, real *, integer *);
|
|
integer lgn, msd2, smm1, spm1, spm2;
|
|
|
|
|
|
/* -- 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__;
|
|
--e;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
qstore_dim1 = *ldqs;
|
|
qstore_offset = 1 + qstore_dim1 * 1;
|
|
qstore -= qstore_offset;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
if (*icompq < 0 || *icompq > 2) {
|
|
*info = -1;
|
|
} else if (*icompq == 1 && *qsiz < f2cmax(0,*n)) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*ldq < f2cmax(1,*n)) {
|
|
*info = -7;
|
|
} else if (*ldqs < f2cmax(1,*n)) {
|
|
*info = -9;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SLAED0", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
smlsiz = ilaenv_(&c__9, "SLAED0", " ", &c__0, &c__0, &c__0, &c__0, (
|
|
ftnlen)6, (ftnlen)1);
|
|
|
|
/* Determine the size and placement of the submatrices, and save in */
|
|
/* the leading elements of IWORK. */
|
|
|
|
iwork[1] = *n;
|
|
subpbs = 1;
|
|
tlvls = 0;
|
|
L10:
|
|
if (iwork[subpbs] > smlsiz) {
|
|
for (j = subpbs; j >= 1; --j) {
|
|
iwork[j * 2] = (iwork[j] + 1) / 2;
|
|
iwork[(j << 1) - 1] = iwork[j] / 2;
|
|
/* L20: */
|
|
}
|
|
++tlvls;
|
|
subpbs <<= 1;
|
|
goto L10;
|
|
}
|
|
i__1 = subpbs;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
iwork[j] += iwork[j - 1];
|
|
/* L30: */
|
|
}
|
|
|
|
/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */
|
|
/* using rank-1 modifications (cuts). */
|
|
|
|
spm1 = subpbs - 1;
|
|
i__1 = spm1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
submat = iwork[i__] + 1;
|
|
smm1 = submat - 1;
|
|
d__[smm1] -= (r__1 = e[smm1], abs(r__1));
|
|
d__[submat] -= (r__1 = e[smm1], abs(r__1));
|
|
/* L40: */
|
|
}
|
|
|
|
indxq = (*n << 2) + 3;
|
|
if (*icompq != 2) {
|
|
|
|
/* Set up workspaces for eigenvalues only/accumulate new vectors */
|
|
/* routine */
|
|
|
|
temp = log((real) (*n)) / log(2.f);
|
|
lgn = (integer) temp;
|
|
if (pow_ii(c__2, lgn) < *n) {
|
|
++lgn;
|
|
}
|
|
if (pow_ii(c__2, lgn) < *n) {
|
|
++lgn;
|
|
}
|
|
iprmpt = indxq + *n + 1;
|
|
iperm = iprmpt + *n * lgn;
|
|
iqptr = iperm + *n * lgn;
|
|
igivpt = iqptr + *n + 2;
|
|
igivcl = igivpt + *n * lgn;
|
|
|
|
igivnm = 1;
|
|
iq = igivnm + (*n << 1) * lgn;
|
|
/* Computing 2nd power */
|
|
i__1 = *n;
|
|
iwrem = iq + i__1 * i__1 + 1;
|
|
|
|
/* Initialize pointers */
|
|
|
|
i__1 = subpbs;
|
|
for (i__ = 0; i__ <= i__1; ++i__) {
|
|
iwork[iprmpt + i__] = 1;
|
|
iwork[igivpt + i__] = 1;
|
|
/* L50: */
|
|
}
|
|
iwork[iqptr] = 1;
|
|
}
|
|
|
|
/* Solve each submatrix eigenproblem at the bottom of the divide and */
|
|
/* conquer tree. */
|
|
|
|
curr = 0;
|
|
i__1 = spm1;
|
|
for (i__ = 0; i__ <= i__1; ++i__) {
|
|
if (i__ == 0) {
|
|
submat = 1;
|
|
matsiz = iwork[1];
|
|
} else {
|
|
submat = iwork[i__] + 1;
|
|
matsiz = iwork[i__ + 1] - iwork[i__];
|
|
}
|
|
if (*icompq == 2) {
|
|
ssteqr_("I", &matsiz, &d__[submat], &e[submat], &q[submat +
|
|
submat * q_dim1], ldq, &work[1], info);
|
|
if (*info != 0) {
|
|
goto L130;
|
|
}
|
|
} else {
|
|
ssteqr_("I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 +
|
|
iwork[iqptr + curr]], &matsiz, &work[1], info);
|
|
if (*info != 0) {
|
|
goto L130;
|
|
}
|
|
if (*icompq == 1) {
|
|
sgemm_("N", "N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat *
|
|
q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]],
|
|
&matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1],
|
|
ldqs);
|
|
}
|
|
/* Computing 2nd power */
|
|
i__2 = matsiz;
|
|
iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
|
|
++curr;
|
|
}
|
|
k = 1;
|
|
i__2 = iwork[i__ + 1];
|
|
for (j = submat; j <= i__2; ++j) {
|
|
iwork[indxq + j] = k;
|
|
++k;
|
|
/* L60: */
|
|
}
|
|
/* L70: */
|
|
}
|
|
|
|
/* Successively merge eigensystems of adjacent submatrices */
|
|
/* into eigensystem for the corresponding larger matrix. */
|
|
|
|
/* while ( SUBPBS > 1 ) */
|
|
|
|
curlvl = 1;
|
|
L80:
|
|
if (subpbs > 1) {
|
|
spm2 = subpbs - 2;
|
|
i__1 = spm2;
|
|
for (i__ = 0; i__ <= i__1; i__ += 2) {
|
|
if (i__ == 0) {
|
|
submat = 1;
|
|
matsiz = iwork[2];
|
|
msd2 = iwork[1];
|
|
curprb = 0;
|
|
} else {
|
|
submat = iwork[i__] + 1;
|
|
matsiz = iwork[i__ + 2] - iwork[i__];
|
|
msd2 = matsiz / 2;
|
|
++curprb;
|
|
}
|
|
|
|
/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */
|
|
/* into an eigensystem of size MATSIZ. */
|
|
/* SLAED1 is used only for the full eigensystem of a tridiagonal */
|
|
/* matrix. */
|
|
/* SLAED7 handles the cases in which eigenvalues only or eigenvalues */
|
|
/* and eigenvectors of a full symmetric matrix (which was reduced to */
|
|
/* tridiagonal form) are desired. */
|
|
|
|
if (*icompq == 2) {
|
|
slaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1],
|
|
ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], &
|
|
msd2, &work[1], &iwork[subpbs + 1], info);
|
|
} else {
|
|
slaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[
|
|
submat], &qstore[submat * qstore_dim1 + 1], ldqs, &
|
|
iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, &
|
|
work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm]
|
|
, &iwork[igivpt], &iwork[igivcl], &work[igivnm], &
|
|
work[iwrem], &iwork[subpbs + 1], info);
|
|
}
|
|
if (*info != 0) {
|
|
goto L130;
|
|
}
|
|
iwork[i__ / 2 + 1] = iwork[i__ + 2];
|
|
/* L90: */
|
|
}
|
|
subpbs /= 2;
|
|
++curlvl;
|
|
goto L80;
|
|
}
|
|
|
|
/* end while */
|
|
|
|
/* Re-merge the eigenvalues/vectors which were deflated at the final */
|
|
/* merge step. */
|
|
|
|
if (*icompq == 1) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
j = iwork[indxq + i__];
|
|
work[i__] = d__[j];
|
|
scopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1
|
|
+ 1], &c__1);
|
|
/* L100: */
|
|
}
|
|
scopy_(n, &work[1], &c__1, &d__[1], &c__1);
|
|
} else if (*icompq == 2) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
j = iwork[indxq + i__];
|
|
work[i__] = d__[j];
|
|
scopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1);
|
|
/* L110: */
|
|
}
|
|
scopy_(n, &work[1], &c__1, &d__[1], &c__1);
|
|
slacpy_("A", n, n, &work[*n + 1], n, &q[q_offset], ldq);
|
|
} else {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
j = iwork[indxq + i__];
|
|
work[i__] = d__[j];
|
|
/* L120: */
|
|
}
|
|
scopy_(n, &work[1], &c__1, &d__[1], &c__1);
|
|
}
|
|
goto L140;
|
|
|
|
L130:
|
|
*info = submat * (*n + 1) + submat + matsiz - 1;
|
|
|
|
L140:
|
|
return;
|
|
|
|
/* End of SLAED0 */
|
|
|
|
} /* slaed0_ */
|
|
|