904 lines
26 KiB
C
904 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]/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 integer c__1 = 1;
|
|
|
|
/* > \brief \b ZGETSQRHRT */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZGETSQRHRT + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgetsqr
|
|
hrt.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgetsqr
|
|
hrt.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgetsqr
|
|
hrt.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, */
|
|
/* $ LWORK, INFO ) */
|
|
/* IMPLICIT NONE */
|
|
|
|
/* INTEGER INFO, LDA, LDT, LWORK, M, N, NB1, NB2, MB1 */
|
|
/* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZGETSQRHRT computes a NB2-sized column blocked QR-factorization */
|
|
/* > of a complex M-by-N matrix A with M >= N, */
|
|
/* > */
|
|
/* > A = Q * R. */
|
|
/* > */
|
|
/* > The routine uses internally a NB1-sized column blocked and MB1-sized */
|
|
/* > row blocked TSQR-factorization and perfors the reconstruction */
|
|
/* > of the Householder vectors from the TSQR output. The routine also */
|
|
/* > converts the R_tsqr factor from the TSQR-factorization output into */
|
|
/* > the R factor that corresponds to the Householder QR-factorization, */
|
|
/* > */
|
|
/* > A = Q_tsqr * R_tsqr = Q * R. */
|
|
/* > */
|
|
/* > The output Q and R factors are stored in the same format as in ZGEQRT */
|
|
/* > (Q is in blocked compact WY-representation). See the documentation */
|
|
/* > of ZGEQRT for more details on the format. */
|
|
/* > \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. M >= N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] MB1 */
|
|
/* > \verbatim */
|
|
/* > MB1 is INTEGER */
|
|
/* > The row block size to be used in the blocked TSQR. */
|
|
/* > MB1 > N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NB1 */
|
|
/* > \verbatim */
|
|
/* > NB1 is INTEGER */
|
|
/* > The column block size to be used in the blocked TSQR. */
|
|
/* > N >= NB1 >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NB2 */
|
|
/* > \verbatim */
|
|
/* > NB2 is INTEGER */
|
|
/* > The block size to be used in the blocked QR that is */
|
|
/* > output. NB2 >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension (LDA,N) */
|
|
/* > */
|
|
/* > On entry: an M-by-N matrix A. */
|
|
/* > */
|
|
/* > On exit: */
|
|
/* > a) the elements on and above the diagonal */
|
|
/* > of the array contain the N-by-N upper-triangular */
|
|
/* > matrix R corresponding to the Householder QR; */
|
|
/* > b) the elements below the diagonal represent Q by */
|
|
/* > the columns of blocked V (compact WY-representation). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] T */
|
|
/* > \verbatim */
|
|
/* > T is COMPLEX*16 array, dimension (LDT,N)) */
|
|
/* > The upper triangular block reflectors stored in compact form */
|
|
/* > as a sequence of upper triangular blocks. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. LDT >= NB2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > The dimension of the array WORK. */
|
|
/* > LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), */
|
|
/* > where */
|
|
/* > NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), */
|
|
/* > NB1LOCAL = MIN(NB1,N). */
|
|
/* > LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, */
|
|
/* > LW1 = NB1LOCAL * N, */
|
|
/* > LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ), */
|
|
/* > If LWORK = -1, then a workspace query is assumed. */
|
|
/* > The routine only calculates the optimal size of the WORK */
|
|
/* > array, returns this value as the first entry of the WORK */
|
|
/* > array, and no error message related to LWORK is issued */
|
|
/* > by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \ingroup comlpex16OTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > November 2020, Igor Kozachenko, */
|
|
/* > Computer Science Division, */
|
|
/* > University of California, Berkeley */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int zgetsqrhrt_(integer *m, integer *n, integer *mb1,
|
|
integer *nb1, integer *nb2, doublecomplex *a, integer *lda,
|
|
doublecomplex *t, integer *ldt, doublecomplex *work, integer *lwork,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4;
|
|
doublereal d__1, d__2, d__3;
|
|
doublecomplex z__1, z__2;
|
|
|
|
/* Local variables */
|
|
integer ldwt, lworkopt, i__, j, iinfo;
|
|
extern /* Subroutine */ int zungtsqr_row_(integer *, integer *, integer *
|
|
, integer *, doublecomplex *, integer *, doublecomplex *, integer
|
|
*, doublecomplex *, integer *, integer *), zcopy_(integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *),
|
|
zunhr_col_(integer *, integer *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *, integer *)
|
|
, xerbla_(char *, integer *, ftnlen);
|
|
logical lquery;
|
|
integer lw1, lw2, num_all_row_blocks__, lwt, nb1local, nb2local;
|
|
extern /* Subroutine */ int zlatsqr_(integer *, integer *, integer *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, integer *);
|
|
|
|
|
|
/* -- LAPACK computational routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input arguments */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0 || *m < *n) {
|
|
*info = -2;
|
|
} else if (*mb1 <= *n) {
|
|
*info = -3;
|
|
} else if (*nb1 < 1) {
|
|
*info = -4;
|
|
} else if (*nb2 < 1) {
|
|
*info = -5;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -7;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = f2cmin(*nb2,*n);
|
|
if (*ldt < f2cmax(i__1,i__2)) {
|
|
*info = -9;
|
|
} else {
|
|
|
|
/* Test the input LWORK for the dimension of the array WORK. */
|
|
/* This workspace is used to store array: */
|
|
/* a) Matrix T and WORK for ZLATSQR; */
|
|
/* b) N-by-N upper-triangular factor R_tsqr; */
|
|
/* c) Matrix T and array WORK for ZUNGTSQR_ROW; */
|
|
/* d) Diagonal D for ZUNHR_COL. */
|
|
|
|
if (*lwork < *n * *n + 1 && ! lquery) {
|
|
*info = -11;
|
|
} else {
|
|
|
|
/* Set block size for column blocks */
|
|
|
|
nb1local = f2cmin(*nb1,*n);
|
|
|
|
/* Computing MAX */
|
|
d__3 = (doublereal) (*m - *n) / (doublereal) (*mb1 - *n) +
|
|
.5f;
|
|
d__1 = 1., d__2 = d_int(&d__3);
|
|
num_all_row_blocks__ = (integer) f2cmax(d__1,d__2);
|
|
|
|
/* Length and leading dimension of WORK array to place */
|
|
/* T array in TSQR. */
|
|
|
|
lwt = num_all_row_blocks__ * *n * nb1local;
|
|
ldwt = nb1local;
|
|
|
|
/* Length of TSQR work array */
|
|
|
|
lw1 = nb1local * *n;
|
|
|
|
/* Length of ZUNGTSQR_ROW work array. */
|
|
|
|
/* Computing MAX */
|
|
i__1 = nb1local, i__2 = *n - nb1local;
|
|
lw2 = nb1local * f2cmax(i__1,i__2);
|
|
|
|
/* Computing MAX */
|
|
/* Computing MAX */
|
|
i__3 = lwt + *n * *n + lw2, i__4 = lwt + *n * *n + *n;
|
|
i__1 = lwt + lw1, i__2 = f2cmax(i__3,i__4);
|
|
lworkopt = f2cmax(i__1,i__2);
|
|
|
|
if (*lwork < f2cmax(1,lworkopt) && ! lquery) {
|
|
*info = -11;
|
|
}
|
|
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Handle error in the input parameters and return workspace query. */
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZGETSQRHRT", &i__1, (ftnlen)10);
|
|
return 0;
|
|
} else if (lquery) {
|
|
z__1.r = (doublereal) lworkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (f2cmin(*m,*n) == 0) {
|
|
z__1.r = (doublereal) lworkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return 0;
|
|
}
|
|
|
|
nb2local = f2cmin(*nb2,*n);
|
|
|
|
|
|
/* (1) Perform TSQR-factorization of the M-by-N matrix A. */
|
|
|
|
zlatsqr_(m, n, mb1, &nb1local, &a[a_offset], lda, &work[1], &ldwt, &work[
|
|
lwt + 1], &lw1, &iinfo);
|
|
|
|
/* (2) Copy the factor R_tsqr stored in the upper-triangular part */
|
|
/* of A into the square matrix in the work array */
|
|
/* WORK(LWT+1:LWT+N*N) column-by-column. */
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(&j, &a[j * a_dim1 + 1], &c__1, &work[lwt + *n * (j - 1) + 1], &
|
|
c__1);
|
|
}
|
|
|
|
/* (3) Generate a M-by-N matrix Q with orthonormal columns from */
|
|
/* the result stored below the diagonal in the array A in place. */
|
|
|
|
zungtsqr_row_(m, n, mb1, &nb1local, &a[a_offset], lda, &work[1], &ldwt, &
|
|
work[lwt + *n * *n + 1], &lw2, &iinfo);
|
|
|
|
/* (4) Perform the reconstruction of Householder vectors from */
|
|
/* the matrix Q (stored in A) in place. */
|
|
|
|
zunhr_col_(m, n, &nb2local, &a[a_offset], lda, &t[t_offset], ldt, &work[
|
|
lwt + *n * *n + 1], &iinfo);
|
|
|
|
/* (5) Copy the factor R_tsqr stored in the square matrix in the */
|
|
/* work array WORK(LWT+1:LWT+N*N) into the upper-triangular */
|
|
/* part of A. */
|
|
|
|
/* (6) Compute from R_tsqr the factor R_hr corresponding to */
|
|
/* the reconstructed Householder vectors, i.e. R_hr = S * R_tsqr. */
|
|
/* This multiplication by the sign matrix S on the left means */
|
|
/* changing the sign of I-th row of the matrix R_tsqr according */
|
|
/* to sign of the I-th diagonal element DIAG(I) of the matrix S. */
|
|
/* DIAG is stored in WORK( LWT+N*N+1 ) from the ZUNHR_COL output. */
|
|
|
|
/* (5) and (6) can be combined in a single loop, so the rows in A */
|
|
/* are accessed only once. */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = lwt + *n * *n + i__;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
if (work[i__2].r == z__1.r && work[i__2].i == z__1.i) {
|
|
i__2 = *n;
|
|
for (j = i__; j <= i__2; ++j) {
|
|
i__3 = i__ + j * a_dim1;
|
|
z__2.r = -1., z__2.i = 0.;
|
|
i__4 = lwt + *n * (j - 1) + i__;
|
|
z__1.r = z__2.r * work[i__4].r - z__2.i * work[i__4].i,
|
|
z__1.i = z__2.r * work[i__4].i + z__2.i * work[i__4]
|
|
.r;
|
|
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
|
|
}
|
|
} else {
|
|
i__2 = *n - i__ + 1;
|
|
zcopy_(&i__2, &work[lwt + *n * (i__ - 1) + i__], n, &a[i__ + i__ *
|
|
a_dim1], lda);
|
|
}
|
|
}
|
|
|
|
z__1.r = (doublereal) lworkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return 0;
|
|
|
|
/* End of ZGETSQRHRT */
|
|
|
|
} /* zgetsqrhrt_ */
|
|
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