1381 lines
37 KiB
C
1381 lines
37 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/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;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZHBTRD */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZHBTRD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbtrd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbtrd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbtrd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, */
|
|
/* WORK, INFO ) */
|
|
|
|
/* CHARACTER UPLO, VECT */
|
|
/* INTEGER INFO, KD, LDAB, LDQ, N */
|
|
/* DOUBLE PRECISION D( * ), E( * ) */
|
|
/* COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZHBTRD reduces a complex Hermitian band matrix A to real symmetric */
|
|
/* > tridiagonal form T by a unitary similarity transformation: */
|
|
/* > Q**H * A * Q = T. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] VECT */
|
|
/* > \verbatim */
|
|
/* > VECT is CHARACTER*1 */
|
|
/* > = 'N': do not form Q; */
|
|
/* > = 'V': form Q; */
|
|
/* > = 'U': update a matrix X, by forming X*Q. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': Upper triangle of A is stored; */
|
|
/* > = 'L': Lower triangle of A is stored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KD */
|
|
/* > \verbatim */
|
|
/* > KD is INTEGER */
|
|
/* > The number of superdiagonals of the matrix A if UPLO = 'U', */
|
|
/* > or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AB */
|
|
/* > \verbatim */
|
|
/* > AB is COMPLEX*16 array, dimension (LDAB,N) */
|
|
/* > On entry, the upper or lower triangle of the Hermitian band */
|
|
/* > matrix A, stored in the first KD+1 rows of the array. The */
|
|
/* > j-th column of A is stored in the j-th column of the array AB */
|
|
/* > as follows: */
|
|
/* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
|
|
/* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
|
|
/* > On exit, the diagonal elements of AB are overwritten by the */
|
|
/* > diagonal elements of the tridiagonal matrix T; if KD > 0, the */
|
|
/* > elements on the first superdiagonal (if UPLO = 'U') or the */
|
|
/* > first subdiagonal (if UPLO = 'L') are overwritten by the */
|
|
/* > off-diagonal elements of T; the rest of AB is overwritten by */
|
|
/* > values generated during the reduction. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array AB. LDAB >= KD+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The diagonal elements of the tridiagonal matrix T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The off-diagonal elements of the tridiagonal matrix T: */
|
|
/* > E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is COMPLEX*16 array, dimension (LDQ,N) */
|
|
/* > On entry, if VECT = 'U', then Q must contain an N-by-N */
|
|
/* > matrix X; if VECT = 'N' or 'V', then Q need not be set. */
|
|
/* > */
|
|
/* > On exit: */
|
|
/* > if VECT = 'V', Q contains the N-by-N unitary matrix Q; */
|
|
/* > if VECT = 'U', Q contains the product X*Q; */
|
|
/* > if VECT = 'N', the array Q is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. */
|
|
/* > LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Modified by Linda Kaufman, Bell Labs. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zhbtrd_(char *vect, char *uplo, integer *n, integer *kd,
|
|
doublecomplex *ab, integer *ldab, doublereal *d__, doublereal *e,
|
|
doublecomplex *q, integer *ldq, doublecomplex *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, q_dim1, q_offset, i__1, i__2, i__3, i__4,
|
|
i__5, i__6;
|
|
doublereal d__1;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
integer inca, jend, lend, jinc;
|
|
doublereal abst;
|
|
integer incx, last;
|
|
doublecomplex temp;
|
|
extern /* Subroutine */ void zrot_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublereal *, doublecomplex *);
|
|
integer j1end, j1inc, i__, j, k, l;
|
|
doublecomplex t;
|
|
integer iqend;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void zscal_(integer *, doublecomplex *,
|
|
doublecomplex *, integer *);
|
|
logical initq, wantq, upper;
|
|
integer i2, j1, j2;
|
|
extern /* Subroutine */ void zlar2v_(integer *, doublecomplex *,
|
|
doublecomplex *, doublecomplex *, integer *, doublereal *,
|
|
doublecomplex *, integer *);
|
|
integer nq, nr, iqaend;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern void zlacgv_(
|
|
integer *, doublecomplex *, integer *);
|
|
integer kd1;
|
|
extern /* Subroutine */ void zlaset_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlartg_(doublecomplex *, doublecomplex *, doublereal *,
|
|
doublecomplex *, doublecomplex *), zlargv_(integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *, integer *), zlartv_(integer *, doublecomplex *,
|
|
integer *, doublecomplex *, integer *, doublereal *,
|
|
doublecomplex *, integer *);
|
|
integer ibl, iqb, kdn, jin, nrt, kdm1;
|
|
|
|
|
|
/* -- 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 parameters */
|
|
|
|
/* Parameter adjustments */
|
|
ab_dim1 = *ldab;
|
|
ab_offset = 1 + ab_dim1 * 1;
|
|
ab -= ab_offset;
|
|
--d__;
|
|
--e;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
initq = lsame_(vect, "V");
|
|
wantq = initq || lsame_(vect, "U");
|
|
upper = lsame_(uplo, "U");
|
|
kd1 = *kd + 1;
|
|
kdm1 = *kd - 1;
|
|
incx = *ldab - 1;
|
|
iqend = 1;
|
|
|
|
*info = 0;
|
|
if (! wantq && ! lsame_(vect, "N")) {
|
|
*info = -1;
|
|
} else if (! upper && ! lsame_(uplo, "L")) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*kd < 0) {
|
|
*info = -4;
|
|
} else if (*ldab < kd1) {
|
|
*info = -6;
|
|
} else if (*ldq < f2cmax(1,*n) && wantq) {
|
|
*info = -10;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZHBTRD", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Initialize Q to the unit matrix, if needed */
|
|
|
|
if (initq) {
|
|
zlaset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
|
|
}
|
|
|
|
/* Wherever possible, plane rotations are generated and applied in */
|
|
/* vector operations of length NR over the index set J1:J2:KD1. */
|
|
|
|
/* The real cosines and complex sines of the plane rotations are */
|
|
/* stored in the arrays D and WORK. */
|
|
|
|
inca = kd1 * *ldab;
|
|
/* Computing MIN */
|
|
i__1 = *n - 1;
|
|
kdn = f2cmin(i__1,*kd);
|
|
if (upper) {
|
|
|
|
if (*kd > 1) {
|
|
|
|
/* Reduce to complex Hermitian tridiagonal form, working with */
|
|
/* the upper triangle */
|
|
|
|
nr = 0;
|
|
j1 = kdn + 2;
|
|
j2 = 1;
|
|
|
|
i__1 = kd1 + ab_dim1;
|
|
i__2 = kd1 + ab_dim1;
|
|
d__1 = ab[i__2].r;
|
|
ab[i__1].r = d__1, ab[i__1].i = 0.;
|
|
i__1 = *n - 2;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
/* Reduce i-th row of matrix to tridiagonal form */
|
|
|
|
for (k = kdn + 1; k >= 2; --k) {
|
|
j1 += kdn;
|
|
j2 += kdn;
|
|
|
|
if (nr > 0) {
|
|
|
|
/* generate plane rotations to annihilate nonzero */
|
|
/* elements which have been created outside the band */
|
|
|
|
zlargv_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &inca, &
|
|
work[j1], &kd1, &d__[j1], &kd1);
|
|
|
|
/* apply rotations from the right */
|
|
|
|
|
|
/* Dependent on the the number of diagonals either */
|
|
/* ZLARTV or ZROT is used */
|
|
|
|
if (nr >= (*kd << 1) - 1) {
|
|
i__2 = *kd - 1;
|
|
for (l = 1; l <= i__2; ++l) {
|
|
zlartv_(&nr, &ab[l + 1 + (j1 - 1) * ab_dim1],
|
|
&inca, &ab[l + j1 * ab_dim1], &inca, &
|
|
d__[j1], &work[j1], &kd1);
|
|
/* L10: */
|
|
}
|
|
|
|
} else {
|
|
jend = j1 + (nr - 1) * kd1;
|
|
i__2 = jend;
|
|
i__3 = kd1;
|
|
for (jinc = j1; i__3 < 0 ? jinc >= i__2 : jinc <=
|
|
i__2; jinc += i__3) {
|
|
zrot_(&kdm1, &ab[(jinc - 1) * ab_dim1 + 2], &
|
|
c__1, &ab[jinc * ab_dim1 + 1], &c__1,
|
|
&d__[jinc], &work[jinc]);
|
|
/* L20: */
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
if (k > 2) {
|
|
if (k <= *n - i__ + 1) {
|
|
|
|
/* generate plane rotation to annihilate a(i,i+k-1) */
|
|
/* within the band */
|
|
|
|
zlartg_(&ab[*kd - k + 3 + (i__ + k - 2) * ab_dim1]
|
|
, &ab[*kd - k + 2 + (i__ + k - 1) *
|
|
ab_dim1], &d__[i__ + k - 1], &work[i__ +
|
|
k - 1], &temp);
|
|
i__3 = *kd - k + 3 + (i__ + k - 2) * ab_dim1;
|
|
ab[i__3].r = temp.r, ab[i__3].i = temp.i;
|
|
|
|
/* apply rotation from the right */
|
|
|
|
i__3 = k - 3;
|
|
zrot_(&i__3, &ab[*kd - k + 4 + (i__ + k - 2) *
|
|
ab_dim1], &c__1, &ab[*kd - k + 3 + (i__ +
|
|
k - 1) * ab_dim1], &c__1, &d__[i__ + k -
|
|
1], &work[i__ + k - 1]);
|
|
}
|
|
++nr;
|
|
j1 = j1 - kdn - 1;
|
|
}
|
|
|
|
/* apply plane rotations from both sides to diagonal */
|
|
/* blocks */
|
|
|
|
if (nr > 0) {
|
|
zlar2v_(&nr, &ab[kd1 + (j1 - 1) * ab_dim1], &ab[kd1 +
|
|
j1 * ab_dim1], &ab[*kd + j1 * ab_dim1], &inca,
|
|
&d__[j1], &work[j1], &kd1);
|
|
}
|
|
|
|
/* apply plane rotations from the left */
|
|
|
|
if (nr > 0) {
|
|
zlacgv_(&nr, &work[j1], &kd1);
|
|
if ((*kd << 1) - 1 < nr) {
|
|
|
|
/* Dependent on the the number of diagonals either */
|
|
/* ZLARTV or ZROT is used */
|
|
|
|
i__3 = *kd - 1;
|
|
for (l = 1; l <= i__3; ++l) {
|
|
if (j2 + l > *n) {
|
|
nrt = nr - 1;
|
|
} else {
|
|
nrt = nr;
|
|
}
|
|
if (nrt > 0) {
|
|
zlartv_(&nrt, &ab[*kd - l + (j1 + l) *
|
|
ab_dim1], &inca, &ab[*kd - l + 1
|
|
+ (j1 + l) * ab_dim1], &inca, &
|
|
d__[j1], &work[j1], &kd1);
|
|
}
|
|
/* L30: */
|
|
}
|
|
} else {
|
|
j1end = j1 + kd1 * (nr - 2);
|
|
if (j1end >= j1) {
|
|
i__3 = j1end;
|
|
i__2 = kd1;
|
|
for (jin = j1; i__2 < 0 ? jin >= i__3 : jin <=
|
|
i__3; jin += i__2) {
|
|
i__4 = *kd - 1;
|
|
zrot_(&i__4, &ab[*kd - 1 + (jin + 1) *
|
|
ab_dim1], &incx, &ab[*kd + (jin +
|
|
1) * ab_dim1], &incx, &d__[jin], &
|
|
work[jin]);
|
|
/* L40: */
|
|
}
|
|
}
|
|
/* Computing MIN */
|
|
i__2 = kdm1, i__3 = *n - j2;
|
|
lend = f2cmin(i__2,i__3);
|
|
last = j1end + kd1;
|
|
if (lend > 0) {
|
|
zrot_(&lend, &ab[*kd - 1 + (last + 1) *
|
|
ab_dim1], &incx, &ab[*kd + (last + 1)
|
|
* ab_dim1], &incx, &d__[last], &work[
|
|
last]);
|
|
}
|
|
}
|
|
}
|
|
|
|
if (wantq) {
|
|
|
|
/* accumulate product of plane rotations in Q */
|
|
|
|
if (initq) {
|
|
|
|
/* take advantage of the fact that Q was */
|
|
/* initially the Identity matrix */
|
|
|
|
iqend = f2cmax(iqend,j2);
|
|
/* Computing MAX */
|
|
i__2 = 0, i__3 = k - 3;
|
|
i2 = f2cmax(i__2,i__3);
|
|
iqaend = i__ * *kd + 1;
|
|
if (k == 2) {
|
|
iqaend += *kd;
|
|
}
|
|
iqaend = f2cmin(iqaend,iqend);
|
|
i__2 = j2;
|
|
i__3 = kd1;
|
|
for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j
|
|
+= i__3) {
|
|
ibl = i__ - i2 / kdm1;
|
|
++i2;
|
|
/* Computing MAX */
|
|
i__4 = 1, i__5 = j - ibl;
|
|
iqb = f2cmax(i__4,i__5);
|
|
nq = iqaend + 1 - iqb;
|
|
/* Computing MIN */
|
|
i__4 = iqaend + *kd;
|
|
iqaend = f2cmin(i__4,iqend);
|
|
d_cnjg(&z__1, &work[j]);
|
|
zrot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1,
|
|
&q[iqb + j * q_dim1], &c__1, &d__[j],
|
|
&z__1);
|
|
/* L50: */
|
|
}
|
|
} else {
|
|
|
|
i__3 = j2;
|
|
i__2 = kd1;
|
|
for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j
|
|
+= i__2) {
|
|
d_cnjg(&z__1, &work[j]);
|
|
zrot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[
|
|
j * q_dim1 + 1], &c__1, &d__[j], &
|
|
z__1);
|
|
/* L60: */
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
if (j2 + kdn > *n) {
|
|
|
|
/* adjust J2 to keep within the bounds of the matrix */
|
|
|
|
--nr;
|
|
j2 = j2 - kdn - 1;
|
|
}
|
|
|
|
i__2 = j2;
|
|
i__3 = kd1;
|
|
for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3)
|
|
{
|
|
|
|
/* create nonzero element a(j-1,j+kd) outside the band */
|
|
/* and store it in WORK */
|
|
|
|
i__4 = j + *kd;
|
|
i__5 = j;
|
|
i__6 = (j + *kd) * ab_dim1 + 1;
|
|
z__1.r = work[i__5].r * ab[i__6].r - work[i__5].i *
|
|
ab[i__6].i, z__1.i = work[i__5].r * ab[i__6]
|
|
.i + work[i__5].i * ab[i__6].r;
|
|
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
|
|
i__4 = (j + *kd) * ab_dim1 + 1;
|
|
i__5 = j;
|
|
i__6 = (j + *kd) * ab_dim1 + 1;
|
|
z__1.r = d__[i__5] * ab[i__6].r, z__1.i = d__[i__5] *
|
|
ab[i__6].i;
|
|
ab[i__4].r = z__1.r, ab[i__4].i = z__1.i;
|
|
/* L70: */
|
|
}
|
|
/* L80: */
|
|
}
|
|
/* L90: */
|
|
}
|
|
}
|
|
|
|
if (*kd > 0) {
|
|
|
|
/* make off-diagonal elements real and copy them to E */
|
|
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__3 = *kd + (i__ + 1) * ab_dim1;
|
|
t.r = ab[i__3].r, t.i = ab[i__3].i;
|
|
abst = z_abs(&t);
|
|
i__3 = *kd + (i__ + 1) * ab_dim1;
|
|
ab[i__3].r = abst, ab[i__3].i = 0.;
|
|
e[i__] = abst;
|
|
if (abst != 0.) {
|
|
z__1.r = t.r / abst, z__1.i = t.i / abst;
|
|
t.r = z__1.r, t.i = z__1.i;
|
|
} else {
|
|
t.r = 1., t.i = 0.;
|
|
}
|
|
if (i__ < *n - 1) {
|
|
i__3 = *kd + (i__ + 2) * ab_dim1;
|
|
i__2 = *kd + (i__ + 2) * ab_dim1;
|
|
z__1.r = ab[i__2].r * t.r - ab[i__2].i * t.i, z__1.i = ab[
|
|
i__2].r * t.i + ab[i__2].i * t.r;
|
|
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
|
|
}
|
|
if (wantq) {
|
|
d_cnjg(&z__1, &t);
|
|
zscal_(n, &z__1, &q[(i__ + 1) * q_dim1 + 1], &c__1);
|
|
}
|
|
/* L100: */
|
|
}
|
|
} else {
|
|
|
|
/* set E to zero if original matrix was diagonal */
|
|
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
e[i__] = 0.;
|
|
/* L110: */
|
|
}
|
|
}
|
|
|
|
/* copy diagonal elements to D */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__3 = i__;
|
|
i__2 = kd1 + i__ * ab_dim1;
|
|
d__[i__3] = ab[i__2].r;
|
|
/* L120: */
|
|
}
|
|
|
|
} else {
|
|
|
|
if (*kd > 1) {
|
|
|
|
/* Reduce to complex Hermitian tridiagonal form, working with */
|
|
/* the lower triangle */
|
|
|
|
nr = 0;
|
|
j1 = kdn + 2;
|
|
j2 = 1;
|
|
|
|
i__1 = ab_dim1 + 1;
|
|
i__3 = ab_dim1 + 1;
|
|
d__1 = ab[i__3].r;
|
|
ab[i__1].r = d__1, ab[i__1].i = 0.;
|
|
i__1 = *n - 2;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
/* Reduce i-th column of matrix to tridiagonal form */
|
|
|
|
for (k = kdn + 1; k >= 2; --k) {
|
|
j1 += kdn;
|
|
j2 += kdn;
|
|
|
|
if (nr > 0) {
|
|
|
|
/* generate plane rotations to annihilate nonzero */
|
|
/* elements which have been created outside the band */
|
|
|
|
zlargv_(&nr, &ab[kd1 + (j1 - kd1) * ab_dim1], &inca, &
|
|
work[j1], &kd1, &d__[j1], &kd1);
|
|
|
|
/* apply plane rotations from one side */
|
|
|
|
|
|
/* Dependent on the the number of diagonals either */
|
|
/* ZLARTV or ZROT is used */
|
|
|
|
if (nr > (*kd << 1) - 1) {
|
|
i__3 = *kd - 1;
|
|
for (l = 1; l <= i__3; ++l) {
|
|
zlartv_(&nr, &ab[kd1 - l + (j1 - kd1 + l) *
|
|
ab_dim1], &inca, &ab[kd1 - l + 1 + (
|
|
j1 - kd1 + l) * ab_dim1], &inca, &d__[
|
|
j1], &work[j1], &kd1);
|
|
/* L130: */
|
|
}
|
|
} else {
|
|
jend = j1 + kd1 * (nr - 1);
|
|
i__3 = jend;
|
|
i__2 = kd1;
|
|
for (jinc = j1; i__2 < 0 ? jinc >= i__3 : jinc <=
|
|
i__3; jinc += i__2) {
|
|
zrot_(&kdm1, &ab[*kd + (jinc - *kd) * ab_dim1]
|
|
, &incx, &ab[kd1 + (jinc - *kd) *
|
|
ab_dim1], &incx, &d__[jinc], &work[
|
|
jinc]);
|
|
/* L140: */
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
if (k > 2) {
|
|
if (k <= *n - i__ + 1) {
|
|
|
|
/* generate plane rotation to annihilate a(i+k-1,i) */
|
|
/* within the band */
|
|
|
|
zlartg_(&ab[k - 1 + i__ * ab_dim1], &ab[k + i__ *
|
|
ab_dim1], &d__[i__ + k - 1], &work[i__ +
|
|
k - 1], &temp);
|
|
i__2 = k - 1 + i__ * ab_dim1;
|
|
ab[i__2].r = temp.r, ab[i__2].i = temp.i;
|
|
|
|
/* apply rotation from the left */
|
|
|
|
i__2 = k - 3;
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
zrot_(&i__2, &ab[k - 2 + (i__ + 1) * ab_dim1], &
|
|
i__3, &ab[k - 1 + (i__ + 1) * ab_dim1], &
|
|
i__4, &d__[i__ + k - 1], &work[i__ + k -
|
|
1]);
|
|
}
|
|
++nr;
|
|
j1 = j1 - kdn - 1;
|
|
}
|
|
|
|
/* apply plane rotations from both sides to diagonal */
|
|
/* blocks */
|
|
|
|
if (nr > 0) {
|
|
zlar2v_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &ab[j1 *
|
|
ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 2], &
|
|
inca, &d__[j1], &work[j1], &kd1);
|
|
}
|
|
|
|
/* apply plane rotations from the right */
|
|
|
|
|
|
/* Dependent on the the number of diagonals either */
|
|
/* ZLARTV or ZROT is used */
|
|
|
|
if (nr > 0) {
|
|
zlacgv_(&nr, &work[j1], &kd1);
|
|
if (nr > (*kd << 1) - 1) {
|
|
i__2 = *kd - 1;
|
|
for (l = 1; l <= i__2; ++l) {
|
|
if (j2 + l > *n) {
|
|
nrt = nr - 1;
|
|
} else {
|
|
nrt = nr;
|
|
}
|
|
if (nrt > 0) {
|
|
zlartv_(&nrt, &ab[l + 2 + (j1 - 1) *
|
|
ab_dim1], &inca, &ab[l + 1 + j1 *
|
|
ab_dim1], &inca, &d__[j1], &work[
|
|
j1], &kd1);
|
|
}
|
|
/* L150: */
|
|
}
|
|
} else {
|
|
j1end = j1 + kd1 * (nr - 2);
|
|
if (j1end >= j1) {
|
|
i__2 = j1end;
|
|
i__3 = kd1;
|
|
for (j1inc = j1; i__3 < 0 ? j1inc >= i__2 :
|
|
j1inc <= i__2; j1inc += i__3) {
|
|
zrot_(&kdm1, &ab[(j1inc - 1) * ab_dim1 +
|
|
3], &c__1, &ab[j1inc * ab_dim1 +
|
|
2], &c__1, &d__[j1inc], &work[
|
|
j1inc]);
|
|
/* L160: */
|
|
}
|
|
}
|
|
/* Computing MIN */
|
|
i__3 = kdm1, i__2 = *n - j2;
|
|
lend = f2cmin(i__3,i__2);
|
|
last = j1end + kd1;
|
|
if (lend > 0) {
|
|
zrot_(&lend, &ab[(last - 1) * ab_dim1 + 3], &
|
|
c__1, &ab[last * ab_dim1 + 2], &c__1,
|
|
&d__[last], &work[last]);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
if (wantq) {
|
|
|
|
/* accumulate product of plane rotations in Q */
|
|
|
|
if (initq) {
|
|
|
|
/* take advantage of the fact that Q was */
|
|
/* initially the Identity matrix */
|
|
|
|
iqend = f2cmax(iqend,j2);
|
|
/* Computing MAX */
|
|
i__3 = 0, i__2 = k - 3;
|
|
i2 = f2cmax(i__3,i__2);
|
|
iqaend = i__ * *kd + 1;
|
|
if (k == 2) {
|
|
iqaend += *kd;
|
|
}
|
|
iqaend = f2cmin(iqaend,iqend);
|
|
i__3 = j2;
|
|
i__2 = kd1;
|
|
for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j
|
|
+= i__2) {
|
|
ibl = i__ - i2 / kdm1;
|
|
++i2;
|
|
/* Computing MAX */
|
|
i__4 = 1, i__5 = j - ibl;
|
|
iqb = f2cmax(i__4,i__5);
|
|
nq = iqaend + 1 - iqb;
|
|
/* Computing MIN */
|
|
i__4 = iqaend + *kd;
|
|
iqaend = f2cmin(i__4,iqend);
|
|
zrot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1,
|
|
&q[iqb + j * q_dim1], &c__1, &d__[j],
|
|
&work[j]);
|
|
/* L170: */
|
|
}
|
|
} else {
|
|
|
|
i__2 = j2;
|
|
i__3 = kd1;
|
|
for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j
|
|
+= i__3) {
|
|
zrot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[
|
|
j * q_dim1 + 1], &c__1, &d__[j], &
|
|
work[j]);
|
|
/* L180: */
|
|
}
|
|
}
|
|
}
|
|
|
|
if (j2 + kdn > *n) {
|
|
|
|
/* adjust J2 to keep within the bounds of the matrix */
|
|
|
|
--nr;
|
|
j2 = j2 - kdn - 1;
|
|
}
|
|
|
|
i__3 = j2;
|
|
i__2 = kd1;
|
|
for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2)
|
|
{
|
|
|
|
/* create nonzero element a(j+kd,j-1) outside the */
|
|
/* band and store it in WORK */
|
|
|
|
i__4 = j + *kd;
|
|
i__5 = j;
|
|
i__6 = kd1 + j * ab_dim1;
|
|
z__1.r = work[i__5].r * ab[i__6].r - work[i__5].i *
|
|
ab[i__6].i, z__1.i = work[i__5].r * ab[i__6]
|
|
.i + work[i__5].i * ab[i__6].r;
|
|
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
|
|
i__4 = kd1 + j * ab_dim1;
|
|
i__5 = j;
|
|
i__6 = kd1 + j * ab_dim1;
|
|
z__1.r = d__[i__5] * ab[i__6].r, z__1.i = d__[i__5] *
|
|
ab[i__6].i;
|
|
ab[i__4].r = z__1.r, ab[i__4].i = z__1.i;
|
|
/* L190: */
|
|
}
|
|
/* L200: */
|
|
}
|
|
/* L210: */
|
|
}
|
|
}
|
|
|
|
if (*kd > 0) {
|
|
|
|
/* make off-diagonal elements real and copy them to E */
|
|
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__ * ab_dim1 + 2;
|
|
t.r = ab[i__2].r, t.i = ab[i__2].i;
|
|
abst = z_abs(&t);
|
|
i__2 = i__ * ab_dim1 + 2;
|
|
ab[i__2].r = abst, ab[i__2].i = 0.;
|
|
e[i__] = abst;
|
|
if (abst != 0.) {
|
|
z__1.r = t.r / abst, z__1.i = t.i / abst;
|
|
t.r = z__1.r, t.i = z__1.i;
|
|
} else {
|
|
t.r = 1., t.i = 0.;
|
|
}
|
|
if (i__ < *n - 1) {
|
|
i__2 = (i__ + 1) * ab_dim1 + 2;
|
|
i__3 = (i__ + 1) * ab_dim1 + 2;
|
|
z__1.r = ab[i__3].r * t.r - ab[i__3].i * t.i, z__1.i = ab[
|
|
i__3].r * t.i + ab[i__3].i * t.r;
|
|
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
|
|
}
|
|
if (wantq) {
|
|
zscal_(n, &t, &q[(i__ + 1) * q_dim1 + 1], &c__1);
|
|
}
|
|
/* L220: */
|
|
}
|
|
} else {
|
|
|
|
/* set E to zero if original matrix was diagonal */
|
|
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
e[i__] = 0.;
|
|
/* L230: */
|
|
}
|
|
}
|
|
|
|
/* copy diagonal elements to D */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
i__3 = i__ * ab_dim1 + 1;
|
|
d__[i__2] = ab[i__3].r;
|
|
/* L240: */
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZHBTRD */
|
|
|
|
} /* zhbtrd_ */
|
|
|