918 lines
27 KiB
C
918 lines
27 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 doublereal c_b5 = -1.;
|
|
static doublereal c_b6 = 1.;
|
|
static integer c__1 = 1;
|
|
static doublereal c_b16 = 0.;
|
|
|
|
/* > \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago
|
|
nal form by an orthogonal similarity transformation. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLATRD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatrd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlatrd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlatrd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER LDA, LDW, N, NB */
|
|
/* DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLATRD reduces NB rows and columns of a real symmetric matrix A to */
|
|
/* > symmetric tridiagonal form by an orthogonal similarity */
|
|
/* > transformation Q**T * A * Q, and returns the matrices V and W which are */
|
|
/* > needed to apply the transformation to the unreduced part of A. */
|
|
/* > */
|
|
/* > If UPLO = 'U', DLATRD reduces the last NB rows and columns of a */
|
|
/* > matrix, of which the upper triangle is supplied; */
|
|
/* > if UPLO = 'L', DLATRD reduces the first NB rows and columns of a */
|
|
/* > matrix, of which the lower triangle is supplied. */
|
|
/* > */
|
|
/* > This is an auxiliary routine called by DSYTRD. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > Specifies whether the upper or lower triangular part of the */
|
|
/* > symmetric matrix A is stored: */
|
|
/* > = 'U': Upper triangular */
|
|
/* > = 'L': Lower triangular */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NB */
|
|
/* > \verbatim */
|
|
/* > NB is INTEGER */
|
|
/* > The number of rows and columns to be reduced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
|
|
/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */
|
|
/* > n-by-n upper triangular part of A contains the upper */
|
|
/* > triangular part of the matrix A, and the strictly lower */
|
|
/* > triangular part of A is not referenced. If UPLO = 'L', the */
|
|
/* > leading n-by-n lower triangular part of A contains the lower */
|
|
/* > triangular part of the matrix A, and the strictly upper */
|
|
/* > triangular part of A is not referenced. */
|
|
/* > On exit: */
|
|
/* > if UPLO = 'U', the last NB columns have been reduced to */
|
|
/* > tridiagonal form, with the diagonal elements overwriting */
|
|
/* > the diagonal elements of A; the elements above the diagonal */
|
|
/* > with the array TAU, represent the orthogonal matrix Q as a */
|
|
/* > product of elementary reflectors; */
|
|
/* > if UPLO = 'L', the first NB columns have been reduced to */
|
|
/* > tridiagonal form, with the diagonal elements overwriting */
|
|
/* > the diagonal elements of A; the elements below the diagonal */
|
|
/* > with the array TAU, represent the orthogonal matrix Q as a */
|
|
/* > product of elementary reflectors. */
|
|
/* > See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= (1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */
|
|
/* > elements of the last NB columns of the reduced matrix; */
|
|
/* > if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */
|
|
/* > the first NB columns of the reduced matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] TAU */
|
|
/* > \verbatim */
|
|
/* > TAU is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The scalar factors of the elementary reflectors, stored in */
|
|
/* > TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */
|
|
/* > See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] W */
|
|
/* > \verbatim */
|
|
/* > W is DOUBLE PRECISION array, dimension (LDW,NB) */
|
|
/* > The n-by-nb matrix W required to update the unreduced part */
|
|
/* > of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDW */
|
|
/* > \verbatim */
|
|
/* > LDW is INTEGER */
|
|
/* > The leading dimension of the array W. LDW >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleOTHERauxiliary */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */
|
|
/* > reflectors */
|
|
/* > */
|
|
/* > Q = H(n) H(n-1) . . . H(n-nb+1). */
|
|
/* > */
|
|
/* > Each H(i) has the form */
|
|
/* > */
|
|
/* > H(i) = I - tau * v * v**T */
|
|
/* > */
|
|
/* > where tau is a real scalar, and v is a real vector with */
|
|
/* > v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */
|
|
/* > and tau in TAU(i-1). */
|
|
/* > */
|
|
/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */
|
|
/* > reflectors */
|
|
/* > */
|
|
/* > Q = H(1) H(2) . . . H(nb). */
|
|
/* > */
|
|
/* > Each H(i) has the form */
|
|
/* > */
|
|
/* > H(i) = I - tau * v * v**T */
|
|
/* > */
|
|
/* > where tau is a real scalar, and v is a real vector with */
|
|
/* > v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
|
|
/* > and tau in TAU(i). */
|
|
/* > */
|
|
/* > The elements of the vectors v together form the n-by-nb matrix V */
|
|
/* > which is needed, with W, to apply the transformation to the unreduced */
|
|
/* > part of the matrix, using a symmetric rank-2k update of the form: */
|
|
/* > A := A - V*W**T - W*V**T. */
|
|
/* > */
|
|
/* > The contents of A on exit are illustrated by the following examples */
|
|
/* > with n = 5 and nb = 2: */
|
|
/* > */
|
|
/* > if UPLO = 'U': if UPLO = 'L': */
|
|
/* > */
|
|
/* > ( a a a v4 v5 ) ( d ) */
|
|
/* > ( a a v4 v5 ) ( 1 d ) */
|
|
/* > ( a 1 v5 ) ( v1 1 a ) */
|
|
/* > ( d 1 ) ( v1 v2 a a ) */
|
|
/* > ( d ) ( v1 v2 a a a ) */
|
|
/* > */
|
|
/* > where d denotes a diagonal element of the reduced matrix, a denotes */
|
|
/* > an element of the original matrix that is unchanged, and vi denotes */
|
|
/* > an element of the vector defining H(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlatrd_(char *uplo, integer *n, integer *nb, doublereal *
|
|
a, integer *lda, doublereal *e, doublereal *tau, doublereal *w,
|
|
integer *ldw)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
|
|
|
|
/* Local variables */
|
|
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
|
|
integer *);
|
|
integer i__;
|
|
doublereal alpha;
|
|
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
|
|
integer *);
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void dgemv_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *), daxpy_(integer *,
|
|
doublereal *, doublereal *, integer *, doublereal *, integer *),
|
|
dsymv_(char *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *), dlarfg_(integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *);
|
|
integer iw;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Quick return if possible */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--e;
|
|
--tau;
|
|
w_dim1 = *ldw;
|
|
w_offset = 1 + w_dim1 * 1;
|
|
w -= w_offset;
|
|
|
|
/* Function Body */
|
|
if (*n <= 0) {
|
|
return;
|
|
}
|
|
|
|
if (lsame_(uplo, "U")) {
|
|
|
|
/* Reduce last NB columns of upper triangle */
|
|
|
|
i__1 = *n - *nb + 1;
|
|
for (i__ = *n; i__ >= i__1; --i__) {
|
|
iw = i__ - *n + *nb;
|
|
if (i__ < *n) {
|
|
|
|
/* Update A(1:i,i) */
|
|
|
|
i__2 = *n - i__;
|
|
dgemv_("No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) *
|
|
a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
|
|
c_b6, &a[i__ * a_dim1 + 1], &c__1);
|
|
i__2 = *n - i__;
|
|
dgemv_("No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) *
|
|
w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
|
|
c_b6, &a[i__ * a_dim1 + 1], &c__1);
|
|
}
|
|
if (i__ > 1) {
|
|
|
|
/* Generate elementary reflector H(i) to annihilate */
|
|
/* A(1:i-2,i) */
|
|
|
|
i__2 = i__ - 1;
|
|
dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 +
|
|
1], &c__1, &tau[i__ - 1]);
|
|
e[i__ - 1] = a[i__ - 1 + i__ * a_dim1];
|
|
a[i__ - 1 + i__ * a_dim1] = 1.;
|
|
|
|
/* Compute W(1:i-1,i) */
|
|
|
|
i__2 = i__ - 1;
|
|
dsymv_("Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ *
|
|
a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], &
|
|
c__1);
|
|
if (i__ < *n) {
|
|
i__2 = i__ - 1;
|
|
i__3 = *n - i__;
|
|
dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) *
|
|
w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, &
|
|
c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);
|
|
i__2 = i__ - 1;
|
|
i__3 = *n - i__;
|
|
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *
|
|
a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &
|
|
c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);
|
|
i__2 = i__ - 1;
|
|
i__3 = *n - i__;
|
|
dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) *
|
|
a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, &
|
|
c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);
|
|
i__2 = i__ - 1;
|
|
i__3 = *n - i__;
|
|
dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) *
|
|
w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &
|
|
c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);
|
|
}
|
|
i__2 = i__ - 1;
|
|
dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
|
|
i__2 = i__ - 1;
|
|
alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1],
|
|
&c__1, &a[i__ * a_dim1 + 1], &c__1);
|
|
i__2 = i__ - 1;
|
|
daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw *
|
|
w_dim1 + 1], &c__1);
|
|
}
|
|
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
|
|
/* Reduce first NB columns of lower triangle */
|
|
|
|
i__1 = *nb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
/* Update A(i:n,i) */
|
|
|
|
i__2 = *n - i__ + 1;
|
|
i__3 = i__ - 1;
|
|
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda,
|
|
&w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], &
|
|
c__1);
|
|
i__2 = *n - i__ + 1;
|
|
i__3 = i__ - 1;
|
|
dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw,
|
|
&a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], &
|
|
c__1);
|
|
if (i__ < *n) {
|
|
|
|
/* Generate elementary reflector H(i) to annihilate */
|
|
/* A(i+2:n,i) */
|
|
|
|
i__2 = *n - i__;
|
|
/* Computing MIN */
|
|
i__3 = i__ + 2;
|
|
dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[f2cmin(i__3,*n) +
|
|
i__ * a_dim1], &c__1, &tau[i__]);
|
|
e[i__] = a[i__ + 1 + i__ * a_dim1];
|
|
a[i__ + 1 + i__ * a_dim1] = 1.;
|
|
|
|
/* Compute W(i+1:n,i) */
|
|
|
|
i__2 = *n - i__;
|
|
dsymv_("Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1]
|
|
, lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
|
|
i__ + 1 + i__ * w_dim1], &c__1);
|
|
i__2 = *n - i__;
|
|
i__3 = i__ - 1;
|
|
dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1],
|
|
ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
|
|
i__ * w_dim1 + 1], &c__1);
|
|
i__2 = *n - i__;
|
|
i__3 = i__ - 1;
|
|
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 +
|
|
a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
|
|
i__ + 1 + i__ * w_dim1], &c__1);
|
|
i__2 = *n - i__;
|
|
i__3 = i__ - 1;
|
|
dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1],
|
|
lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
|
|
i__ * w_dim1 + 1], &c__1);
|
|
i__2 = *n - i__;
|
|
i__3 = i__ - 1;
|
|
dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 +
|
|
w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
|
|
i__ + 1 + i__ * w_dim1], &c__1);
|
|
i__2 = *n - i__;
|
|
dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
|
|
i__2 = *n - i__;
|
|
alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ *
|
|
w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
|
|
i__2 = *n - i__;
|
|
daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
|
|
i__ + 1 + i__ * w_dim1], &c__1);
|
|
}
|
|
|
|
/* L20: */
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DLATRD */
|
|
|
|
} /* dlatrd_ */
|
|
|