1229 lines
36 KiB
C
1229 lines
36 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 complex c_b1 = {0.f,0.f};
|
|
static complex c_b2 = {1.f,0.f};
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static logical c_true = TRUE_;
|
|
static integer c__12 = 12;
|
|
|
|
/* > \brief \b CLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and defl
|
|
ate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CLAQR3 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/claqr3.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/claqr3.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/claqr3.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, */
|
|
/* IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, */
|
|
/* NV, WV, LDWV, WORK, LWORK ) */
|
|
|
|
/* INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV, */
|
|
/* $ LDZ, LWORK, N, ND, NH, NS, NV, NW */
|
|
/* LOGICAL WANTT, WANTZ */
|
|
/* COMPLEX H( LDH, * ), SH( * ), T( LDT, * ), V( LDV, * ), */
|
|
/* $ WORK( * ), WV( LDWV, * ), Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Aggressive early deflation: */
|
|
/* > */
|
|
/* > CLAQR3 accepts as input an upper Hessenberg matrix */
|
|
/* > H and performs an unitary similarity transformation */
|
|
/* > designed to detect and deflate fully converged eigenvalues from */
|
|
/* > a trailing principal submatrix. On output H has been over- */
|
|
/* > written by a new Hessenberg matrix that is a perturbation of */
|
|
/* > an unitary similarity transformation of H. It is to be */
|
|
/* > hoped that the final version of H has many zero subdiagonal */
|
|
/* > entries. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] WANTT */
|
|
/* > \verbatim */
|
|
/* > WANTT is LOGICAL */
|
|
/* > If .TRUE., then the Hessenberg matrix H is fully updated */
|
|
/* > so that the triangular Schur factor may be */
|
|
/* > computed (in cooperation with the calling subroutine). */
|
|
/* > If .FALSE., then only enough of H is updated to preserve */
|
|
/* > the eigenvalues. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WANTZ */
|
|
/* > \verbatim */
|
|
/* > WANTZ is LOGICAL */
|
|
/* > If .TRUE., then the unitary matrix Z is updated so */
|
|
/* > so that the unitary Schur factor may be computed */
|
|
/* > (in cooperation with the calling subroutine). */
|
|
/* > If .FALSE., then Z is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix H and (if WANTZ is .TRUE.) the */
|
|
/* > order of the unitary matrix Z. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KTOP */
|
|
/* > \verbatim */
|
|
/* > KTOP is INTEGER */
|
|
/* > It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. */
|
|
/* > KBOT and KTOP together determine an isolated block */
|
|
/* > along the diagonal of the Hessenberg matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KBOT */
|
|
/* > \verbatim */
|
|
/* > KBOT is INTEGER */
|
|
/* > It is assumed without a check that either */
|
|
/* > KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together */
|
|
/* > determine an isolated block along the diagonal of the */
|
|
/* > Hessenberg matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NW */
|
|
/* > \verbatim */
|
|
/* > NW is INTEGER */
|
|
/* > Deflation window size. 1 <= NW <= (KBOT-KTOP+1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] H */
|
|
/* > \verbatim */
|
|
/* > H is COMPLEX array, dimension (LDH,N) */
|
|
/* > On input the initial N-by-N section of H stores the */
|
|
/* > Hessenberg matrix undergoing aggressive early deflation. */
|
|
/* > On output H has been transformed by a unitary */
|
|
/* > similarity transformation, perturbed, and the returned */
|
|
/* > to Hessenberg form that (it is to be hoped) has some */
|
|
/* > zero subdiagonal entries. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDH */
|
|
/* > \verbatim */
|
|
/* > LDH is INTEGER */
|
|
/* > Leading dimension of H just as declared in the calling */
|
|
/* > subroutine. N <= LDH */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ILOZ */
|
|
/* > \verbatim */
|
|
/* > ILOZ is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IHIZ */
|
|
/* > \verbatim */
|
|
/* > IHIZ is INTEGER */
|
|
/* > Specify the rows of Z to which transformations must be */
|
|
/* > applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX array, dimension (LDZ,N) */
|
|
/* > IF WANTZ is .TRUE., then on output, the unitary */
|
|
/* > similarity transformation mentioned above has been */
|
|
/* > accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. */
|
|
/* > If WANTZ is .FALSE., then Z is unreferenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of Z just as declared in the */
|
|
/* > calling subroutine. 1 <= LDZ. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] NS */
|
|
/* > \verbatim */
|
|
/* > NS is INTEGER */
|
|
/* > The number of unconverged (ie approximate) eigenvalues */
|
|
/* > returned in SR and SI that may be used as shifts by the */
|
|
/* > calling subroutine. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ND */
|
|
/* > \verbatim */
|
|
/* > ND is INTEGER */
|
|
/* > The number of converged eigenvalues uncovered by this */
|
|
/* > subroutine. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SH */
|
|
/* > \verbatim */
|
|
/* > SH is COMPLEX array, dimension (KBOT) */
|
|
/* > On output, approximate eigenvalues that may */
|
|
/* > be used for shifts are stored in SH(KBOT-ND-NS+1) */
|
|
/* > through SR(KBOT-ND). Converged eigenvalues are */
|
|
/* > stored in SH(KBOT-ND+1) through SH(KBOT). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] V */
|
|
/* > \verbatim */
|
|
/* > V is COMPLEX array, dimension (LDV,NW) */
|
|
/* > An NW-by-NW work array. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDV */
|
|
/* > \verbatim */
|
|
/* > LDV is INTEGER */
|
|
/* > The leading dimension of V just as declared in the */
|
|
/* > calling subroutine. NW <= LDV */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NH */
|
|
/* > \verbatim */
|
|
/* > NH is INTEGER */
|
|
/* > The number of columns of T. NH >= NW. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] T */
|
|
/* > \verbatim */
|
|
/* > T is COMPLEX array, dimension (LDT,NW) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of T just as declared in the */
|
|
/* > calling subroutine. NW <= LDT */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NV */
|
|
/* > \verbatim */
|
|
/* > NV is INTEGER */
|
|
/* > The number of rows of work array WV available for */
|
|
/* > workspace. NV >= NW. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WV */
|
|
/* > \verbatim */
|
|
/* > WV is COMPLEX array, dimension (LDWV,NW) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDWV */
|
|
/* > \verbatim */
|
|
/* > LDWV is INTEGER */
|
|
/* > The leading dimension of W just as declared in the */
|
|
/* > calling subroutine. NW <= LDV */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX array, dimension (LWORK) */
|
|
/* > On exit, WORK(1) is set to an estimate of the optimal value */
|
|
/* > of LWORK for the given values of N, NW, KTOP and KBOT. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the work array WORK. LWORK = 2*NW */
|
|
/* > suffices, but greater efficiency may result from larger */
|
|
/* > values of LWORK. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; CLAQR3 */
|
|
/* > only estimates the optimal workspace size for the given */
|
|
/* > values of N, NW, KTOP and KBOT. The estimate is returned */
|
|
/* > in WORK(1). No error message related to LWORK is issued */
|
|
/* > by XERBLA. Neither H nor Z are accessed. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup complexOTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Karen Braman and Ralph Byers, Department of Mathematics, */
|
|
/* > University of Kansas, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void claqr3_(logical *wantt, logical *wantz, integer *n,
|
|
integer *ktop, integer *kbot, integer *nw, complex *h__, integer *ldh,
|
|
integer *iloz, integer *ihiz, complex *z__, integer *ldz, integer *
|
|
ns, integer *nd, complex *sh, complex *v, integer *ldv, integer *nh,
|
|
complex *t, integer *ldt, integer *nv, complex *wv, integer *ldwv,
|
|
complex *work, integer *lwork)
|
|
{
|
|
/* System generated locals */
|
|
integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1,
|
|
wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
|
|
real r__1, r__2, r__3, r__4, r__5, r__6;
|
|
complex q__1, q__2;
|
|
|
|
/* Local variables */
|
|
complex beta;
|
|
integer kcol, info, nmin, ifst, ilst, ltop, krow, i__, j;
|
|
complex s;
|
|
extern /* Subroutine */ void clarf_(char *, integer *, integer *, complex *
|
|
, integer *, complex *, complex *, integer *, complex *),
|
|
cgemm_(char *, char *, integer *, integer *, integer *, complex *,
|
|
complex *, integer *, complex *, integer *, complex *, complex *,
|
|
integer *), ccopy_(integer *, complex *, integer
|
|
*, complex *, integer *);
|
|
integer infqr, kwtop;
|
|
extern /* Subroutine */ void claqr4_(logical *, logical *, integer *,
|
|
integer *, integer *, complex *, integer *, complex *, integer *,
|
|
integer *, complex *, integer *, complex *, integer *, integer *),
|
|
slabad_(real *, real *), cgehrd_(integer *, integer *, integer *,
|
|
complex *, integer *, complex *, complex *, integer *, integer *)
|
|
, clarfg_(integer *, complex *, complex *, integer *, complex *);
|
|
integer jw;
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ void clahqr_(logical *, logical *, integer *,
|
|
integer *, integer *, complex *, integer *, complex *, integer *,
|
|
integer *, complex *, integer *, integer *), clacpy_(char *,
|
|
integer *, integer *, complex *, integer *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex
|
|
*, complex *, integer *);
|
|
real safmin, safmax;
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ void ctrexc_(char *, integer *, complex *, integer
|
|
*, complex *, integer *, integer *, integer *, integer *),
|
|
cunmhr_(char *, char *, integer *, integer *, integer *, integer
|
|
*, complex *, integer *, complex *, complex *, integer *, complex
|
|
*, integer *, integer *);
|
|
real smlnum;
|
|
integer lwkopt;
|
|
real foo;
|
|
integer kln;
|
|
complex tau;
|
|
integer knt;
|
|
real ulp;
|
|
integer lwk1, lwk2, lwk3;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ================================================================ */
|
|
|
|
|
|
/* ==== Estimate optimal workspace. ==== */
|
|
|
|
/* Parameter adjustments */
|
|
h_dim1 = *ldh;
|
|
h_offset = 1 + h_dim1 * 1;
|
|
h__ -= h_offset;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--sh;
|
|
v_dim1 = *ldv;
|
|
v_offset = 1 + v_dim1 * 1;
|
|
v -= v_offset;
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
wv_dim1 = *ldwv;
|
|
wv_offset = 1 + wv_dim1 * 1;
|
|
wv -= wv_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
/* Computing MIN */
|
|
i__1 = *nw, i__2 = *kbot - *ktop + 1;
|
|
jw = f2cmin(i__1,i__2);
|
|
if (jw <= 2) {
|
|
lwkopt = 1;
|
|
} else {
|
|
|
|
/* ==== Workspace query call to CGEHRD ==== */
|
|
|
|
i__1 = jw - 1;
|
|
cgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
|
|
c_n1, &info);
|
|
lwk1 = (integer) work[1].r;
|
|
|
|
/* ==== Workspace query call to CUNMHR ==== */
|
|
|
|
i__1 = jw - 1;
|
|
cunmhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1],
|
|
&v[v_offset], ldv, &work[1], &c_n1, &info);
|
|
lwk2 = (integer) work[1].r;
|
|
|
|
/* ==== Workspace query call to CLAQR4 ==== */
|
|
|
|
claqr4_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[1],
|
|
&c__1, &jw, &v[v_offset], ldv, &work[1], &c_n1, &infqr);
|
|
lwk3 = (integer) work[1].r;
|
|
|
|
/* ==== Optimal workspace ==== */
|
|
|
|
/* Computing MAX */
|
|
i__1 = jw + f2cmax(lwk1,lwk2);
|
|
lwkopt = f2cmax(i__1,lwk3);
|
|
}
|
|
|
|
/* ==== Quick return in case of workspace query. ==== */
|
|
|
|
if (*lwork == -1) {
|
|
r__1 = (real) lwkopt;
|
|
q__1.r = r__1, q__1.i = 0.f;
|
|
work[1].r = q__1.r, work[1].i = q__1.i;
|
|
return;
|
|
}
|
|
|
|
/* ==== Nothing to do ... */
|
|
/* ... for an empty active block ... ==== */
|
|
*ns = 0;
|
|
*nd = 0;
|
|
work[1].r = 1.f, work[1].i = 0.f;
|
|
if (*ktop > *kbot) {
|
|
return;
|
|
}
|
|
/* ... nor for an empty deflation window. ==== */
|
|
if (*nw < 1) {
|
|
return;
|
|
}
|
|
|
|
/* ==== Machine constants ==== */
|
|
|
|
safmin = slamch_("SAFE MINIMUM");
|
|
safmax = 1.f / safmin;
|
|
slabad_(&safmin, &safmax);
|
|
ulp = slamch_("PRECISION");
|
|
smlnum = safmin * ((real) (*n) / ulp);
|
|
|
|
/* ==== Setup deflation window ==== */
|
|
|
|
/* Computing MIN */
|
|
i__1 = *nw, i__2 = *kbot - *ktop + 1;
|
|
jw = f2cmin(i__1,i__2);
|
|
kwtop = *kbot - jw + 1;
|
|
if (kwtop == *ktop) {
|
|
s.r = 0.f, s.i = 0.f;
|
|
} else {
|
|
i__1 = kwtop + (kwtop - 1) * h_dim1;
|
|
s.r = h__[i__1].r, s.i = h__[i__1].i;
|
|
}
|
|
|
|
if (*kbot == kwtop) {
|
|
|
|
/* ==== 1-by-1 deflation window: not much to do ==== */
|
|
|
|
i__1 = kwtop;
|
|
i__2 = kwtop + kwtop * h_dim1;
|
|
sh[i__1].r = h__[i__2].r, sh[i__1].i = h__[i__2].i;
|
|
*ns = 1;
|
|
*nd = 0;
|
|
/* Computing MAX */
|
|
i__1 = kwtop + kwtop * h_dim1;
|
|
r__5 = smlnum, r__6 = ulp * ((r__1 = h__[i__1].r, abs(r__1)) + (r__2 =
|
|
r_imag(&h__[kwtop + kwtop * h_dim1]), abs(r__2)));
|
|
if ((r__3 = s.r, abs(r__3)) + (r__4 = r_imag(&s), abs(r__4)) <= f2cmax(
|
|
r__5,r__6)) {
|
|
*ns = 0;
|
|
*nd = 1;
|
|
if (kwtop > *ktop) {
|
|
i__1 = kwtop + (kwtop - 1) * h_dim1;
|
|
h__[i__1].r = 0.f, h__[i__1].i = 0.f;
|
|
}
|
|
}
|
|
work[1].r = 1.f, work[1].i = 0.f;
|
|
return;
|
|
}
|
|
|
|
/* ==== Convert to spike-triangular form. (In case of a */
|
|
/* . rare QR failure, this routine continues to do */
|
|
/* . aggressive early deflation using that part of */
|
|
/* . the deflation window that converged using INFQR */
|
|
/* . here and there to keep track.) ==== */
|
|
|
|
clacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset],
|
|
ldt);
|
|
i__1 = jw - 1;
|
|
i__2 = *ldh + 1;
|
|
i__3 = *ldt + 1;
|
|
ccopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], &
|
|
i__3);
|
|
|
|
claset_("A", &jw, &jw, &c_b1, &c_b2, &v[v_offset], ldv);
|
|
nmin = ilaenv_(&c__12, "CLAQR3", "SV", &jw, &c__1, &jw, lwork, (ftnlen)6,
|
|
(ftnlen)2);
|
|
if (jw > nmin) {
|
|
claqr4_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[
|
|
kwtop], &c__1, &jw, &v[v_offset], ldv, &work[1], lwork, &
|
|
infqr);
|
|
} else {
|
|
clahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[
|
|
kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);
|
|
}
|
|
|
|
/* ==== Deflation detection loop ==== */
|
|
|
|
*ns = jw;
|
|
ilst = infqr + 1;
|
|
i__1 = jw;
|
|
for (knt = infqr + 1; knt <= i__1; ++knt) {
|
|
|
|
/* ==== Small spike tip deflation test ==== */
|
|
|
|
i__2 = *ns + *ns * t_dim1;
|
|
foo = (r__1 = t[i__2].r, abs(r__1)) + (r__2 = r_imag(&t[*ns + *ns *
|
|
t_dim1]), abs(r__2));
|
|
if (foo == 0.f) {
|
|
foo = (r__1 = s.r, abs(r__1)) + (r__2 = r_imag(&s), abs(r__2));
|
|
}
|
|
i__2 = *ns * v_dim1 + 1;
|
|
/* Computing MAX */
|
|
r__5 = smlnum, r__6 = ulp * foo;
|
|
if (((r__1 = s.r, abs(r__1)) + (r__2 = r_imag(&s), abs(r__2))) * ((
|
|
r__3 = v[i__2].r, abs(r__3)) + (r__4 = r_imag(&v[*ns * v_dim1
|
|
+ 1]), abs(r__4))) <= f2cmax(r__5,r__6)) {
|
|
|
|
/* ==== One more converged eigenvalue ==== */
|
|
|
|
--(*ns);
|
|
} else {
|
|
|
|
/* ==== One undeflatable eigenvalue. Move it up out of the */
|
|
/* . way. (CTREXC can not fail in this case.) ==== */
|
|
|
|
ifst = *ns;
|
|
ctrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, &
|
|
ilst, &info);
|
|
++ilst;
|
|
}
|
|
/* L10: */
|
|
}
|
|
|
|
/* ==== Return to Hessenberg form ==== */
|
|
|
|
if (*ns == 0) {
|
|
s.r = 0.f, s.i = 0.f;
|
|
}
|
|
|
|
if (*ns < jw) {
|
|
|
|
/* ==== sorting the diagonal of T improves accuracy for */
|
|
/* . graded matrices. ==== */
|
|
|
|
i__1 = *ns;
|
|
for (i__ = infqr + 1; i__ <= i__1; ++i__) {
|
|
ifst = i__;
|
|
i__2 = *ns;
|
|
for (j = i__ + 1; j <= i__2; ++j) {
|
|
i__3 = j + j * t_dim1;
|
|
i__4 = ifst + ifst * t_dim1;
|
|
if ((r__1 = t[i__3].r, abs(r__1)) + (r__2 = r_imag(&t[j + j *
|
|
t_dim1]), abs(r__2)) > (r__3 = t[i__4].r, abs(r__3))
|
|
+ (r__4 = r_imag(&t[ifst + ifst * t_dim1]), abs(r__4))
|
|
) {
|
|
ifst = j;
|
|
}
|
|
/* L20: */
|
|
}
|
|
ilst = i__;
|
|
if (ifst != ilst) {
|
|
ctrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
|
|
&ilst, &info);
|
|
}
|
|
/* L30: */
|
|
}
|
|
}
|
|
|
|
/* ==== Restore shift/eigenvalue array from T ==== */
|
|
|
|
i__1 = jw;
|
|
for (i__ = infqr + 1; i__ <= i__1; ++i__) {
|
|
i__2 = kwtop + i__ - 1;
|
|
i__3 = i__ + i__ * t_dim1;
|
|
sh[i__2].r = t[i__3].r, sh[i__2].i = t[i__3].i;
|
|
/* L40: */
|
|
}
|
|
|
|
|
|
if (*ns < jw || s.r == 0.f && s.i == 0.f) {
|
|
if (*ns > 1 && (s.r != 0.f || s.i != 0.f)) {
|
|
|
|
/* ==== Reflect spike back into lower triangle ==== */
|
|
|
|
ccopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
|
|
i__1 = *ns;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
r_cnjg(&q__1, &work[i__]);
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
/* L50: */
|
|
}
|
|
beta.r = work[1].r, beta.i = work[1].i;
|
|
clarfg_(ns, &beta, &work[2], &c__1, &tau);
|
|
work[1].r = 1.f, work[1].i = 0.f;
|
|
|
|
i__1 = jw - 2;
|
|
i__2 = jw - 2;
|
|
claset_("L", &i__1, &i__2, &c_b1, &c_b1, &t[t_dim1 + 3], ldt);
|
|
|
|
r_cnjg(&q__1, &tau);
|
|
clarf_("L", ns, &jw, &work[1], &c__1, &q__1, &t[t_offset], ldt, &
|
|
work[jw + 1]);
|
|
clarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, &
|
|
work[jw + 1]);
|
|
clarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, &
|
|
work[jw + 1]);
|
|
|
|
i__1 = *lwork - jw;
|
|
cgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
|
|
, &i__1, &info);
|
|
}
|
|
|
|
/* ==== Copy updated reduced window into place ==== */
|
|
|
|
if (kwtop > 1) {
|
|
i__1 = kwtop + (kwtop - 1) * h_dim1;
|
|
r_cnjg(&q__2, &v[v_dim1 + 1]);
|
|
q__1.r = s.r * q__2.r - s.i * q__2.i, q__1.i = s.r * q__2.i + s.i
|
|
* q__2.r;
|
|
h__[i__1].r = q__1.r, h__[i__1].i = q__1.i;
|
|
}
|
|
clacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1]
|
|
, ldh);
|
|
i__1 = jw - 1;
|
|
i__2 = *ldt + 1;
|
|
i__3 = *ldh + 1;
|
|
ccopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1],
|
|
&i__3);
|
|
|
|
/* ==== Accumulate orthogonal matrix in order update */
|
|
/* . H and Z, if requested. ==== */
|
|
|
|
if (*ns > 1 && (s.r != 0.f || s.i != 0.f)) {
|
|
i__1 = *lwork - jw;
|
|
cunmhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1],
|
|
&v[v_offset], ldv, &work[jw + 1], &i__1, &info);
|
|
}
|
|
|
|
/* ==== Update vertical slab in H ==== */
|
|
|
|
if (*wantt) {
|
|
ltop = 1;
|
|
} else {
|
|
ltop = *ktop;
|
|
}
|
|
i__1 = kwtop - 1;
|
|
i__2 = *nv;
|
|
for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *nv, i__4 = kwtop - krow;
|
|
kln = f2cmin(i__3,i__4);
|
|
cgemm_("N", "N", &kln, &jw, &jw, &c_b2, &h__[krow + kwtop *
|
|
h_dim1], ldh, &v[v_offset], ldv, &c_b1, &wv[wv_offset],
|
|
ldwv);
|
|
clacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop *
|
|
h_dim1], ldh);
|
|
/* L60: */
|
|
}
|
|
|
|
/* ==== Update horizontal slab in H ==== */
|
|
|
|
if (*wantt) {
|
|
i__2 = *n;
|
|
i__1 = *nh;
|
|
for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2;
|
|
kcol += i__1) {
|
|
/* Computing MIN */
|
|
i__3 = *nh, i__4 = *n - kcol + 1;
|
|
kln = f2cmin(i__3,i__4);
|
|
cgemm_("C", "N", &jw, &kln, &jw, &c_b2, &v[v_offset], ldv, &
|
|
h__[kwtop + kcol * h_dim1], ldh, &c_b1, &t[t_offset],
|
|
ldt);
|
|
clacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol *
|
|
h_dim1], ldh);
|
|
/* L70: */
|
|
}
|
|
}
|
|
|
|
/* ==== Update vertical slab in Z ==== */
|
|
|
|
if (*wantz) {
|
|
i__1 = *ihiz;
|
|
i__2 = *nv;
|
|
for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *nv, i__4 = *ihiz - krow + 1;
|
|
kln = f2cmin(i__3,i__4);
|
|
cgemm_("N", "N", &kln, &jw, &jw, &c_b2, &z__[krow + kwtop *
|
|
z_dim1], ldz, &v[v_offset], ldv, &c_b1, &wv[wv_offset]
|
|
, ldwv);
|
|
clacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow +
|
|
kwtop * z_dim1], ldz);
|
|
/* L80: */
|
|
}
|
|
}
|
|
}
|
|
|
|
/* ==== Return the number of deflations ... ==== */
|
|
|
|
*nd = jw - *ns;
|
|
|
|
/* ==== ... and the number of shifts. (Subtracting */
|
|
/* . INFQR from the spike length takes care */
|
|
/* . of the case of a rare QR failure while */
|
|
/* . calculating eigenvalues of the deflation */
|
|
/* . window.) ==== */
|
|
|
|
*ns -= infqr;
|
|
|
|
/* ==== Return optimal workspace. ==== */
|
|
|
|
r__1 = (real) lwkopt;
|
|
q__1.r = r__1, q__1.i = 0.f;
|
|
work[1].r = q__1.r, work[1].i = q__1.i;
|
|
|
|
/* ==== End of CLAQR3 ==== */
|
|
|
|
return;
|
|
} /* claqr3_ */
|
|
|