876 lines
24 KiB
C
876 lines
24 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) */
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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)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* > \brief \b DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B su
|
|
ch that the rows of the transformed A and B are parallel. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLAGS2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlags2.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlags2.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlags2.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, */
|
|
/* SNV, CSQ, SNQ ) */
|
|
|
|
/* LOGICAL UPPER */
|
|
/* DOUBLE PRECISION A1, A2, A3, B1, B2, B3, CSQ, CSU, CSV, SNQ, */
|
|
/* $ SNU, SNV */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such */
|
|
/* > that if ( UPPER ) then */
|
|
/* > */
|
|
/* > U**T *A*Q = U**T *( A1 A2 )*Q = ( x 0 ) */
|
|
/* > ( 0 A3 ) ( x x ) */
|
|
/* > and */
|
|
/* > V**T*B*Q = V**T *( B1 B2 )*Q = ( x 0 ) */
|
|
/* > ( 0 B3 ) ( x x ) */
|
|
/* > */
|
|
/* > or if ( .NOT.UPPER ) then */
|
|
/* > */
|
|
/* > U**T *A*Q = U**T *( A1 0 )*Q = ( x x ) */
|
|
/* > ( A2 A3 ) ( 0 x ) */
|
|
/* > and */
|
|
/* > V**T*B*Q = V**T*( B1 0 )*Q = ( x x ) */
|
|
/* > ( B2 B3 ) ( 0 x ) */
|
|
/* > */
|
|
/* > The rows of the transformed A and B are parallel, where */
|
|
/* > */
|
|
/* > U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) */
|
|
/* > ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) */
|
|
/* > */
|
|
/* > Z**T denotes the transpose of Z. */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPPER */
|
|
/* > \verbatim */
|
|
/* > UPPER is LOGICAL */
|
|
/* > = .TRUE.: the input matrices A and B are upper triangular. */
|
|
/* > = .FALSE.: the input matrices A and B are lower triangular. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A1 */
|
|
/* > \verbatim */
|
|
/* > A1 is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A2 */
|
|
/* > \verbatim */
|
|
/* > A2 is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A3 */
|
|
/* > \verbatim */
|
|
/* > A3 is DOUBLE PRECISION */
|
|
/* > On entry, A1, A2 and A3 are elements of the input 2-by-2 */
|
|
/* > upper (lower) triangular matrix A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B1 */
|
|
/* > \verbatim */
|
|
/* > B1 is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B2 */
|
|
/* > \verbatim */
|
|
/* > B2 is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B3 */
|
|
/* > \verbatim */
|
|
/* > B3 is DOUBLE PRECISION */
|
|
/* > On entry, B1, B2 and B3 are elements of the input 2-by-2 */
|
|
/* > upper (lower) triangular matrix B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] CSU */
|
|
/* > \verbatim */
|
|
/* > CSU is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SNU */
|
|
/* > \verbatim */
|
|
/* > SNU is DOUBLE PRECISION */
|
|
/* > The desired orthogonal matrix U. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] CSV */
|
|
/* > \verbatim */
|
|
/* > CSV is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SNV */
|
|
/* > \verbatim */
|
|
/* > SNV is DOUBLE PRECISION */
|
|
/* > The desired orthogonal matrix V. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] CSQ */
|
|
/* > \verbatim */
|
|
/* > CSQ is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SNQ */
|
|
/* > \verbatim */
|
|
/* > SNQ is DOUBLE PRECISION */
|
|
/* > The desired orthogonal matrix Q. */
|
|
/* > \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 dlags2_(logical *upper, doublereal *a1, doublereal *a2,
|
|
doublereal *a3, doublereal *b1, doublereal *b2, doublereal *b3,
|
|
doublereal *csu, doublereal *snu, doublereal *csv, doublereal *snv,
|
|
doublereal *csq, doublereal *snq)
|
|
{
|
|
/* System generated locals */
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
doublereal aua11, aua12, aua21, aua22, avb11, avb12, avb21, avb22, ua11r,
|
|
ua22r, vb11r, vb22r, a, b, c__, d__, r__, s1, s2;
|
|
extern /* Subroutine */ void dlasv2_(doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *), dlartg_(doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *);
|
|
doublereal ua11, ua12, ua21, ua22, vb11, vb12, vb21, vb22, csl, csr, snl,
|
|
snr;
|
|
|
|
|
|
/* -- 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
if (*upper) {
|
|
|
|
/* Input matrices A and B are upper triangular matrices */
|
|
|
|
/* Form matrix C = A*adj(B) = ( a b ) */
|
|
/* ( 0 d ) */
|
|
|
|
a = *a1 * *b3;
|
|
d__ = *a3 * *b1;
|
|
b = *a2 * *b1 - *a1 * *b2;
|
|
|
|
/* The SVD of real 2-by-2 triangular C */
|
|
|
|
/* ( CSL -SNL )*( A B )*( CSR SNR ) = ( R 0 ) */
|
|
/* ( SNL CSL ) ( 0 D ) ( -SNR CSR ) ( 0 T ) */
|
|
|
|
dlasv2_(&a, &b, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
|
|
|
|
if (abs(csl) >= abs(snl) || abs(csr) >= abs(snr)) {
|
|
|
|
/* Compute the (1,1) and (1,2) elements of U**T *A and V**T *B, */
|
|
/* and (1,2) element of |U|**T *|A| and |V|**T *|B|. */
|
|
|
|
ua11r = csl * *a1;
|
|
ua12 = csl * *a2 + snl * *a3;
|
|
|
|
vb11r = csr * *b1;
|
|
vb12 = csr * *b2 + snr * *b3;
|
|
|
|
aua12 = abs(csl) * abs(*a2) + abs(snl) * abs(*a3);
|
|
avb12 = abs(csr) * abs(*b2) + abs(snr) * abs(*b3);
|
|
|
|
/* zero (1,2) elements of U**T *A and V**T *B */
|
|
|
|
if (abs(ua11r) + abs(ua12) != 0.) {
|
|
if (aua12 / (abs(ua11r) + abs(ua12)) <= avb12 / (abs(vb11r) +
|
|
abs(vb12))) {
|
|
d__1 = -ua11r;
|
|
dlartg_(&d__1, &ua12, csq, snq, &r__);
|
|
} else {
|
|
d__1 = -vb11r;
|
|
dlartg_(&d__1, &vb12, csq, snq, &r__);
|
|
}
|
|
} else {
|
|
d__1 = -vb11r;
|
|
dlartg_(&d__1, &vb12, csq, snq, &r__);
|
|
}
|
|
|
|
*csu = csl;
|
|
*snu = -snl;
|
|
*csv = csr;
|
|
*snv = -snr;
|
|
|
|
} else {
|
|
|
|
/* Compute the (2,1) and (2,2) elements of U**T *A and V**T *B, */
|
|
/* and (2,2) element of |U|**T *|A| and |V|**T *|B|. */
|
|
|
|
ua21 = -snl * *a1;
|
|
ua22 = -snl * *a2 + csl * *a3;
|
|
|
|
vb21 = -snr * *b1;
|
|
vb22 = -snr * *b2 + csr * *b3;
|
|
|
|
aua22 = abs(snl) * abs(*a2) + abs(csl) * abs(*a3);
|
|
avb22 = abs(snr) * abs(*b2) + abs(csr) * abs(*b3);
|
|
|
|
/* zero (2,2) elements of U**T*A and V**T*B, and then swap. */
|
|
|
|
if (abs(ua21) + abs(ua22) != 0.) {
|
|
if (aua22 / (abs(ua21) + abs(ua22)) <= avb22 / (abs(vb21) +
|
|
abs(vb22))) {
|
|
d__1 = -ua21;
|
|
dlartg_(&d__1, &ua22, csq, snq, &r__);
|
|
} else {
|
|
d__1 = -vb21;
|
|
dlartg_(&d__1, &vb22, csq, snq, &r__);
|
|
}
|
|
} else {
|
|
d__1 = -vb21;
|
|
dlartg_(&d__1, &vb22, csq, snq, &r__);
|
|
}
|
|
|
|
*csu = snl;
|
|
*snu = csl;
|
|
*csv = snr;
|
|
*snv = csr;
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Input matrices A and B are lower triangular matrices */
|
|
|
|
/* Form matrix C = A*adj(B) = ( a 0 ) */
|
|
/* ( c d ) */
|
|
|
|
a = *a1 * *b3;
|
|
d__ = *a3 * *b1;
|
|
c__ = *a2 * *b3 - *a3 * *b2;
|
|
|
|
/* The SVD of real 2-by-2 triangular C */
|
|
|
|
/* ( CSL -SNL )*( A 0 )*( CSR SNR ) = ( R 0 ) */
|
|
/* ( SNL CSL ) ( C D ) ( -SNR CSR ) ( 0 T ) */
|
|
|
|
dlasv2_(&a, &c__, &d__, &s1, &s2, &snr, &csr, &snl, &csl);
|
|
|
|
if (abs(csr) >= abs(snr) || abs(csl) >= abs(snl)) {
|
|
|
|
/* Compute the (2,1) and (2,2) elements of U**T *A and V**T *B, */
|
|
/* and (2,1) element of |U|**T *|A| and |V|**T *|B|. */
|
|
|
|
ua21 = -snr * *a1 + csr * *a2;
|
|
ua22r = csr * *a3;
|
|
|
|
vb21 = -snl * *b1 + csl * *b2;
|
|
vb22r = csl * *b3;
|
|
|
|
aua21 = abs(snr) * abs(*a1) + abs(csr) * abs(*a2);
|
|
avb21 = abs(snl) * abs(*b1) + abs(csl) * abs(*b2);
|
|
|
|
/* zero (2,1) elements of U**T *A and V**T *B. */
|
|
|
|
if (abs(ua21) + abs(ua22r) != 0.) {
|
|
if (aua21 / (abs(ua21) + abs(ua22r)) <= avb21 / (abs(vb21) +
|
|
abs(vb22r))) {
|
|
dlartg_(&ua22r, &ua21, csq, snq, &r__);
|
|
} else {
|
|
dlartg_(&vb22r, &vb21, csq, snq, &r__);
|
|
}
|
|
} else {
|
|
dlartg_(&vb22r, &vb21, csq, snq, &r__);
|
|
}
|
|
|
|
*csu = csr;
|
|
*snu = -snr;
|
|
*csv = csl;
|
|
*snv = -snl;
|
|
|
|
} else {
|
|
|
|
/* Compute the (1,1) and (1,2) elements of U**T *A and V**T *B, */
|
|
/* and (1,1) element of |U|**T *|A| and |V|**T *|B|. */
|
|
|
|
ua11 = csr * *a1 + snr * *a2;
|
|
ua12 = snr * *a3;
|
|
|
|
vb11 = csl * *b1 + snl * *b2;
|
|
vb12 = snl * *b3;
|
|
|
|
aua11 = abs(csr) * abs(*a1) + abs(snr) * abs(*a2);
|
|
avb11 = abs(csl) * abs(*b1) + abs(snl) * abs(*b2);
|
|
|
|
/* zero (1,1) elements of U**T*A and V**T*B, and then swap. */
|
|
|
|
if (abs(ua11) + abs(ua12) != 0.) {
|
|
if (aua11 / (abs(ua11) + abs(ua12)) <= avb11 / (abs(vb11) +
|
|
abs(vb12))) {
|
|
dlartg_(&ua12, &ua11, csq, snq, &r__);
|
|
} else {
|
|
dlartg_(&vb12, &vb11, csq, snq, &r__);
|
|
}
|
|
} else {
|
|
dlartg_(&vb12, &vb11, csq, snq, &r__);
|
|
}
|
|
|
|
*csu = snr;
|
|
*snu = csr;
|
|
*csv = snl;
|
|
*snv = csl;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DLAGS2 */
|
|
|
|
} /* dlags2_ */
|
|
|