1025 lines
28 KiB
C
1025 lines
28 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef 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 integer c__1 = 1;
|
|
static integer c__4 = 4;
|
|
static logical c_false = FALSE_;
|
|
static integer c_n1 = -1;
|
|
static integer c__2 = 2;
|
|
static integer c__3 = 3;
|
|
|
|
/* > \brief \b DLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonica
|
|
l form, by an orthogonal similarity transformation. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLAEXC + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaexc.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaexc.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaexc.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLAEXC( WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, */
|
|
/* INFO ) */
|
|
|
|
/* LOGICAL WANTQ */
|
|
/* INTEGER INFO, J1, LDQ, LDT, N, N1, N2 */
|
|
/* DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in */
|
|
/* > an upper quasi-triangular matrix T by an orthogonal similarity */
|
|
/* > transformation. */
|
|
/* > */
|
|
/* > T must be in Schur canonical form, that is, block upper triangular */
|
|
/* > with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block */
|
|
/* > has its diagonal elemnts equal and its off-diagonal elements of */
|
|
/* > opposite sign. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] WANTQ */
|
|
/* > \verbatim */
|
|
/* > WANTQ is LOGICAL */
|
|
/* > = .TRUE. : accumulate the transformation in the matrix Q; */
|
|
/* > = .FALSE.: do not accumulate the transformation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix T. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] T */
|
|
/* > \verbatim */
|
|
/* > T is DOUBLE PRECISION array, dimension (LDT,N) */
|
|
/* > On entry, the upper quasi-triangular matrix T, in Schur */
|
|
/* > canonical form. */
|
|
/* > On exit, the updated matrix T, again in Schur canonical form. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. LDT >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
|
|
/* > On entry, if WANTQ is .TRUE., the orthogonal matrix Q. */
|
|
/* > On exit, if WANTQ is .TRUE., the updated matrix Q. */
|
|
/* > If WANTQ is .FALSE., Q is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. */
|
|
/* > LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] J1 */
|
|
/* > \verbatim */
|
|
/* > J1 is INTEGER */
|
|
/* > The index of the first row of the first block T11. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N1 */
|
|
/* > \verbatim */
|
|
/* > N1 is INTEGER */
|
|
/* > The order of the first block T11. N1 = 0, 1 or 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N2 */
|
|
/* > \verbatim */
|
|
/* > N2 is INTEGER */
|
|
/* > The order of the second block T22. N2 = 0, 1 or 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > = 1: the transformed matrix T would be too far from Schur */
|
|
/* > form; the blocks are not swapped and T and Q are */
|
|
/* > unchanged. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleOTHERauxiliary */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlaexc_(logical *wantq, integer *n, doublereal *t,
|
|
integer *ldt, doublereal *q, integer *ldq, integer *j1, integer *n1,
|
|
integer *n2, doublereal *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer q_dim1, q_offset, t_dim1, t_offset, i__1;
|
|
doublereal d__1, d__2, d__3;
|
|
|
|
/* Local variables */
|
|
integer ierr;
|
|
doublereal temp;
|
|
extern /* Subroutine */ void drot_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *);
|
|
doublereal d__[16] /* was [4][4] */;
|
|
integer k;
|
|
doublereal u[3], scale, x[4] /* was [2][2] */, dnorm;
|
|
integer j2, j3, j4;
|
|
doublereal xnorm, u1[3], u2[3];
|
|
extern /* Subroutine */ void dlanv2_(doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *), dlasy2_(
|
|
logical *, logical *, integer *, integer *, integer *, doublereal
|
|
*, integer *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *, doublereal *, integer *);
|
|
integer nd;
|
|
doublereal cs, t11, t22;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal t33;
|
|
extern doublereal dlange_(char *, integer *, integer *, doublereal *,
|
|
integer *, doublereal *);
|
|
extern /* Subroutine */ void dlarfg_(integer *, doublereal *, doublereal *,
|
|
integer *, doublereal *);
|
|
doublereal sn;
|
|
extern /* Subroutine */ void dlacpy_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *),
|
|
dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *), dlarfx_(char *, integer *, integer *, doublereal *,
|
|
doublereal *, doublereal *, integer *, doublereal *);
|
|
doublereal thresh, smlnum, wi1, wi2, wr1, wr2, eps, tau, tau1, tau2;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0 || *n1 == 0 || *n2 == 0) {
|
|
return;
|
|
}
|
|
if (*j1 + *n1 > *n) {
|
|
return;
|
|
}
|
|
|
|
j2 = *j1 + 1;
|
|
j3 = *j1 + 2;
|
|
j4 = *j1 + 3;
|
|
|
|
if (*n1 == 1 && *n2 == 1) {
|
|
|
|
/* Swap two 1-by-1 blocks. */
|
|
|
|
t11 = t[*j1 + *j1 * t_dim1];
|
|
t22 = t[j2 + j2 * t_dim1];
|
|
|
|
/* Determine the transformation to perform the interchange. */
|
|
|
|
d__1 = t22 - t11;
|
|
dlartg_(&t[*j1 + j2 * t_dim1], &d__1, &cs, &sn, &temp);
|
|
|
|
/* Apply transformation to the matrix T. */
|
|
|
|
if (j3 <= *n) {
|
|
i__1 = *n - *j1 - 1;
|
|
drot_(&i__1, &t[*j1 + j3 * t_dim1], ldt, &t[j2 + j3 * t_dim1],
|
|
ldt, &cs, &sn);
|
|
}
|
|
i__1 = *j1 - 1;
|
|
drot_(&i__1, &t[*j1 * t_dim1 + 1], &c__1, &t[j2 * t_dim1 + 1], &c__1,
|
|
&cs, &sn);
|
|
|
|
t[*j1 + *j1 * t_dim1] = t22;
|
|
t[j2 + j2 * t_dim1] = t11;
|
|
|
|
if (*wantq) {
|
|
|
|
/* Accumulate transformation in the matrix Q. */
|
|
|
|
drot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[j2 * q_dim1 + 1], &c__1,
|
|
&cs, &sn);
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Swapping involves at least one 2-by-2 block. */
|
|
|
|
/* Copy the diagonal block of order N1+N2 to the local array D */
|
|
/* and compute its norm. */
|
|
|
|
nd = *n1 + *n2;
|
|
dlacpy_("Full", &nd, &nd, &t[*j1 + *j1 * t_dim1], ldt, d__, &c__4);
|
|
dnorm = dlange_("Max", &nd, &nd, d__, &c__4, &work[1]);
|
|
|
|
/* Compute machine-dependent threshold for test for accepting */
|
|
/* swap. */
|
|
|
|
eps = dlamch_("P");
|
|
smlnum = dlamch_("S") / eps;
|
|
/* Computing MAX */
|
|
d__1 = eps * 10. * dnorm;
|
|
thresh = f2cmax(d__1,smlnum);
|
|
|
|
/* Solve T11*X - X*T22 = scale*T12 for X. */
|
|
|
|
dlasy2_(&c_false, &c_false, &c_n1, n1, n2, d__, &c__4, &d__[*n1 + 1 +
|
|
(*n1 + 1 << 2) - 5], &c__4, &d__[(*n1 + 1 << 2) - 4], &c__4, &
|
|
scale, x, &c__2, &xnorm, &ierr);
|
|
|
|
/* Swap the adjacent diagonal blocks. */
|
|
|
|
k = *n1 + *n1 + *n2 - 3;
|
|
switch (k) {
|
|
case 1: goto L10;
|
|
case 2: goto L20;
|
|
case 3: goto L30;
|
|
}
|
|
|
|
L10:
|
|
|
|
/* N1 = 1, N2 = 2: generate elementary reflector H so that: */
|
|
|
|
/* ( scale, X11, X12 ) H = ( 0, 0, * ) */
|
|
|
|
u[0] = scale;
|
|
u[1] = x[0];
|
|
u[2] = x[2];
|
|
dlarfg_(&c__3, &u[2], u, &c__1, &tau);
|
|
u[2] = 1.;
|
|
t11 = t[*j1 + *j1 * t_dim1];
|
|
|
|
/* Perform swap provisionally on diagonal block in D. */
|
|
|
|
dlarfx_("L", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
|
|
dlarfx_("R", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
|
|
|
|
/* Test whether to reject swap. */
|
|
|
|
/* Computing MAX */
|
|
d__2 = abs(d__[2]), d__3 = abs(d__[6]), d__2 = f2cmax(d__2,d__3), d__3 =
|
|
(d__1 = d__[10] - t11, abs(d__1));
|
|
if (f2cmax(d__2,d__3) > thresh) {
|
|
goto L50;
|
|
}
|
|
|
|
/* Accept swap: apply transformation to the entire matrix T. */
|
|
|
|
i__1 = *n - *j1 + 1;
|
|
dlarfx_("L", &c__3, &i__1, u, &tau, &t[*j1 + *j1 * t_dim1], ldt, &
|
|
work[1]);
|
|
dlarfx_("R", &j2, &c__3, u, &tau, &t[*j1 * t_dim1 + 1], ldt, &work[1]);
|
|
|
|
t[j3 + *j1 * t_dim1] = 0.;
|
|
t[j3 + j2 * t_dim1] = 0.;
|
|
t[j3 + j3 * t_dim1] = t11;
|
|
|
|
if (*wantq) {
|
|
|
|
/* Accumulate transformation in the matrix Q. */
|
|
|
|
dlarfx_("R", n, &c__3, u, &tau, &q[*j1 * q_dim1 + 1], ldq, &work[
|
|
1]);
|
|
}
|
|
goto L40;
|
|
|
|
L20:
|
|
|
|
/* N1 = 2, N2 = 1: generate elementary reflector H so that: */
|
|
|
|
/* H ( -X11 ) = ( * ) */
|
|
/* ( -X21 ) = ( 0 ) */
|
|
/* ( scale ) = ( 0 ) */
|
|
|
|
u[0] = -x[0];
|
|
u[1] = -x[1];
|
|
u[2] = scale;
|
|
dlarfg_(&c__3, u, &u[1], &c__1, &tau);
|
|
u[0] = 1.;
|
|
t33 = t[j3 + j3 * t_dim1];
|
|
|
|
/* Perform swap provisionally on diagonal block in D. */
|
|
|
|
dlarfx_("L", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
|
|
dlarfx_("R", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
|
|
|
|
/* Test whether to reject swap. */
|
|
|
|
/* Computing MAX */
|
|
d__2 = abs(d__[1]), d__3 = abs(d__[2]), d__2 = f2cmax(d__2,d__3), d__3 =
|
|
(d__1 = d__[0] - t33, abs(d__1));
|
|
if (f2cmax(d__2,d__3) > thresh) {
|
|
goto L50;
|
|
}
|
|
|
|
/* Accept swap: apply transformation to the entire matrix T. */
|
|
|
|
dlarfx_("R", &j3, &c__3, u, &tau, &t[*j1 * t_dim1 + 1], ldt, &work[1]);
|
|
i__1 = *n - *j1;
|
|
dlarfx_("L", &c__3, &i__1, u, &tau, &t[*j1 + j2 * t_dim1], ldt, &work[
|
|
1]);
|
|
|
|
t[*j1 + *j1 * t_dim1] = t33;
|
|
t[j2 + *j1 * t_dim1] = 0.;
|
|
t[j3 + *j1 * t_dim1] = 0.;
|
|
|
|
if (*wantq) {
|
|
|
|
/* Accumulate transformation in the matrix Q. */
|
|
|
|
dlarfx_("R", n, &c__3, u, &tau, &q[*j1 * q_dim1 + 1], ldq, &work[
|
|
1]);
|
|
}
|
|
goto L40;
|
|
|
|
L30:
|
|
|
|
/* N1 = 2, N2 = 2: generate elementary reflectors H(1) and H(2) so */
|
|
/* that: */
|
|
|
|
/* H(2) H(1) ( -X11 -X12 ) = ( * * ) */
|
|
/* ( -X21 -X22 ) ( 0 * ) */
|
|
/* ( scale 0 ) ( 0 0 ) */
|
|
/* ( 0 scale ) ( 0 0 ) */
|
|
|
|
u1[0] = -x[0];
|
|
u1[1] = -x[1];
|
|
u1[2] = scale;
|
|
dlarfg_(&c__3, u1, &u1[1], &c__1, &tau1);
|
|
u1[0] = 1.;
|
|
|
|
temp = -tau1 * (x[2] + u1[1] * x[3]);
|
|
u2[0] = -temp * u1[1] - x[3];
|
|
u2[1] = -temp * u1[2];
|
|
u2[2] = scale;
|
|
dlarfg_(&c__3, u2, &u2[1], &c__1, &tau2);
|
|
u2[0] = 1.;
|
|
|
|
/* Perform swap provisionally on diagonal block in D. */
|
|
|
|
dlarfx_("L", &c__3, &c__4, u1, &tau1, d__, &c__4, &work[1])
|
|
;
|
|
dlarfx_("R", &c__4, &c__3, u1, &tau1, d__, &c__4, &work[1])
|
|
;
|
|
dlarfx_("L", &c__3, &c__4, u2, &tau2, &d__[1], &c__4, &work[1]);
|
|
dlarfx_("R", &c__4, &c__3, u2, &tau2, &d__[4], &c__4, &work[1]);
|
|
|
|
/* Test whether to reject swap. */
|
|
|
|
/* Computing MAX */
|
|
d__1 = abs(d__[2]), d__2 = abs(d__[6]), d__1 = f2cmax(d__1,d__2), d__2 =
|
|
abs(d__[3]), d__1 = f2cmax(d__1,d__2), d__2 = abs(d__[7]);
|
|
if (f2cmax(d__1,d__2) > thresh) {
|
|
goto L50;
|
|
}
|
|
|
|
/* Accept swap: apply transformation to the entire matrix T. */
|
|
|
|
i__1 = *n - *j1 + 1;
|
|
dlarfx_("L", &c__3, &i__1, u1, &tau1, &t[*j1 + *j1 * t_dim1], ldt, &
|
|
work[1]);
|
|
dlarfx_("R", &j4, &c__3, u1, &tau1, &t[*j1 * t_dim1 + 1], ldt, &work[
|
|
1]);
|
|
i__1 = *n - *j1 + 1;
|
|
dlarfx_("L", &c__3, &i__1, u2, &tau2, &t[j2 + *j1 * t_dim1], ldt, &
|
|
work[1]);
|
|
dlarfx_("R", &j4, &c__3, u2, &tau2, &t[j2 * t_dim1 + 1], ldt, &work[1]
|
|
);
|
|
|
|
t[j3 + *j1 * t_dim1] = 0.;
|
|
t[j3 + j2 * t_dim1] = 0.;
|
|
t[j4 + *j1 * t_dim1] = 0.;
|
|
t[j4 + j2 * t_dim1] = 0.;
|
|
|
|
if (*wantq) {
|
|
|
|
/* Accumulate transformation in the matrix Q. */
|
|
|
|
dlarfx_("R", n, &c__3, u1, &tau1, &q[*j1 * q_dim1 + 1], ldq, &
|
|
work[1]);
|
|
dlarfx_("R", n, &c__3, u2, &tau2, &q[j2 * q_dim1 + 1], ldq, &work[
|
|
1]);
|
|
}
|
|
|
|
L40:
|
|
|
|
if (*n2 == 2) {
|
|
|
|
/* Standardize new 2-by-2 block T11 */
|
|
|
|
dlanv2_(&t[*j1 + *j1 * t_dim1], &t[*j1 + j2 * t_dim1], &t[j2 + *
|
|
j1 * t_dim1], &t[j2 + j2 * t_dim1], &wr1, &wi1, &wr2, &
|
|
wi2, &cs, &sn);
|
|
i__1 = *n - *j1 - 1;
|
|
drot_(&i__1, &t[*j1 + (*j1 + 2) * t_dim1], ldt, &t[j2 + (*j1 + 2)
|
|
* t_dim1], ldt, &cs, &sn);
|
|
i__1 = *j1 - 1;
|
|
drot_(&i__1, &t[*j1 * t_dim1 + 1], &c__1, &t[j2 * t_dim1 + 1], &
|
|
c__1, &cs, &sn);
|
|
if (*wantq) {
|
|
drot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[j2 * q_dim1 + 1], &
|
|
c__1, &cs, &sn);
|
|
}
|
|
}
|
|
|
|
if (*n1 == 2) {
|
|
|
|
/* Standardize new 2-by-2 block T22 */
|
|
|
|
j3 = *j1 + *n2;
|
|
j4 = j3 + 1;
|
|
dlanv2_(&t[j3 + j3 * t_dim1], &t[j3 + j4 * t_dim1], &t[j4 + j3 *
|
|
t_dim1], &t[j4 + j4 * t_dim1], &wr1, &wi1, &wr2, &wi2, &
|
|
cs, &sn);
|
|
if (j3 + 2 <= *n) {
|
|
i__1 = *n - j3 - 1;
|
|
drot_(&i__1, &t[j3 + (j3 + 2) * t_dim1], ldt, &t[j4 + (j3 + 2)
|
|
* t_dim1], ldt, &cs, &sn);
|
|
}
|
|
i__1 = j3 - 1;
|
|
drot_(&i__1, &t[j3 * t_dim1 + 1], &c__1, &t[j4 * t_dim1 + 1], &
|
|
c__1, &cs, &sn);
|
|
if (*wantq) {
|
|
drot_(n, &q[j3 * q_dim1 + 1], &c__1, &q[j4 * q_dim1 + 1], &
|
|
c__1, &cs, &sn);
|
|
}
|
|
}
|
|
|
|
}
|
|
return;
|
|
|
|
/* Exit with INFO = 1 if swap was rejected. */
|
|
|
|
L50:
|
|
*info = 1;
|
|
return;
|
|
|
|
/* End of DLAEXC */
|
|
|
|
} /* dlaexc_ */
|
|
|