1189 lines
		
	
	
		
			31 KiB
		
	
	
	
		
			C
		
	
	
	
			
		
		
	
	
			1189 lines
		
	
	
		
			31 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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 | 
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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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#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;
 | 
						|
		for(u = n; ; ) {
 | 
						|
			if(u & 01) pow *= x;
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						|
			if(u >>= 1) x *= x;
 | 
						|
			else break;
 | 
						|
		}
 | 
						|
	}
 | 
						|
	return pow;
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						|
}
 | 
						|
#endif
 | 
						|
#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];
 | 
						|
		for(u = n; ; ) {
 | 
						|
			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;
 | 
						|
		}
 | 
						|
	}
 | 
						|
	_Dcomplex p = {pow._Val[0], pow._Val[1]};
 | 
						|
	return p;
 | 
						|
}
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						|
#else
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						|
static _Complex double zpow_ui(_Complex double x, integer n) {
 | 
						|
	_Complex double pow=1.0; unsigned long int u;
 | 
						|
	if(n != 0) {
 | 
						|
		if(n < 0) n = -n, x = 1/x;
 | 
						|
		for(u = n; ; ) {
 | 
						|
			if(u & 01) pow *= x;
 | 
						|
			if(u >>= 1) x *= x;
 | 
						|
			else break;
 | 
						|
		}
 | 
						|
	}
 | 
						|
	return pow;
 | 
						|
}
 | 
						|
#endif
 | 
						|
static integer pow_ii(integer x, integer n) {
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						|
	integer pow; unsigned long int u;
 | 
						|
	if (n <= 0) {
 | 
						|
		if (n == 0 || x == 1) pow = 1;
 | 
						|
		else if (x != -1) pow = x == 0 ? 1/x : 0;
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						|
		else n = -n;
 | 
						|
	}
 | 
						|
	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
 | 
						|
		u = n;
 | 
						|
		for(pow = 1; ; ) {
 | 
						|
			if(u & 01) pow *= x;
 | 
						|
			if(u >>= 1) x *= x;
 | 
						|
			else break;
 | 
						|
		}
 | 
						|
	}
 | 
						|
	return pow;
 | 
						|
}
 | 
						|
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
 | 
						|
{
 | 
						|
	double m; integer i, mi;
 | 
						|
	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
 | 
						|
		if (w[i-1]>m) mi=i ,m=w[i-1];
 | 
						|
	return mi-s+1;
 | 
						|
}
 | 
						|
static integer smaxloc_(float *w, integer s, integer e, integer *n)
 | 
						|
{
 | 
						|
	float m; integer i, mi;
 | 
						|
	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];
 | 
						|
	return mi-s+1;
 | 
						|
}
 | 
						|
static inline void cdotc_(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] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
 | 
						|
			zdotc._Val[1] += conjf(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] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
 | 
						|
			zdotc._Val[1] += conjf(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 += conjf(Cf(&x[i])) * Cf(&y[i]);
 | 
						|
		}
 | 
						|
	} else {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
 | 
						|
		}
 | 
						|
	}
 | 
						|
	pCf(z) = zdotc;
 | 
						|
}
 | 
						|
#endif
 | 
						|
static inline void zdotc_(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] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
 | 
						|
			zdotc._Val[1] += conj(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] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
 | 
						|
			zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
 | 
						|
		}
 | 
						|
	}
 | 
						|
	pCd(z) = zdotc;
 | 
						|
}
 | 
						|
#else
 | 
						|
	_Complex double zdotc = 0.0;
 | 
						|
	if (incx == 1 && incy == 1) {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
 | 
						|
		}
 | 
						|
	} else {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
 | 
						|
		}
 | 
						|
	}
 | 
						|
	pCd(z) = zdotc;
 | 
						|
}
 | 
						|
#endif	
 | 
						|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
 | 
						|
	integer n = *n_, incx = *incx_, incy = *incy_, i;
 | 
						|
#ifdef _MSC_VER
 | 
						|
	_Fcomplex zdotc = {0.0, 0.0};
 | 
						|
	if (incx == 1 && incy == 1) {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
 | 
						|
			zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
 | 
						|
		}
 | 
						|
	} else {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
 | 
						|
			zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
 | 
						|
		}
 | 
						|
	}
 | 
						|
	pCf(z) = zdotc;
 | 
						|
}
 | 
						|
#else
 | 
						|
	_Complex float zdotc = 0.0;
 | 
						|
	if (incx == 1 && incy == 1) {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc += Cf(&x[i]) * Cf(&y[i]);
 | 
						|
		}
 | 
						|
	} else {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
 | 
						|
		}
 | 
						|
	}
 | 
						|
	pCf(z) = zdotc;
 | 
						|
}
 | 
						|
#endif
 | 
						|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
 | 
						|
	integer n = *n_, incx = *incx_, incy = *incy_, i;
 | 
						|
#ifdef _MSC_VER
 | 
						|
	_Dcomplex zdotc = {0.0, 0.0};
 | 
						|
	if (incx == 1 && incy == 1) {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
 | 
						|
			zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
 | 
						|
		}
 | 
						|
	} else {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
 | 
						|
			zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
 | 
						|
		}
 | 
						|
	}
 | 
						|
	pCd(z) = zdotc;
 | 
						|
}
 | 
						|
#else
 | 
						|
	_Complex double zdotc = 0.0;
 | 
						|
	if (incx == 1 && incy == 1) {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc += Cd(&x[i]) * Cd(&y[i]);
 | 
						|
		}
 | 
						|
	} else {
 | 
						|
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 | 
						|
			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
 | 
						|
		}
 | 
						|
	}
 | 
						|
	pCd(z) = zdotc;
 | 
						|
}
 | 
						|
#endif
 | 
						|
/*  -- translated by f2c (version 20000121).
 | 
						|
   You must link the resulting object file with the libraries:
 | 
						|
	-lf2c -lm   (in that order)
 | 
						|
*/
 | 
						|
 | 
						|
 | 
						|
 | 
						|
 | 
						|
/* Table of constant values */
 | 
						|
 | 
						|
static integer c__1 = 1;
 | 
						|
static integer c__2 = 2;
 | 
						|
 | 
						|
/* > \brief \b SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix assoc
 | 
						|
iated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. */
 | 
						|
 | 
						|
/*  =========== DOCUMENTATION =========== */
 | 
						|
 | 
						|
/* Online html documentation available at */
 | 
						|
/*            http://www.netlib.org/lapack/explore-html/ */
 | 
						|
 | 
						|
/* > \htmlonly */
 | 
						|
/* > Download SLASQ2 + dependencies */
 | 
						|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasq2.
 | 
						|
f"> */
 | 
						|
/* > [TGZ]</a> */
 | 
						|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasq2.
 | 
						|
f"> */
 | 
						|
/* > [ZIP]</a> */
 | 
						|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasq2.
 | 
						|
f"> */
 | 
						|
/* > [TXT]</a> */
 | 
						|
/* > \endhtmlonly */
 | 
						|
 | 
						|
/*  Definition: */
 | 
						|
/*  =========== */
 | 
						|
 | 
						|
/*       SUBROUTINE SLASQ2( N, Z, INFO ) */
 | 
						|
 | 
						|
/*       INTEGER            INFO, N */
 | 
						|
/*       REAL               Z( * ) */
 | 
						|
 | 
						|
 | 
						|
/* > \par Purpose: */
 | 
						|
/*  ============= */
 | 
						|
/* > */
 | 
						|
/* > \verbatim */
 | 
						|
/* > */
 | 
						|
/* > SLASQ2 computes all the eigenvalues of the symmetric positive */
 | 
						|
/* > definite tridiagonal matrix associated with the qd array Z to high */
 | 
						|
/* > relative accuracy are computed to high relative accuracy, in the */
 | 
						|
/* > absence of denormalization, underflow and overflow. */
 | 
						|
/* > */
 | 
						|
/* > To see the relation of Z to the tridiagonal matrix, let L be a */
 | 
						|
/* > unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and */
 | 
						|
/* > let U be an upper bidiagonal matrix with 1's above and diagonal */
 | 
						|
/* > Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the */
 | 
						|
/* > symmetric tridiagonal to which it is similar. */
 | 
						|
/* > */
 | 
						|
/* > Note : SLASQ2 defines a logical variable, IEEE, which is true */
 | 
						|
/* > on machines which follow ieee-754 floating-point standard in their */
 | 
						|
/* > handling of infinities and NaNs, and false otherwise. This variable */
 | 
						|
/* > is passed to SLASQ3. */
 | 
						|
/* > \endverbatim */
 | 
						|
 | 
						|
/*  Arguments: */
 | 
						|
/*  ========== */
 | 
						|
 | 
						|
/* > \param[in] N */
 | 
						|
/* > \verbatim */
 | 
						|
/* >          N is INTEGER */
 | 
						|
/* >        The number of rows and columns in the matrix. N >= 0. */
 | 
						|
/* > \endverbatim */
 | 
						|
/* > */
 | 
						|
/* > \param[in,out] Z */
 | 
						|
/* > \verbatim */
 | 
						|
/* >          Z is REAL array, dimension ( 4*N ) */
 | 
						|
/* >        On entry Z holds the qd array. On exit, entries 1 to N hold */
 | 
						|
/* >        the eigenvalues in decreasing order, Z( 2*N+1 ) holds the */
 | 
						|
/* >        trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If */
 | 
						|
/* >        N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) */
 | 
						|
/* >        holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of */
 | 
						|
/* >        shifts that failed. */
 | 
						|
/* > \endverbatim */
 | 
						|
/* > */
 | 
						|
/* > \param[out] INFO */
 | 
						|
/* > \verbatim */
 | 
						|
/* >          INFO is INTEGER */
 | 
						|
/* >        = 0: successful exit */
 | 
						|
/* >        < 0: if the i-th argument is a scalar and had an illegal */
 | 
						|
/* >             value, then INFO = -i, if the i-th argument is an */
 | 
						|
/* >             array and the j-entry had an illegal value, then */
 | 
						|
/* >             INFO = -(i*100+j) */
 | 
						|
/* >        > 0: the algorithm failed */
 | 
						|
/* >              = 1, a split was marked by a positive value in E */
 | 
						|
/* >              = 2, current block of Z not diagonalized after 100*N */
 | 
						|
/* >                   iterations (in inner while loop).  On exit Z holds */
 | 
						|
/* >                   a qd array with the same eigenvalues as the given Z. */
 | 
						|
/* >              = 3, termination criterion of outer while loop not met */
 | 
						|
/* >                   (program created more than N unreduced blocks) */
 | 
						|
/* > \endverbatim */
 | 
						|
 | 
						|
/*  Authors: */
 | 
						|
/*  ======== */
 | 
						|
 | 
						|
/* > \author Univ. of Tennessee */
 | 
						|
/* > \author Univ. of California Berkeley */
 | 
						|
/* > \author Univ. of Colorado Denver */
 | 
						|
/* > \author NAG Ltd. */
 | 
						|
 | 
						|
/* > \date December 2016 */
 | 
						|
 | 
						|
/* > \ingroup auxOTHERcomputational */
 | 
						|
 | 
						|
/* > \par Further Details: */
 | 
						|
/*  ===================== */
 | 
						|
/* > */
 | 
						|
/* > \verbatim */
 | 
						|
/* > */
 | 
						|
/* >  Local Variables: I0:N0 defines a current unreduced segment of Z. */
 | 
						|
/* >  The shifts are accumulated in SIGMA. Iteration count is in ITER. */
 | 
						|
/* >  Ping-pong is controlled by PP (alternates between 0 and 1). */
 | 
						|
/* > \endverbatim */
 | 
						|
/* > */
 | 
						|
/*  ===================================================================== */
 | 
						|
/* Subroutine */ int slasq2_(integer *n, real *z__, integer *info)
 | 
						|
{
 | 
						|
    /* System generated locals */
 | 
						|
    integer i__1, i__2, i__3;
 | 
						|
    real r__1, r__2;
 | 
						|
 | 
						|
    /* Local variables */
 | 
						|
    logical ieee;
 | 
						|
    integer nbig;
 | 
						|
    real dmin__, emin, emax;
 | 
						|
    integer kmin, ndiv, iter;
 | 
						|
    real qmin, temp, qmax, zmax;
 | 
						|
    integer splt;
 | 
						|
    real dmin1, dmin2, d__, e, g;
 | 
						|
    integer k;
 | 
						|
    real s, t;
 | 
						|
    integer nfail;
 | 
						|
    real desig, trace, sigma;
 | 
						|
    integer iinfo;
 | 
						|
    real tempe, tempq;
 | 
						|
    integer i0, i1, i4, n0, n1, ttype;
 | 
						|
    extern /* Subroutine */ int slasq3_(integer *, integer *, real *, integer 
 | 
						|
	    *, real *, real *, real *, real *, integer *, integer *, integer *
 | 
						|
	    , logical *, integer *, real *, real *, real *, real *, real *, 
 | 
						|
	    real *, real *);
 | 
						|
    real dn;
 | 
						|
    integer pp;
 | 
						|
    real deemin;
 | 
						|
    extern real slamch_(char *);
 | 
						|
    integer iwhila, iwhilb;
 | 
						|
    real oldemn, safmin;
 | 
						|
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
 | 
						|
    real dn1, dn2;
 | 
						|
    extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);
 | 
						|
    real dee, eps, tau, tol;
 | 
						|
    integer ipn4;
 | 
						|
    real tol2;
 | 
						|
 | 
						|
 | 
						|
/*  -- LAPACK computational 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 */
 | 
						|
 | 
						|
 | 
						|
/*  ===================================================================== */
 | 
						|
 | 
						|
 | 
						|
/*     Test the input arguments. */
 | 
						|
/*     (in case SLASQ2 is not called by SLASQ1) */
 | 
						|
 | 
						|
    /* Parameter adjustments */
 | 
						|
    --z__;
 | 
						|
 | 
						|
    /* Function Body */
 | 
						|
    *info = 0;
 | 
						|
    eps = slamch_("Precision");
 | 
						|
    safmin = slamch_("Safe minimum");
 | 
						|
    tol = eps * 100.f;
 | 
						|
/* Computing 2nd power */
 | 
						|
    r__1 = tol;
 | 
						|
    tol2 = r__1 * r__1;
 | 
						|
 | 
						|
    if (*n < 0) {
 | 
						|
	*info = -1;
 | 
						|
	xerbla_("SLASQ2", &c__1, (ftnlen)6);
 | 
						|
	return 0;
 | 
						|
    } else if (*n == 0) {
 | 
						|
	return 0;
 | 
						|
    } else if (*n == 1) {
 | 
						|
 | 
						|
/*        1-by-1 case. */
 | 
						|
 | 
						|
	if (z__[1] < 0.f) {
 | 
						|
	    *info = -201;
 | 
						|
	    xerbla_("SLASQ2", &c__2, (ftnlen)6);
 | 
						|
	}
 | 
						|
	return 0;
 | 
						|
    } else if (*n == 2) {
 | 
						|
 | 
						|
/*        2-by-2 case. */
 | 
						|
 | 
						|
	if (z__[1] < 0.f) {
 | 
						|
	    *info = -201;
 | 
						|
	    xerbla_("SLASQ2", &c__2, (ftnlen)6);
 | 
						|
	    return 0;
 | 
						|
	} else if (z__[2] < 0.f) {
 | 
						|
	    *info = -202;
 | 
						|
	    xerbla_("SLASQ2", &c__2, (ftnlen)6);
 | 
						|
	    return 0;
 | 
						|
	} else if (z__[3] < 0.f) {
 | 
						|
	    *info = -203;
 | 
						|
	    xerbla_("SLASQ2", &c__2, (ftnlen)6);
 | 
						|
	    return 0;
 | 
						|
	} else if (z__[3] > z__[1]) {
 | 
						|
	    d__ = z__[3];
 | 
						|
	    z__[3] = z__[1];
 | 
						|
	    z__[1] = d__;
 | 
						|
	}
 | 
						|
	z__[5] = z__[1] + z__[2] + z__[3];
 | 
						|
	if (z__[2] > z__[3] * tol2) {
 | 
						|
	    t = (z__[1] - z__[3] + z__[2]) * .5f;
 | 
						|
	    s = z__[3] * (z__[2] / t);
 | 
						|
	    if (s <= t) {
 | 
						|
		s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.f) + 1.f)));
 | 
						|
	    } else {
 | 
						|
		s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s)));
 | 
						|
	    }
 | 
						|
	    t = z__[1] + (s + z__[2]);
 | 
						|
	    z__[3] *= z__[1] / t;
 | 
						|
	    z__[1] = t;
 | 
						|
	}
 | 
						|
	z__[2] = z__[3];
 | 
						|
	z__[6] = z__[2] + z__[1];
 | 
						|
	return 0;
 | 
						|
    }
 | 
						|
 | 
						|
/*     Check for negative data and compute sums of q's and e's. */
 | 
						|
 | 
						|
    z__[*n * 2] = 0.f;
 | 
						|
    emin = z__[2];
 | 
						|
    qmax = 0.f;
 | 
						|
    zmax = 0.f;
 | 
						|
    d__ = 0.f;
 | 
						|
    e = 0.f;
 | 
						|
 | 
						|
    i__1 = *n - 1 << 1;
 | 
						|
    for (k = 1; k <= i__1; k += 2) {
 | 
						|
	if (z__[k] < 0.f) {
 | 
						|
	    *info = -(k + 200);
 | 
						|
	    xerbla_("SLASQ2", &c__2, (ftnlen)6);
 | 
						|
	    return 0;
 | 
						|
	} else if (z__[k + 1] < 0.f) {
 | 
						|
	    *info = -(k + 201);
 | 
						|
	    xerbla_("SLASQ2", &c__2, (ftnlen)6);
 | 
						|
	    return 0;
 | 
						|
	}
 | 
						|
	d__ += z__[k];
 | 
						|
	e += z__[k + 1];
 | 
						|
/* Computing MAX */
 | 
						|
	r__1 = qmax, r__2 = z__[k];
 | 
						|
	qmax = f2cmax(r__1,r__2);
 | 
						|
/* Computing MIN */
 | 
						|
	r__1 = emin, r__2 = z__[k + 1];
 | 
						|
	emin = f2cmin(r__1,r__2);
 | 
						|
/* Computing MAX */
 | 
						|
	r__1 = f2cmax(qmax,zmax), r__2 = z__[k + 1];
 | 
						|
	zmax = f2cmax(r__1,r__2);
 | 
						|
/* L10: */
 | 
						|
    }
 | 
						|
    if (z__[(*n << 1) - 1] < 0.f) {
 | 
						|
	*info = -((*n << 1) + 199);
 | 
						|
	xerbla_("SLASQ2", &c__2, (ftnlen)6);
 | 
						|
	return 0;
 | 
						|
    }
 | 
						|
    d__ += z__[(*n << 1) - 1];
 | 
						|
/* Computing MAX */
 | 
						|
    r__1 = qmax, r__2 = z__[(*n << 1) - 1];
 | 
						|
    qmax = f2cmax(r__1,r__2);
 | 
						|
    zmax = f2cmax(qmax,zmax);
 | 
						|
 | 
						|
/*     Check for diagonality. */
 | 
						|
 | 
						|
    if (e == 0.f) {
 | 
						|
	i__1 = *n;
 | 
						|
	for (k = 2; k <= i__1; ++k) {
 | 
						|
	    z__[k] = z__[(k << 1) - 1];
 | 
						|
/* L20: */
 | 
						|
	}
 | 
						|
	slasrt_("D", n, &z__[1], &iinfo);
 | 
						|
	z__[(*n << 1) - 1] = d__;
 | 
						|
	return 0;
 | 
						|
    }
 | 
						|
 | 
						|
    trace = d__ + e;
 | 
						|
 | 
						|
/*     Check for zero data. */
 | 
						|
 | 
						|
    if (trace == 0.f) {
 | 
						|
	z__[(*n << 1) - 1] = 0.f;
 | 
						|
	return 0;
 | 
						|
    }
 | 
						|
 | 
						|
/*     Check whether the machine is IEEE conformable. */
 | 
						|
 | 
						|
/*     IEEE = ILAENV( 10, 'SLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 .AND. */
 | 
						|
/*    $       ILAENV( 11, 'SLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 */
 | 
						|
 | 
						|
/*     [11/15/2008] The case IEEE=.TRUE. has a problem in single precision with */
 | 
						|
/*     some the test matrices of type 16. The double precision code is fine. */
 | 
						|
 | 
						|
    ieee = FALSE_;
 | 
						|
 | 
						|
/*     Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */
 | 
						|
 | 
						|
    for (k = *n << 1; k >= 2; k += -2) {
 | 
						|
	z__[k * 2] = 0.f;
 | 
						|
	z__[(k << 1) - 1] = z__[k];
 | 
						|
	z__[(k << 1) - 2] = 0.f;
 | 
						|
	z__[(k << 1) - 3] = z__[k - 1];
 | 
						|
/* L30: */
 | 
						|
    }
 | 
						|
 | 
						|
    i0 = 1;
 | 
						|
    n0 = *n;
 | 
						|
 | 
						|
/*     Reverse the qd-array, if warranted. */
 | 
						|
 | 
						|
    if (z__[(i0 << 2) - 3] * 1.5f < z__[(n0 << 2) - 3]) {
 | 
						|
	ipn4 = i0 + n0 << 2;
 | 
						|
	i__1 = i0 + n0 - 1 << 1;
 | 
						|
	for (i4 = i0 << 2; i4 <= i__1; i4 += 4) {
 | 
						|
	    temp = z__[i4 - 3];
 | 
						|
	    z__[i4 - 3] = z__[ipn4 - i4 - 3];
 | 
						|
	    z__[ipn4 - i4 - 3] = temp;
 | 
						|
	    temp = z__[i4 - 1];
 | 
						|
	    z__[i4 - 1] = z__[ipn4 - i4 - 5];
 | 
						|
	    z__[ipn4 - i4 - 5] = temp;
 | 
						|
/* L40: */
 | 
						|
	}
 | 
						|
    }
 | 
						|
 | 
						|
/*     Initial split checking via dqd and Li's test. */
 | 
						|
 | 
						|
    pp = 0;
 | 
						|
 | 
						|
    for (k = 1; k <= 2; ++k) {
 | 
						|
 | 
						|
	d__ = z__[(n0 << 2) + pp - 3];
 | 
						|
	i__1 = (i0 << 2) + pp;
 | 
						|
	for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) {
 | 
						|
	    if (z__[i4 - 1] <= tol2 * d__) {
 | 
						|
		z__[i4 - 1] = 0.f;
 | 
						|
		d__ = z__[i4 - 3];
 | 
						|
	    } else {
 | 
						|
		d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1]));
 | 
						|
	    }
 | 
						|
/* L50: */
 | 
						|
	}
 | 
						|
 | 
						|
/*        dqd maps Z to ZZ plus Li's test. */
 | 
						|
 | 
						|
	emin = z__[(i0 << 2) + pp + 1];
 | 
						|
	d__ = z__[(i0 << 2) + pp - 3];
 | 
						|
	i__1 = (n0 - 1 << 2) + pp;
 | 
						|
	for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) {
 | 
						|
	    z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1];
 | 
						|
	    if (z__[i4 - 1] <= tol2 * d__) {
 | 
						|
		z__[i4 - 1] = 0.f;
 | 
						|
		z__[i4 - (pp << 1) - 2] = d__;
 | 
						|
		z__[i4 - (pp << 1)] = 0.f;
 | 
						|
		d__ = z__[i4 + 1];
 | 
						|
	    } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] && 
 | 
						|
		    safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) {
 | 
						|
		temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2];
 | 
						|
		z__[i4 - (pp << 1)] = z__[i4 - 1] * temp;
 | 
						|
		d__ *= temp;
 | 
						|
	    } else {
 | 
						|
		z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - (
 | 
						|
			pp << 1) - 2]);
 | 
						|
		d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]);
 | 
						|
	    }
 | 
						|
/* Computing MIN */
 | 
						|
	    r__1 = emin, r__2 = z__[i4 - (pp << 1)];
 | 
						|
	    emin = f2cmin(r__1,r__2);
 | 
						|
/* L60: */
 | 
						|
	}
 | 
						|
	z__[(n0 << 2) - pp - 2] = d__;
 | 
						|
 | 
						|
/*        Now find qmax. */
 | 
						|
 | 
						|
	qmax = z__[(i0 << 2) - pp - 2];
 | 
						|
	i__1 = (n0 << 2) - pp - 2;
 | 
						|
	for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) {
 | 
						|
/* Computing MAX */
 | 
						|
	    r__1 = qmax, r__2 = z__[i4];
 | 
						|
	    qmax = f2cmax(r__1,r__2);
 | 
						|
/* L70: */
 | 
						|
	}
 | 
						|
 | 
						|
/*        Prepare for the next iteration on K. */
 | 
						|
 | 
						|
	pp = 1 - pp;
 | 
						|
/* L80: */
 | 
						|
    }
 | 
						|
 | 
						|
/*     Initialise variables to pass to SLASQ3. */
 | 
						|
 | 
						|
    ttype = 0;
 | 
						|
    dmin1 = 0.f;
 | 
						|
    dmin2 = 0.f;
 | 
						|
    dn = 0.f;
 | 
						|
    dn1 = 0.f;
 | 
						|
    dn2 = 0.f;
 | 
						|
    g = 0.f;
 | 
						|
    tau = 0.f;
 | 
						|
 | 
						|
    iter = 2;
 | 
						|
    nfail = 0;
 | 
						|
    ndiv = n0 - i0 << 1;
 | 
						|
 | 
						|
    i__1 = *n + 1;
 | 
						|
    for (iwhila = 1; iwhila <= i__1; ++iwhila) {
 | 
						|
	if (n0 < 1) {
 | 
						|
	    goto L170;
 | 
						|
	}
 | 
						|
 | 
						|
/*        While array unfinished do */
 | 
						|
 | 
						|
/*        E(N0) holds the value of SIGMA when submatrix in I0:N0 */
 | 
						|
/*        splits from the rest of the array, but is negated. */
 | 
						|
 | 
						|
	desig = 0.f;
 | 
						|
	if (n0 == *n) {
 | 
						|
	    sigma = 0.f;
 | 
						|
	} else {
 | 
						|
	    sigma = -z__[(n0 << 2) - 1];
 | 
						|
	}
 | 
						|
	if (sigma < 0.f) {
 | 
						|
	    *info = 1;
 | 
						|
	    return 0;
 | 
						|
	}
 | 
						|
 | 
						|
/*        Find last unreduced submatrix's top index I0, find QMAX and */
 | 
						|
/*        EMIN. Find Gershgorin-type bound if Q's much greater than E's. */
 | 
						|
 | 
						|
	emax = 0.f;
 | 
						|
	if (n0 > i0) {
 | 
						|
	    emin = (r__1 = z__[(n0 << 2) - 5], abs(r__1));
 | 
						|
	} else {
 | 
						|
	    emin = 0.f;
 | 
						|
	}
 | 
						|
	qmin = z__[(n0 << 2) - 3];
 | 
						|
	qmax = qmin;
 | 
						|
	for (i4 = n0 << 2; i4 >= 8; i4 += -4) {
 | 
						|
	    if (z__[i4 - 5] <= 0.f) {
 | 
						|
		goto L100;
 | 
						|
	    }
 | 
						|
	    if (qmin >= emax * 4.f) {
 | 
						|
/* Computing MIN */
 | 
						|
		r__1 = qmin, r__2 = z__[i4 - 3];
 | 
						|
		qmin = f2cmin(r__1,r__2);
 | 
						|
/* Computing MAX */
 | 
						|
		r__1 = emax, r__2 = z__[i4 - 5];
 | 
						|
		emax = f2cmax(r__1,r__2);
 | 
						|
	    }
 | 
						|
/* Computing MAX */
 | 
						|
	    r__1 = qmax, r__2 = z__[i4 - 7] + z__[i4 - 5];
 | 
						|
	    qmax = f2cmax(r__1,r__2);
 | 
						|
/* Computing MIN */
 | 
						|
	    r__1 = emin, r__2 = z__[i4 - 5];
 | 
						|
	    emin = f2cmin(r__1,r__2);
 | 
						|
/* L90: */
 | 
						|
	}
 | 
						|
	i4 = 4;
 | 
						|
 | 
						|
L100:
 | 
						|
	i0 = i4 / 4;
 | 
						|
	pp = 0;
 | 
						|
 | 
						|
	if (n0 - i0 > 1) {
 | 
						|
	    dee = z__[(i0 << 2) - 3];
 | 
						|
	    deemin = dee;
 | 
						|
	    kmin = i0;
 | 
						|
	    i__2 = (n0 << 2) - 3;
 | 
						|
	    for (i4 = (i0 << 2) + 1; i4 <= i__2; i4 += 4) {
 | 
						|
		dee = z__[i4] * (dee / (dee + z__[i4 - 2]));
 | 
						|
		if (dee <= deemin) {
 | 
						|
		    deemin = dee;
 | 
						|
		    kmin = (i4 + 3) / 4;
 | 
						|
		}
 | 
						|
/* L110: */
 | 
						|
	    }
 | 
						|
	    if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] * 
 | 
						|
		    .5f) {
 | 
						|
		ipn4 = i0 + n0 << 2;
 | 
						|
		pp = 2;
 | 
						|
		i__2 = i0 + n0 - 1 << 1;
 | 
						|
		for (i4 = i0 << 2; i4 <= i__2; i4 += 4) {
 | 
						|
		    temp = z__[i4 - 3];
 | 
						|
		    z__[i4 - 3] = z__[ipn4 - i4 - 3];
 | 
						|
		    z__[ipn4 - i4 - 3] = temp;
 | 
						|
		    temp = z__[i4 - 2];
 | 
						|
		    z__[i4 - 2] = z__[ipn4 - i4 - 2];
 | 
						|
		    z__[ipn4 - i4 - 2] = temp;
 | 
						|
		    temp = z__[i4 - 1];
 | 
						|
		    z__[i4 - 1] = z__[ipn4 - i4 - 5];
 | 
						|
		    z__[ipn4 - i4 - 5] = temp;
 | 
						|
		    temp = z__[i4];
 | 
						|
		    z__[i4] = z__[ipn4 - i4 - 4];
 | 
						|
		    z__[ipn4 - i4 - 4] = temp;
 | 
						|
/* L120: */
 | 
						|
		}
 | 
						|
	    }
 | 
						|
	}
 | 
						|
 | 
						|
/*        Put -(initial shift) into DMIN. */
 | 
						|
 | 
						|
/* Computing MAX */
 | 
						|
	r__1 = 0.f, r__2 = qmin - sqrt(qmin) * 2.f * sqrt(emax);
 | 
						|
	dmin__ = -f2cmax(r__1,r__2);
 | 
						|
 | 
						|
/*        Now I0:N0 is unreduced. */
 | 
						|
/*        PP = 0 for ping, PP = 1 for pong. */
 | 
						|
/*        PP = 2 indicates that flipping was applied to the Z array and */
 | 
						|
/*               and that the tests for deflation upon entry in SLASQ3 */
 | 
						|
/*               should not be performed. */
 | 
						|
 | 
						|
	nbig = (n0 - i0 + 1) * 100;
 | 
						|
	i__2 = nbig;
 | 
						|
	for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) {
 | 
						|
	    if (i0 > n0) {
 | 
						|
		goto L150;
 | 
						|
	    }
 | 
						|
 | 
						|
/*           While submatrix unfinished take a good dqds step. */
 | 
						|
 | 
						|
	    slasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, &
 | 
						|
		    nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, &
 | 
						|
		    dn1, &dn2, &g, &tau);
 | 
						|
 | 
						|
	    pp = 1 - pp;
 | 
						|
 | 
						|
/*           When EMIN is very small check for splits. */
 | 
						|
 | 
						|
	    if (pp == 0 && n0 - i0 >= 3) {
 | 
						|
		if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 *
 | 
						|
			 sigma) {
 | 
						|
		    splt = i0 - 1;
 | 
						|
		    qmax = z__[(i0 << 2) - 3];
 | 
						|
		    emin = z__[(i0 << 2) - 1];
 | 
						|
		    oldemn = z__[i0 * 4];
 | 
						|
		    i__3 = n0 - 3 << 2;
 | 
						|
		    for (i4 = i0 << 2; i4 <= i__3; i4 += 4) {
 | 
						|
			if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <= 
 | 
						|
				tol2 * sigma) {
 | 
						|
			    z__[i4 - 1] = -sigma;
 | 
						|
			    splt = i4 / 4;
 | 
						|
			    qmax = 0.f;
 | 
						|
			    emin = z__[i4 + 3];
 | 
						|
			    oldemn = z__[i4 + 4];
 | 
						|
			} else {
 | 
						|
/* Computing MAX */
 | 
						|
			    r__1 = qmax, r__2 = z__[i4 + 1];
 | 
						|
			    qmax = f2cmax(r__1,r__2);
 | 
						|
/* Computing MIN */
 | 
						|
			    r__1 = emin, r__2 = z__[i4 - 1];
 | 
						|
			    emin = f2cmin(r__1,r__2);
 | 
						|
/* Computing MIN */
 | 
						|
			    r__1 = oldemn, r__2 = z__[i4];
 | 
						|
			    oldemn = f2cmin(r__1,r__2);
 | 
						|
			}
 | 
						|
/* L130: */
 | 
						|
		    }
 | 
						|
		    z__[(n0 << 2) - 1] = emin;
 | 
						|
		    z__[n0 * 4] = oldemn;
 | 
						|
		    i0 = splt + 1;
 | 
						|
		}
 | 
						|
	    }
 | 
						|
 | 
						|
/* L140: */
 | 
						|
	}
 | 
						|
 | 
						|
	*info = 2;
 | 
						|
 | 
						|
/*        Maximum number of iterations exceeded, restore the shift */
 | 
						|
/*        SIGMA and place the new d's and e's in a qd array. */
 | 
						|
/*        This might need to be done for several blocks */
 | 
						|
 | 
						|
	i1 = i0;
 | 
						|
	n1 = n0;
 | 
						|
L145:
 | 
						|
	tempq = z__[(i0 << 2) - 3];
 | 
						|
	z__[(i0 << 2) - 3] += sigma;
 | 
						|
	i__2 = n0;
 | 
						|
	for (k = i0 + 1; k <= i__2; ++k) {
 | 
						|
	    tempe = z__[(k << 2) - 5];
 | 
						|
	    z__[(k << 2) - 5] *= tempq / z__[(k << 2) - 7];
 | 
						|
	    tempq = z__[(k << 2) - 3];
 | 
						|
	    z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k << 
 | 
						|
		    2) - 5];
 | 
						|
	}
 | 
						|
 | 
						|
/*        Prepare to do this on the previous block if there is one */
 | 
						|
 | 
						|
	if (i1 > 1) {
 | 
						|
	    n1 = i1 - 1;
 | 
						|
	    while(i1 >= 2 && z__[(i1 << 2) - 5] >= 0.f) {
 | 
						|
		--i1;
 | 
						|
	    }
 | 
						|
	    if (i1 >= 1) {
 | 
						|
		sigma = -z__[(n1 << 2) - 1];
 | 
						|
		goto L145;
 | 
						|
	    }
 | 
						|
	}
 | 
						|
	i__2 = *n;
 | 
						|
	for (k = 1; k <= i__2; ++k) {
 | 
						|
	    z__[(k << 1) - 1] = z__[(k << 2) - 3];
 | 
						|
 | 
						|
/*        Only the block 1..N0 is unfinished.  The rest of the e's */
 | 
						|
/*        must be essentially zero, although sometimes other data */
 | 
						|
/*        has been stored in them. */
 | 
						|
 | 
						|
	    if (k < n0) {
 | 
						|
		z__[k * 2] = z__[(k << 2) - 1];
 | 
						|
	    } else {
 | 
						|
		z__[k * 2] = 0.f;
 | 
						|
	    }
 | 
						|
	}
 | 
						|
	return 0;
 | 
						|
 | 
						|
/*        end IWHILB */
 | 
						|
 | 
						|
L150:
 | 
						|
 | 
						|
/* L160: */
 | 
						|
	;
 | 
						|
    }
 | 
						|
 | 
						|
    *info = 3;
 | 
						|
    return 0;
 | 
						|
 | 
						|
/*     end IWHILA */
 | 
						|
 | 
						|
L170:
 | 
						|
 | 
						|
/*     Move q's to the front. */
 | 
						|
 | 
						|
    i__1 = *n;
 | 
						|
    for (k = 2; k <= i__1; ++k) {
 | 
						|
	z__[k] = z__[(k << 2) - 3];
 | 
						|
/* L180: */
 | 
						|
    }
 | 
						|
 | 
						|
/*     Sort and compute sum of eigenvalues. */
 | 
						|
 | 
						|
    slasrt_("D", n, &z__[1], &iinfo);
 | 
						|
 | 
						|
    e = 0.f;
 | 
						|
    for (k = *n; k >= 1; --k) {
 | 
						|
	e += z__[k];
 | 
						|
/* L190: */
 | 
						|
    }
 | 
						|
 | 
						|
/*     Store trace, sum(eigenvalues) and information on performance. */
 | 
						|
 | 
						|
    z__[(*n << 1) + 1] = trace;
 | 
						|
    z__[(*n << 1) + 2] = e;
 | 
						|
    z__[(*n << 1) + 3] = (real) iter;
 | 
						|
/* Computing 2nd power */
 | 
						|
    i__1 = *n;
 | 
						|
    z__[(*n << 1) + 4] = (real) ndiv / (real) (i__1 * i__1);
 | 
						|
    z__[(*n << 1) + 5] = nfail * 100.f / (real) iter;
 | 
						|
    return 0;
 | 
						|
 | 
						|
/*     End of SLASQ2 */
 | 
						|
 | 
						|
} /* slasq2_ */
 | 
						|
 |