1030 lines
29 KiB
C
1030 lines
29 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle_() continue;
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#define myceiling_(w) {ceil(w)}
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#define myhuge_(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
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;
|
|
|
|
/* > \brief \b ZTRSNA */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZTRSNA + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrsna.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrsna.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrsna.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZTRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, */
|
|
/* LDVR, S, SEP, MM, M, WORK, LDWORK, RWORK, */
|
|
/* INFO ) */
|
|
|
|
/* CHARACTER HOWMNY, JOB */
|
|
/* INTEGER INFO, LDT, LDVL, LDVR, LDWORK, M, MM, N */
|
|
/* LOGICAL SELECT( * ) */
|
|
/* DOUBLE PRECISION RWORK( * ), S( * ), SEP( * ) */
|
|
/* COMPLEX*16 T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), */
|
|
/* $ WORK( LDWORK, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZTRSNA estimates reciprocal condition numbers for specified */
|
|
/* > eigenvalues and/or right eigenvectors of a complex upper triangular */
|
|
/* > matrix T (or of any matrix Q*T*Q**H with Q unitary). */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOB */
|
|
/* > \verbatim */
|
|
/* > JOB is CHARACTER*1 */
|
|
/* > Specifies whether condition numbers are required for */
|
|
/* > eigenvalues (S) or eigenvectors (SEP): */
|
|
/* > = 'E': for eigenvalues only (S); */
|
|
/* > = 'V': for eigenvectors only (SEP); */
|
|
/* > = 'B': for both eigenvalues and eigenvectors (S and SEP). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] HOWMNY */
|
|
/* > \verbatim */
|
|
/* > HOWMNY is CHARACTER*1 */
|
|
/* > = 'A': compute condition numbers for all eigenpairs; */
|
|
/* > = 'S': compute condition numbers for selected eigenpairs */
|
|
/* > specified by the array SELECT. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SELECT */
|
|
/* > \verbatim */
|
|
/* > SELECT is LOGICAL array, dimension (N) */
|
|
/* > If HOWMNY = 'S', SELECT specifies the eigenpairs for which */
|
|
/* > condition numbers are required. To select condition numbers */
|
|
/* > for the j-th eigenpair, SELECT(j) must be set to .TRUE.. */
|
|
/* > If HOWMNY = 'A', SELECT is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix T. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] T */
|
|
/* > \verbatim */
|
|
/* > T is COMPLEX*16 array, dimension (LDT,N) */
|
|
/* > The upper triangular matrix T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. LDT >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VL */
|
|
/* > \verbatim */
|
|
/* > VL is COMPLEX*16 array, dimension (LDVL,M) */
|
|
/* > If JOB = 'E' or 'B', VL must contain left eigenvectors of T */
|
|
/* > (or of any Q*T*Q**H with Q unitary), corresponding to the */
|
|
/* > eigenpairs specified by HOWMNY and SELECT. The eigenvectors */
|
|
/* > must be stored in consecutive columns of VL, as returned by */
|
|
/* > ZHSEIN or ZTREVC. */
|
|
/* > If JOB = 'V', VL is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVL */
|
|
/* > \verbatim */
|
|
/* > LDVL is INTEGER */
|
|
/* > The leading dimension of the array VL. */
|
|
/* > LDVL >= 1; and if JOB = 'E' or 'B', LDVL >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VR */
|
|
/* > \verbatim */
|
|
/* > VR is COMPLEX*16 array, dimension (LDVR,M) */
|
|
/* > If JOB = 'E' or 'B', VR must contain right eigenvectors of T */
|
|
/* > (or of any Q*T*Q**H with Q unitary), corresponding to the */
|
|
/* > eigenpairs specified by HOWMNY and SELECT. The eigenvectors */
|
|
/* > must be stored in consecutive columns of VR, as returned by */
|
|
/* > ZHSEIN or ZTREVC. */
|
|
/* > If JOB = 'V', VR is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVR */
|
|
/* > \verbatim */
|
|
/* > LDVR is INTEGER */
|
|
/* > The leading dimension of the array VR. */
|
|
/* > LDVR >= 1; and if JOB = 'E' or 'B', LDVR >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION array, dimension (MM) */
|
|
/* > If JOB = 'E' or 'B', the reciprocal condition numbers of the */
|
|
/* > selected eigenvalues, stored in consecutive elements of the */
|
|
/* > array. Thus S(j), SEP(j), and the j-th columns of VL and VR */
|
|
/* > all correspond to the same eigenpair (but not in general the */
|
|
/* > j-th eigenpair, unless all eigenpairs are selected). */
|
|
/* > If JOB = 'V', S is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SEP */
|
|
/* > \verbatim */
|
|
/* > SEP is DOUBLE PRECISION array, dimension (MM) */
|
|
/* > If JOB = 'V' or 'B', the estimated reciprocal condition */
|
|
/* > numbers of the selected eigenvectors, stored in consecutive */
|
|
/* > elements of the array. */
|
|
/* > If JOB = 'E', SEP is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] MM */
|
|
/* > \verbatim */
|
|
/* > MM is INTEGER */
|
|
/* > The number of elements in the arrays S (if JOB = 'E' or 'B') */
|
|
/* > and/or SEP (if JOB = 'V' or 'B'). MM >= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of elements of the arrays S and/or SEP actually */
|
|
/* > used to store the estimated condition numbers. */
|
|
/* > If HOWMNY = 'A', M is set to N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (LDWORK,N+6) */
|
|
/* > If JOB = 'E', WORK is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDWORK */
|
|
/* > \verbatim */
|
|
/* > LDWORK is INTEGER */
|
|
/* > The leading dimension of the array WORK. */
|
|
/* > LDWORK >= 1; and if JOB = 'V' or 'B', LDWORK >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (N) */
|
|
/* > If JOB = 'E', RWORK is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date November 2017 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The reciprocal of the condition number of an eigenvalue lambda is */
|
|
/* > defined as */
|
|
/* > */
|
|
/* > S(lambda) = |v**H*u| / (norm(u)*norm(v)) */
|
|
/* > */
|
|
/* > where u and v are the right and left eigenvectors of T corresponding */
|
|
/* > to lambda; v**H denotes the conjugate transpose of v, and norm(u) */
|
|
/* > denotes the Euclidean norm. These reciprocal condition numbers always */
|
|
/* > lie between zero (very badly conditioned) and one (very well */
|
|
/* > conditioned). If n = 1, S(lambda) is defined to be 1. */
|
|
/* > */
|
|
/* > An approximate error bound for a computed eigenvalue W(i) is given by */
|
|
/* > */
|
|
/* > EPS * norm(T) / S(i) */
|
|
/* > */
|
|
/* > where EPS is the machine precision. */
|
|
/* > */
|
|
/* > The reciprocal of the condition number of the right eigenvector u */
|
|
/* > corresponding to lambda is defined as follows. Suppose */
|
|
/* > */
|
|
/* > T = ( lambda c ) */
|
|
/* > ( 0 T22 ) */
|
|
/* > */
|
|
/* > Then the reciprocal condition number is */
|
|
/* > */
|
|
/* > SEP( lambda, T22 ) = sigma-f2cmin( T22 - lambda*I ) */
|
|
/* > */
|
|
/* > where sigma-f2cmin denotes the smallest singular value. We approximate */
|
|
/* > the smallest singular value by the reciprocal of an estimate of the */
|
|
/* > one-norm of the inverse of T22 - lambda*I. If n = 1, SEP(1) is */
|
|
/* > defined to be abs(T(1,1)). */
|
|
/* > */
|
|
/* > An approximate error bound for a computed right eigenvector VR(i) */
|
|
/* > is given by */
|
|
/* > */
|
|
/* > EPS * norm(T) / SEP(i) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void ztrsna_(char *job, char *howmny, logical *select,
|
|
integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl,
|
|
integer *ldvl, doublecomplex *vr, integer *ldvr, doublereal *s,
|
|
doublereal *sep, integer *mm, integer *m, doublecomplex *work,
|
|
integer *ldwork, doublereal *rwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset,
|
|
work_dim1, work_offset, i__1, i__2, i__3, i__4, i__5;
|
|
doublereal d__1, d__2;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
integer kase, ierr;
|
|
doublecomplex prod;
|
|
doublereal lnrm, rnrm;
|
|
integer i__, j, k;
|
|
doublereal scale;
|
|
extern logical lsame_(char *, char *);
|
|
integer isave[3];
|
|
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *);
|
|
doublecomplex dummy[1];
|
|
logical wants;
|
|
doublereal xnorm;
|
|
extern /* Subroutine */ void zlacn2_(integer *, doublecomplex *,
|
|
doublecomplex *, doublereal *, integer *, integer *), dlabad_(
|
|
doublereal *, doublereal *);
|
|
extern doublereal dznrm2_(integer *, doublecomplex *, integer *), dlamch_(
|
|
char *);
|
|
integer ks, ix;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
doublereal bignum;
|
|
logical wantbh;
|
|
extern integer izamax_(integer *, doublecomplex *, integer *);
|
|
logical somcon;
|
|
extern /* Subroutine */ void zdrscl_(integer *, doublereal *,
|
|
doublecomplex *, integer *);
|
|
char normin[1];
|
|
extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *);
|
|
doublereal smlnum;
|
|
logical wantsp;
|
|
extern /* Subroutine */ void zlatrs_(char *, char *, char *, char *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *,
|
|
doublereal *, doublereal *, integer *), ztrexc_(char *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, integer *, integer *, integer *);
|
|
doublereal eps, est;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.8.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* November 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode and test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
--select;
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
vl_dim1 = *ldvl;
|
|
vl_offset = 1 + vl_dim1 * 1;
|
|
vl -= vl_offset;
|
|
vr_dim1 = *ldvr;
|
|
vr_offset = 1 + vr_dim1 * 1;
|
|
vr -= vr_offset;
|
|
--s;
|
|
--sep;
|
|
work_dim1 = *ldwork;
|
|
work_offset = 1 + work_dim1 * 1;
|
|
work -= work_offset;
|
|
--rwork;
|
|
|
|
/* Function Body */
|
|
wantbh = lsame_(job, "B");
|
|
wants = lsame_(job, "E") || wantbh;
|
|
wantsp = lsame_(job, "V") || wantbh;
|
|
|
|
somcon = lsame_(howmny, "S");
|
|
|
|
/* Set M to the number of eigenpairs for which condition numbers are */
|
|
/* to be computed. */
|
|
|
|
if (somcon) {
|
|
*m = 0;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (select[j]) {
|
|
++(*m);
|
|
}
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
*m = *n;
|
|
}
|
|
|
|
*info = 0;
|
|
if (! wants && ! wantsp) {
|
|
*info = -1;
|
|
} else if (! lsame_(howmny, "A") && ! somcon) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*ldt < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
} else if (*ldvl < 1 || wants && *ldvl < *n) {
|
|
*info = -8;
|
|
} else if (*ldvr < 1 || wants && *ldvr < *n) {
|
|
*info = -10;
|
|
} else if (*mm < *m) {
|
|
*info = -13;
|
|
} else if (*ldwork < 1 || wantsp && *ldwork < *n) {
|
|
*info = -16;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZTRSNA", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
if (*n == 1) {
|
|
if (somcon) {
|
|
if (! select[1]) {
|
|
return;
|
|
}
|
|
}
|
|
if (wants) {
|
|
s[1] = 1.;
|
|
}
|
|
if (wantsp) {
|
|
sep[1] = z_abs(&t[t_dim1 + 1]);
|
|
}
|
|
return;
|
|
}
|
|
|
|
/* Get machine constants */
|
|
|
|
eps = dlamch_("P");
|
|
smlnum = dlamch_("S") / eps;
|
|
bignum = 1. / smlnum;
|
|
dlabad_(&smlnum, &bignum);
|
|
|
|
ks = 1;
|
|
i__1 = *n;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
|
|
if (somcon) {
|
|
if (! select[k]) {
|
|
goto L50;
|
|
}
|
|
}
|
|
|
|
if (wants) {
|
|
|
|
/* Compute the reciprocal condition number of the k-th */
|
|
/* eigenvalue. */
|
|
|
|
zdotc_(&z__1, n, &vr[ks * vr_dim1 + 1], &c__1, &vl[ks * vl_dim1 +
|
|
1], &c__1);
|
|
prod.r = z__1.r, prod.i = z__1.i;
|
|
rnrm = dznrm2_(n, &vr[ks * vr_dim1 + 1], &c__1);
|
|
lnrm = dznrm2_(n, &vl[ks * vl_dim1 + 1], &c__1);
|
|
s[ks] = z_abs(&prod) / (rnrm * lnrm);
|
|
|
|
}
|
|
|
|
if (wantsp) {
|
|
|
|
/* Estimate the reciprocal condition number of the k-th */
|
|
/* eigenvector. */
|
|
|
|
/* Copy the matrix T to the array WORK and swap the k-th */
|
|
/* diagonal element to the (1,1) position. */
|
|
|
|
zlacpy_("Full", n, n, &t[t_offset], ldt, &work[work_offset],
|
|
ldwork);
|
|
ztrexc_("No Q", n, &work[work_offset], ldwork, dummy, &c__1, &k, &
|
|
c__1, &ierr);
|
|
|
|
/* Form C = T22 - lambda*I in WORK(2:N,2:N). */
|
|
|
|
i__2 = *n;
|
|
for (i__ = 2; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + i__ * work_dim1;
|
|
i__4 = i__ + i__ * work_dim1;
|
|
i__5 = work_dim1 + 1;
|
|
z__1.r = work[i__4].r - work[i__5].r, z__1.i = work[i__4].i -
|
|
work[i__5].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
/* L20: */
|
|
}
|
|
|
|
/* Estimate a lower bound for the 1-norm of inv(C**H). The 1st */
|
|
/* and (N+1)th columns of WORK are used to store work vectors. */
|
|
|
|
sep[ks] = 0.;
|
|
est = 0.;
|
|
kase = 0;
|
|
*(unsigned char *)normin = 'N';
|
|
L30:
|
|
i__2 = *n - 1;
|
|
zlacn2_(&i__2, &work[(*n + 1) * work_dim1 + 1], &work[work_offset]
|
|
, &est, &kase, isave);
|
|
|
|
if (kase != 0) {
|
|
if (kase == 1) {
|
|
|
|
/* Solve C**H*x = scale*b */
|
|
|
|
i__2 = *n - 1;
|
|
zlatrs_("Upper", "Conjugate transpose", "Nonunit", normin,
|
|
&i__2, &work[(work_dim1 << 1) + 2], ldwork, &
|
|
work[work_offset], &scale, &rwork[1], &ierr);
|
|
} else {
|
|
|
|
/* Solve C*x = scale*b */
|
|
|
|
i__2 = *n - 1;
|
|
zlatrs_("Upper", "No transpose", "Nonunit", normin, &i__2,
|
|
&work[(work_dim1 << 1) + 2], ldwork, &work[
|
|
work_offset], &scale, &rwork[1], &ierr);
|
|
}
|
|
*(unsigned char *)normin = 'Y';
|
|
if (scale != 1.) {
|
|
|
|
/* Multiply by 1/SCALE if doing so will not cause */
|
|
/* overflow. */
|
|
|
|
i__2 = *n - 1;
|
|
ix = izamax_(&i__2, &work[work_offset], &c__1);
|
|
i__2 = ix + work_dim1;
|
|
xnorm = (d__1 = work[i__2].r, abs(d__1)) + (d__2 = d_imag(
|
|
&work[ix + work_dim1]), abs(d__2));
|
|
if (scale < xnorm * smlnum || scale == 0.) {
|
|
goto L40;
|
|
}
|
|
zdrscl_(n, &scale, &work[work_offset], &c__1);
|
|
}
|
|
goto L30;
|
|
}
|
|
|
|
sep[ks] = 1. / f2cmax(est,smlnum);
|
|
}
|
|
|
|
L40:
|
|
++ks;
|
|
L50:
|
|
;
|
|
}
|
|
return;
|
|
|
|
/* End of ZTRSNA */
|
|
|
|
} /* ztrsna_ */
|
|
|