948 lines
26 KiB
C
948 lines
26 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by us
|
|
ing BLAS level 3. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZLAQPS + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqps.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqps.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqps.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, */
|
|
/* VN2, AUXV, F, LDF ) */
|
|
|
|
/* INTEGER KB, LDA, LDF, M, N, NB, OFFSET */
|
|
/* INTEGER JPVT( * ) */
|
|
/* DOUBLE PRECISION VN1( * ), VN2( * ) */
|
|
/* COMPLEX*16 A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZLAQPS computes a step of QR factorization with column pivoting */
|
|
/* > of a complex M-by-N matrix A by using Blas-3. It tries to factorize */
|
|
/* > NB columns from A starting from the row OFFSET+1, and updates all */
|
|
/* > of the matrix with Blas-3 xGEMM. */
|
|
/* > */
|
|
/* > In some cases, due to catastrophic cancellations, it cannot */
|
|
/* > factorize NB columns. Hence, the actual number of factorized */
|
|
/* > columns is returned in KB. */
|
|
/* > */
|
|
/* > Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix A. N >= 0 */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] OFFSET */
|
|
/* > \verbatim */
|
|
/* > OFFSET is INTEGER */
|
|
/* > The number of rows of A that have been factorized in */
|
|
/* > previous steps. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NB */
|
|
/* > \verbatim */
|
|
/* > NB is INTEGER */
|
|
/* > The number of columns to factorize. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] KB */
|
|
/* > \verbatim */
|
|
/* > KB is INTEGER */
|
|
/* > The number of columns actually factorized. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, block A(OFFSET+1:M,1:KB) is the triangular */
|
|
/* > factor obtained and block A(1:OFFSET,1:N) has been */
|
|
/* > accordingly pivoted, but no factorized. */
|
|
/* > The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has */
|
|
/* > been updated. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] JPVT */
|
|
/* > \verbatim */
|
|
/* > JPVT is INTEGER array, dimension (N) */
|
|
/* > JPVT(I) = K <==> Column K of the full matrix A has been */
|
|
/* > permuted into position I in AP. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] TAU */
|
|
/* > \verbatim */
|
|
/* > TAU is COMPLEX*16 array, dimension (KB) */
|
|
/* > The scalar factors of the elementary reflectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VN1 */
|
|
/* > \verbatim */
|
|
/* > VN1 is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The vector with the partial column norms. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VN2 */
|
|
/* > \verbatim */
|
|
/* > VN2 is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The vector with the exact column norms. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AUXV */
|
|
/* > \verbatim */
|
|
/* > AUXV is COMPLEX*16 array, dimension (NB) */
|
|
/* > Auxiliary vector. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] F */
|
|
/* > \verbatim */
|
|
/* > F is COMPLEX*16 array, dimension (LDF,NB) */
|
|
/* > Matrix F**H = L * Y**H * A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDF */
|
|
/* > \verbatim */
|
|
/* > LDF is INTEGER */
|
|
/* > The leading dimension of the array F. LDF >= 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 complex16OTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
|
|
/* > X. Sun, Computer Science Dept., Duke University, USA */
|
|
/* > \n */
|
|
/* > Partial column norm updating strategy modified on April 2011 */
|
|
/* > Z. Drmac and Z. Bujanovic, Dept. of Mathematics, */
|
|
/* > University of Zagreb, Croatia. */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > LAPACK Working Note 176 */
|
|
|
|
/* > \htmlonly */
|
|
/* > <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zlaqps_(integer *m, integer *n, integer *offset, integer
|
|
*nb, integer *kb, doublecomplex *a, integer *lda, integer *jpvt,
|
|
doublecomplex *tau, doublereal *vn1, doublereal *vn2, doublecomplex *
|
|
auxv, doublecomplex *f, integer *ldf)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, f_dim1, f_offset, i__1, i__2, i__3;
|
|
doublereal d__1, d__2;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
doublereal temp, temp2;
|
|
integer j, k;
|
|
doublereal tol3z;
|
|
integer itemp;
|
|
extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *), zgemv_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *),
|
|
zswap_(integer *, doublecomplex *, integer *, doublecomplex *,
|
|
integer *);
|
|
extern doublereal dznrm2_(integer *, doublecomplex *, integer *), dlamch_(
|
|
char *);
|
|
integer rk;
|
|
extern integer idamax_(integer *, doublereal *, integer *);
|
|
integer lsticc;
|
|
extern /* Subroutine */ void zlarfg_(integer *, doublecomplex *,
|
|
doublecomplex *, integer *, doublecomplex *);
|
|
integer lastrk;
|
|
doublecomplex akk;
|
|
integer pvt;
|
|
|
|
|
|
/* -- 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--jpvt;
|
|
--tau;
|
|
--vn1;
|
|
--vn2;
|
|
--auxv;
|
|
f_dim1 = *ldf;
|
|
f_offset = 1 + f_dim1 * 1;
|
|
f -= f_offset;
|
|
|
|
/* Function Body */
|
|
/* Computing MIN */
|
|
i__1 = *m, i__2 = *n + *offset;
|
|
lastrk = f2cmin(i__1,i__2);
|
|
lsticc = 0;
|
|
k = 0;
|
|
tol3z = sqrt(dlamch_("Epsilon"));
|
|
|
|
/* Beginning of while loop. */
|
|
|
|
L10:
|
|
if (k < *nb && lsticc == 0) {
|
|
++k;
|
|
rk = *offset + k;
|
|
|
|
/* Determine ith pivot column and swap if necessary */
|
|
|
|
i__1 = *n - k + 1;
|
|
pvt = k - 1 + idamax_(&i__1, &vn1[k], &c__1);
|
|
if (pvt != k) {
|
|
zswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
|
|
i__1 = k - 1;
|
|
zswap_(&i__1, &f[pvt + f_dim1], ldf, &f[k + f_dim1], ldf);
|
|
itemp = jpvt[pvt];
|
|
jpvt[pvt] = jpvt[k];
|
|
jpvt[k] = itemp;
|
|
vn1[pvt] = vn1[k];
|
|
vn2[pvt] = vn2[k];
|
|
}
|
|
|
|
/* Apply previous Householder reflectors to column K: */
|
|
/* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**H. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = k + j * f_dim1;
|
|
d_cnjg(&z__1, &f[k + j * f_dim1]);
|
|
f[i__2].r = z__1.r, f[i__2].i = z__1.i;
|
|
/* L20: */
|
|
}
|
|
i__1 = *m - rk + 1;
|
|
i__2 = k - 1;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemv_("No transpose", &i__1, &i__2, &z__1, &a[rk + a_dim1], lda,
|
|
&f[k + f_dim1], ldf, &c_b2, &a[rk + k * a_dim1], &c__1);
|
|
i__1 = k - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = k + j * f_dim1;
|
|
d_cnjg(&z__1, &f[k + j * f_dim1]);
|
|
f[i__2].r = z__1.r, f[i__2].i = z__1.i;
|
|
/* L30: */
|
|
}
|
|
}
|
|
|
|
/* Generate elementary reflector H(k). */
|
|
|
|
if (rk < *m) {
|
|
i__1 = *m - rk + 1;
|
|
zlarfg_(&i__1, &a[rk + k * a_dim1], &a[rk + 1 + k * a_dim1], &
|
|
c__1, &tau[k]);
|
|
} else {
|
|
zlarfg_(&c__1, &a[rk + k * a_dim1], &a[rk + k * a_dim1], &c__1, &
|
|
tau[k]);
|
|
}
|
|
|
|
i__1 = rk + k * a_dim1;
|
|
akk.r = a[i__1].r, akk.i = a[i__1].i;
|
|
i__1 = rk + k * a_dim1;
|
|
a[i__1].r = 1., a[i__1].i = 0.;
|
|
|
|
/* Compute Kth column of F: */
|
|
|
|
/* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**H*A(RK:M,K). */
|
|
|
|
if (k < *n) {
|
|
i__1 = *m - rk + 1;
|
|
i__2 = *n - k;
|
|
zgemv_("Conjugate transpose", &i__1, &i__2, &tau[k], &a[rk + (k +
|
|
1) * a_dim1], lda, &a[rk + k * a_dim1], &c__1, &c_b1, &f[
|
|
k + 1 + k * f_dim1], &c__1);
|
|
}
|
|
|
|
/* Padding F(1:K,K) with zeros. */
|
|
|
|
i__1 = k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j + k * f_dim1;
|
|
f[i__2].r = 0., f[i__2].i = 0.;
|
|
/* L40: */
|
|
}
|
|
|
|
/* Incremental updating of F: */
|
|
/* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**H */
|
|
/* *A(RK:M,K). */
|
|
|
|
if (k > 1) {
|
|
i__1 = *m - rk + 1;
|
|
i__2 = k - 1;
|
|
i__3 = k;
|
|
z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
|
|
zgemv_("Conjugate transpose", &i__1, &i__2, &z__1, &a[rk + a_dim1]
|
|
, lda, &a[rk + k * a_dim1], &c__1, &c_b1, &auxv[1], &c__1);
|
|
|
|
i__1 = k - 1;
|
|
zgemv_("No transpose", n, &i__1, &c_b2, &f[f_dim1 + 1], ldf, &
|
|
auxv[1], &c__1, &c_b2, &f[k * f_dim1 + 1], &c__1);
|
|
}
|
|
|
|
/* Update the current row of A: */
|
|
/* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**H. */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &c__1, &i__1, &k, &
|
|
z__1, &a[rk + a_dim1], lda, &f[k + 1 + f_dim1], ldf, &
|
|
c_b2, &a[rk + (k + 1) * a_dim1], lda);
|
|
}
|
|
|
|
/* Update partial column norms. */
|
|
|
|
if (rk < lastrk) {
|
|
i__1 = *n;
|
|
for (j = k + 1; j <= i__1; ++j) {
|
|
if (vn1[j] != 0.) {
|
|
|
|
/* NOTE: The following 4 lines follow from the analysis in */
|
|
/* Lapack Working Note 176. */
|
|
|
|
temp = z_abs(&a[rk + j * a_dim1]) / vn1[j];
|
|
/* Computing MAX */
|
|
d__1 = 0., d__2 = (temp + 1.) * (1. - temp);
|
|
temp = f2cmax(d__1,d__2);
|
|
/* Computing 2nd power */
|
|
d__1 = vn1[j] / vn2[j];
|
|
temp2 = temp * (d__1 * d__1);
|
|
if (temp2 <= tol3z) {
|
|
vn2[j] = (doublereal) lsticc;
|
|
lsticc = j;
|
|
} else {
|
|
vn1[j] *= sqrt(temp);
|
|
}
|
|
}
|
|
/* L50: */
|
|
}
|
|
}
|
|
|
|
i__1 = rk + k * a_dim1;
|
|
a[i__1].r = akk.r, a[i__1].i = akk.i;
|
|
|
|
/* End of while loop. */
|
|
|
|
goto L10;
|
|
}
|
|
*kb = k;
|
|
rk = *offset + *kb;
|
|
|
|
/* Apply the block reflector to the rest of the matrix: */
|
|
/* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - */
|
|
/* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**H. */
|
|
|
|
/* Computing MIN */
|
|
i__1 = *n, i__2 = *m - *offset;
|
|
if (*kb < f2cmin(i__1,i__2)) {
|
|
i__1 = *m - rk;
|
|
i__2 = *n - *kb;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &i__1, &i__2, kb, &z__1,
|
|
&a[rk + 1 + a_dim1], lda, &f[*kb + 1 + f_dim1], ldf, &c_b2, &
|
|
a[rk + 1 + (*kb + 1) * a_dim1], lda);
|
|
}
|
|
|
|
/* Recomputation of difficult columns. */
|
|
|
|
L60:
|
|
if (lsticc > 0) {
|
|
itemp = i_dnnt(&vn2[lsticc]);
|
|
i__1 = *m - rk;
|
|
vn1[lsticc] = dznrm2_(&i__1, &a[rk + 1 + lsticc * a_dim1], &c__1);
|
|
|
|
/* NOTE: The computation of VN1( LSTICC ) relies on the fact that */
|
|
/* SNRM2 does not fail on vectors with norm below the value of */
|
|
/* SQRT(DLAMCH('S')) */
|
|
|
|
vn2[lsticc] = vn1[lsticc];
|
|
lsticc = itemp;
|
|
goto L60;
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZLAQPS */
|
|
|
|
} /* zlaqps_ */
|
|
|