1070 lines
34 KiB
C
1070 lines
34 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_b11 = 0.;
|
|
static doublereal c_b12 = 1.;
|
|
static integer c__12 = 12;
|
|
static integer c__2 = 2;
|
|
static integer c__49 = 49;
|
|
|
|
/* > \brief \b DHSEQR */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DHSEQR + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dhseqr.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dhseqr.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dhseqr.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z, */
|
|
/* LDZ, WORK, LWORK, INFO ) */
|
|
|
|
/* INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N */
|
|
/* CHARACTER COMPZ, JOB */
|
|
/* DOUBLE PRECISION H( LDH, * ), WI( * ), WORK( * ), WR( * ), */
|
|
/* $ Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DHSEQR computes the eigenvalues of a Hessenberg matrix H */
|
|
/* > and, optionally, the matrices T and Z from the Schur decomposition */
|
|
/* > H = Z T Z**T, where T is an upper quasi-triangular matrix (the */
|
|
/* > Schur form), and Z is the orthogonal matrix of Schur vectors. */
|
|
/* > */
|
|
/* > Optionally Z may be postmultiplied into an input orthogonal */
|
|
/* > matrix Q so that this routine can give the Schur factorization */
|
|
/* > of a matrix A which has been reduced to the Hessenberg form H */
|
|
/* > by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOB */
|
|
/* > \verbatim */
|
|
/* > JOB is CHARACTER*1 */
|
|
/* > = 'E': compute eigenvalues only; */
|
|
/* > = 'S': compute eigenvalues and the Schur form T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] COMPZ */
|
|
/* > \verbatim */
|
|
/* > COMPZ is CHARACTER*1 */
|
|
/* > = 'N': no Schur vectors are computed; */
|
|
/* > = 'I': Z is initialized to the unit matrix and the matrix Z */
|
|
/* > of Schur vectors of H is returned; */
|
|
/* > = 'V': Z must contain an orthogonal matrix Q on entry, and */
|
|
/* > the product Q*Z is returned. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix H. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ILO */
|
|
/* > \verbatim */
|
|
/* > ILO is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IHI */
|
|
/* > \verbatim */
|
|
/* > IHI is INTEGER */
|
|
/* > */
|
|
/* > It is assumed that H is already upper triangular in rows */
|
|
/* > and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
|
|
/* > set by a previous call to DGEBAL, and then passed to ZGEHRD */
|
|
/* > when the matrix output by DGEBAL is reduced to Hessenberg */
|
|
/* > form. Otherwise ILO and IHI should be set to 1 and N */
|
|
/* > respectively. If N > 0, then 1 <= ILO <= IHI <= N. */
|
|
/* > If N = 0, then ILO = 1 and IHI = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] H */
|
|
/* > \verbatim */
|
|
/* > H is DOUBLE PRECISION array, dimension (LDH,N) */
|
|
/* > On entry, the upper Hessenberg matrix H. */
|
|
/* > On exit, if INFO = 0 and JOB = 'S', then H contains the */
|
|
/* > upper quasi-triangular matrix T from the Schur decomposition */
|
|
/* > (the Schur form); 2-by-2 diagonal blocks (corresponding to */
|
|
/* > complex conjugate pairs of eigenvalues) are returned in */
|
|
/* > standard form, with H(i,i) = H(i+1,i+1) and */
|
|
/* > H(i+1,i)*H(i,i+1) < 0. If INFO = 0 and JOB = 'E', the */
|
|
/* > contents of H are unspecified on exit. (The output value of */
|
|
/* > H when INFO > 0 is given under the description of INFO */
|
|
/* > below.) */
|
|
/* > */
|
|
/* > Unlike earlier versions of DHSEQR, this subroutine may */
|
|
/* > explicitly H(i,j) = 0 for i > j and j = 1, 2, ... ILO-1 */
|
|
/* > or j = IHI+1, IHI+2, ... N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDH */
|
|
/* > \verbatim */
|
|
/* > LDH is INTEGER */
|
|
/* > The leading dimension of the array H. LDH >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WR */
|
|
/* > \verbatim */
|
|
/* > WR is DOUBLE PRECISION array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WI */
|
|
/* > \verbatim */
|
|
/* > WI is DOUBLE PRECISION array, dimension (N) */
|
|
/* > */
|
|
/* > The real and imaginary parts, respectively, of the computed */
|
|
/* > eigenvalues. If two eigenvalues are computed as a complex */
|
|
/* > conjugate pair, they are stored in consecutive elements of */
|
|
/* > WR and WI, say the i-th and (i+1)th, with WI(i) > 0 and */
|
|
/* > WI(i+1) < 0. If JOB = 'S', the eigenvalues are stored in */
|
|
/* > the same order as on the diagonal of the Schur form returned */
|
|
/* > in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 */
|
|
/* > diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and */
|
|
/* > WI(i+1) = -WI(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is DOUBLE PRECISION array, dimension (LDZ,N) */
|
|
/* > If COMPZ = 'N', Z is not referenced. */
|
|
/* > If COMPZ = 'I', on entry Z need not be set and on exit, */
|
|
/* > if INFO = 0, Z contains the orthogonal matrix Z of the Schur */
|
|
/* > vectors of H. If COMPZ = 'V', on entry Z must contain an */
|
|
/* > N-by-N matrix Q, which is assumed to be equal to the unit */
|
|
/* > matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, */
|
|
/* > if INFO = 0, Z contains Q*Z. */
|
|
/* > Normally Q is the orthogonal matrix generated by DORGHR */
|
|
/* > after the call to DGEHRD which formed the Hessenberg matrix */
|
|
/* > H. (The output value of Z when INFO > 0 is given under */
|
|
/* > the description of INFO below.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. if COMPZ = 'I' or */
|
|
/* > COMPZ = 'V', then LDZ >= MAX(1,N). Otherwise, LDZ >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (LWORK) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns an estimate of */
|
|
/* > the optimal value for LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= f2cmax(1,N) */
|
|
/* > is sufficient and delivers very good and sometimes */
|
|
/* > optimal performance. However, LWORK as large as 11*N */
|
|
/* > may be required for optimal performance. A workspace */
|
|
/* > query is recommended to determine the optimal workspace */
|
|
/* > size. */
|
|
/* > */
|
|
/* > If LWORK = -1, then DHSEQR does a workspace query. */
|
|
/* > In this case, DHSEQR checks the input parameters and */
|
|
/* > estimates the optimal workspace size for the given */
|
|
/* > values of N, ILO and IHI. The estimate is returned */
|
|
/* > in WORK(1). No error message related to LWORK is */
|
|
/* > issued by XERBLA. Neither H nor Z are accessed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal */
|
|
/* > value */
|
|
/* > > 0: if INFO = i, DHSEQR failed to compute all of */
|
|
/* > the eigenvalues. Elements 1:ilo-1 and i+1:n of WR */
|
|
/* > and WI contain those eigenvalues which have been */
|
|
/* > successfully computed. (Failures are rare.) */
|
|
/* > */
|
|
/* > If INFO > 0 and JOB = 'E', then on exit, the */
|
|
/* > remaining unconverged eigenvalues are the eigen- */
|
|
/* > values of the upper Hessenberg matrix rows and */
|
|
/* > columns ILO through INFO of the final, output */
|
|
/* > value of H. */
|
|
/* > */
|
|
/* > If INFO > 0 and JOB = 'S', then on exit */
|
|
/* > */
|
|
/* > (*) (initial value of H)*U = U*(final value of H) */
|
|
/* > */
|
|
/* > where U is an orthogonal matrix. The final */
|
|
/* > value of H is upper Hessenberg and quasi-triangular */
|
|
/* > in rows and columns INFO+1 through IHI. */
|
|
/* > */
|
|
/* > If INFO > 0 and COMPZ = 'V', then on exit */
|
|
/* > */
|
|
/* > (final value of Z) = (initial value of Z)*U */
|
|
/* > */
|
|
/* > where U is the orthogonal matrix in (*) (regard- */
|
|
/* > less of the value of JOB.) */
|
|
/* > */
|
|
/* > If INFO > 0 and COMPZ = 'I', then on exit */
|
|
/* > (final value of Z) = U */
|
|
/* > where U is the orthogonal matrix in (*) (regard- */
|
|
/* > less of the value of JOB.) */
|
|
/* > */
|
|
/* > If INFO > 0 and COMPZ = 'N', then Z is not */
|
|
/* > accessed. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleOTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Karen Braman and Ralph Byers, Department of Mathematics, */
|
|
/* > University of Kansas, USA */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Default values supplied by */
|
|
/* > ILAENV(ISPEC,'DHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK). */
|
|
/* > It is suggested that these defaults be adjusted in order */
|
|
/* > to attain best performance in each particular */
|
|
/* > computational environment. */
|
|
/* > */
|
|
/* > ISPEC=12: The DLAHQR vs DLAQR0 crossover point. */
|
|
/* > Default: 75. (Must be at least 11.) */
|
|
/* > */
|
|
/* > ISPEC=13: Recommended deflation window size. */
|
|
/* > This depends on ILO, IHI and NS. NS is the */
|
|
/* > number of simultaneous shifts returned */
|
|
/* > by ILAENV(ISPEC=15). (See ISPEC=15 below.) */
|
|
/* > The default for (IHI-ILO+1) <= 500 is NS. */
|
|
/* > The default for (IHI-ILO+1) > 500 is 3*NS/2. */
|
|
/* > */
|
|
/* > ISPEC=14: Nibble crossover point. (See IPARMQ for */
|
|
/* > details.) Default: 14% of deflation window */
|
|
/* > size. */
|
|
/* > */
|
|
/* > ISPEC=15: Number of simultaneous shifts in a multishift */
|
|
/* > QR iteration. */
|
|
/* > */
|
|
/* > If IHI-ILO+1 is ... */
|
|
/* > */
|
|
/* > greater than ...but less ... the */
|
|
/* > or equal to ... than default is */
|
|
/* > */
|
|
/* > 1 30 NS = 2(+) */
|
|
/* > 30 60 NS = 4(+) */
|
|
/* > 60 150 NS = 10(+) */
|
|
/* > 150 590 NS = ** */
|
|
/* > 590 3000 NS = 64 */
|
|
/* > 3000 6000 NS = 128 */
|
|
/* > 6000 infinity NS = 256 */
|
|
/* > */
|
|
/* > (+) By default some or all matrices of this order */
|
|
/* > are passed to the implicit double shift routine */
|
|
/* > DLAHQR and this parameter is ignored. See */
|
|
/* > ISPEC=12 above and comments in IPARMQ for */
|
|
/* > details. */
|
|
/* > */
|
|
/* > (**) The asterisks (**) indicate an ad-hoc */
|
|
/* > function of N increasing from 10 to 64. */
|
|
/* > */
|
|
/* > ISPEC=16: Select structured matrix multiply. */
|
|
/* > If the number of simultaneous shifts (specified */
|
|
/* > by ISPEC=15) is less than 14, then the default */
|
|
/* > for ISPEC=16 is 0. Otherwise the default for */
|
|
/* > ISPEC=16 is 2. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
|
|
/* > Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */
|
|
/* > Performance, SIAM Journal of Matrix Analysis, volume 23, pages */
|
|
/* > 929--947, 2002. */
|
|
/* > \n */
|
|
/* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
|
|
/* > Algorithm Part II: Aggressive Early Deflation, SIAM Journal */
|
|
/* > of Matrix Analysis, volume 23, pages 948--973, 2002. */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dhseqr_(char *job, char *compz, integer *n, integer *ilo,
|
|
integer *ihi, doublereal *h__, integer *ldh, doublereal *wr,
|
|
doublereal *wi, doublereal *z__, integer *ldz, doublereal *work,
|
|
integer *lwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
address a__1[2];
|
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integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2[2], i__3;
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doublereal d__1;
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char ch__1[2];
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/* Local variables */
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integer kbot, nmin, i__;
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extern logical lsame_(char *, char *);
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logical initz;
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doublereal workl[49];
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logical wantt, wantz;
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extern /* Subroutine */ void dlaqr0_(logical *, logical *, integer *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *, integer *, doublereal *, integer *,
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doublereal *, integer *, integer *);
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doublereal hl[2401] /* was [49][49] */;
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extern /* Subroutine */ void dlahqr_(logical *, logical *, integer *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *, integer *, doublereal *, integer *,
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integer *), dlacpy_(char *, integer *, integer *, doublereal *,
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integer *, doublereal *, integer *), dlaset_(char *,
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integer *, integer *, doublereal *, doublereal *, doublereal *,
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integer *);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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logical lquery;
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/* -- LAPACK computational routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* December 2016 */
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/* ===================================================================== */
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/* ==== Matrices of order NTINY or smaller must be processed by */
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/* . DLAHQR because of insufficient subdiagonal scratch space. */
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/* . (This is a hard limit.) ==== */
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/* ==== NL allocates some local workspace to help small matrices */
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/* . through a rare DLAHQR failure. NL > NTINY = 15 is */
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/* . required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom- */
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/* . mended. (The default value of NMIN is 75.) Using NL = 49 */
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/* . allows up to six simultaneous shifts and a 16-by-16 */
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/* . deflation window. ==== */
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/* ==== Decode and check the input parameters. ==== */
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/* Parameter adjustments */
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h_dim1 = *ldh;
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h_offset = 1 + h_dim1 * 1;
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h__ -= h_offset;
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--wr;
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--wi;
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z_dim1 = *ldz;
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z_offset = 1 + z_dim1 * 1;
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z__ -= z_offset;
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--work;
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/* Function Body */
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wantt = lsame_(job, "S");
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initz = lsame_(compz, "I");
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wantz = initz || lsame_(compz, "V");
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work[1] = (doublereal) f2cmax(1,*n);
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lquery = *lwork == -1;
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*info = 0;
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if (! lsame_(job, "E") && ! wantt) {
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*info = -1;
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} else if (! lsame_(compz, "N") && ! wantz) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (*ilo < 1 || *ilo > f2cmax(1,*n)) {
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*info = -4;
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} else if (*ihi < f2cmin(*ilo,*n) || *ihi > *n) {
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*info = -5;
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} else if (*ldh < f2cmax(1,*n)) {
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*info = -7;
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} else if (*ldz < 1 || wantz && *ldz < f2cmax(1,*n)) {
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*info = -11;
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} else if (*lwork < f2cmax(1,*n) && ! lquery) {
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*info = -13;
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}
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if (*info != 0) {
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/* ==== Quick return in case of invalid argument. ==== */
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i__1 = -(*info);
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xerbla_("DHSEQR", &i__1, (ftnlen)6);
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return;
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} else if (*n == 0) {
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/* ==== Quick return in case N = 0; nothing to do. ==== */
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return;
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} else if (lquery) {
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/* ==== Quick return in case of a workspace query ==== */
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dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[
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1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
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/* ==== Ensure reported workspace size is backward-compatible with */
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/* . previous LAPACK versions. ==== */
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/* Computing MAX */
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d__1 = (doublereal) f2cmax(1,*n);
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work[1] = f2cmax(d__1,work[1]);
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return;
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} else {
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/* ==== copy eigenvalues isolated by DGEBAL ==== */
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i__1 = *ilo - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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wr[i__] = h__[i__ + i__ * h_dim1];
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wi[i__] = 0.;
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/* L10: */
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}
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i__1 = *n;
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for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
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wr[i__] = h__[i__ + i__ * h_dim1];
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wi[i__] = 0.;
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/* L20: */
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}
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/* ==== Initialize Z, if requested ==== */
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if (initz) {
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dlaset_("A", n, n, &c_b11, &c_b12, &z__[z_offset], ldz)
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;
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}
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/* ==== Quick return if possible ==== */
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if (*ilo == *ihi) {
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wr[*ilo] = h__[*ilo + *ilo * h_dim1];
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wi[*ilo] = 0.;
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return;
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}
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/* ==== DLAHQR/DLAQR0 crossover point ==== */
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/* Writing concatenation */
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i__2[0] = 1, a__1[0] = job;
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i__2[1] = 1, a__1[1] = compz;
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s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
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nmin = ilaenv_(&c__12, "DHSEQR", ch__1, n, ilo, ihi, lwork, (ftnlen)6,
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(ftnlen)2);
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nmin = f2cmax(15,nmin);
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/* ==== DLAQR0 for big matrices; DLAHQR for small ones ==== */
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if (*n > nmin) {
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dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1],
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&wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork,
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info);
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} else {
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/* ==== Small matrix ==== */
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dlahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1],
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&wi[1], ilo, ihi, &z__[z_offset], ldz, info);
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if (*info > 0) {
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/* ==== A rare DLAHQR failure! DLAQR0 sometimes succeeds */
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/* . when DLAHQR fails. ==== */
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kbot = *info;
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if (*n >= 49) {
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/* ==== Larger matrices have enough subdiagonal scratch */
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/* . space to call DLAQR0 directly. ==== */
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dlaqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset],
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ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset],
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ldz, &work[1], lwork, info);
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} else {
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/* ==== Tiny matrices don't have enough subdiagonal */
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/* . scratch space to benefit from DLAQR0. Hence, */
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/* . tiny matrices must be copied into a larger */
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/* . array before calling DLAQR0. ==== */
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dlacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49);
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hl[*n + 1 + *n * 49 - 50] = 0.;
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i__1 = 49 - *n;
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dlaset_("A", &c__49, &i__1, &c_b11, &c_b11, &hl[(*n + 1) *
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49 - 49], &c__49);
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dlaqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, &
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wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz,
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workl, &c__49, info);
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if (wantt || *info != 0) {
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dlacpy_("A", n, n, hl, &c__49, &h__[h_offset], ldh);
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}
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}
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}
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}
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/* ==== Clear out the trash, if necessary. ==== */
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if ((wantt || *info != 0) && *n > 2) {
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i__1 = *n - 2;
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i__3 = *n - 2;
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dlaset_("L", &i__1, &i__3, &c_b11, &c_b11, &h__[h_dim1 + 3], ldh);
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}
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/* ==== Ensure reported workspace size is backward-compatible with */
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/* . previous LAPACK versions. ==== */
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/* Computing MAX */
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d__1 = (doublereal) f2cmax(1,*n);
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work[1] = f2cmax(d__1,work[1]);
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}
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/* ==== End of DHSEQR ==== */
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return;
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} /* dhseqr_ */
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