528 lines
15 KiB
C
528 lines
15 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 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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#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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/* Table of constant values */
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static integer c__1 = 1;
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static doublereal c_b8 = 1.;
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/* > \brief \b DTZRQF */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DTZRQF + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtzrqf.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtzrqf.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtzrqf.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO ) */
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/* INTEGER INFO, LDA, M, N */
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/* DOUBLE PRECISION A( LDA, * ), TAU( * ) */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > This routine is deprecated and has been replaced by routine DTZRZF. */
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/* > */
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/* > DTZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A */
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/* > to upper triangular form by means of orthogonal transformations. */
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/* > */
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/* > The upper trapezoidal matrix A is factored as */
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/* > */
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/* > A = ( R 0 ) * Z, */
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/* > */
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/* > where Z is an N-by-N orthogonal matrix and R is an M-by-M upper */
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/* > triangular matrix. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] M */
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/* > \verbatim */
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/* > M is INTEGER */
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/* > The number of rows of the matrix A. M >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The number of columns of the matrix A. N >= M. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
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/* > On entry, the leading M-by-N upper trapezoidal part of the */
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/* > array A must contain the matrix to be factorized. */
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/* > On exit, the leading M-by-M upper triangular part of A */
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/* > contains the upper triangular matrix R, and elements M+1 to */
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/* > N of the first M rows of A, with the array TAU, represent the */
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/* > orthogonal matrix Z as a product of M elementary reflectors. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] TAU */
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/* > \verbatim */
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/* > TAU is DOUBLE PRECISION array, dimension (M) */
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/* > The scalar factors of the elementary reflectors. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date December 2016 */
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/* > \ingroup doubleOTHERcomputational */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > The factorization is obtained by Householder's method. The kth */
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/* > transformation matrix, Z( k ), which is used to introduce zeros into */
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/* > the ( m - k + 1 )th row of A, is given in the form */
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/* > */
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/* > Z( k ) = ( I 0 ), */
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/* > ( 0 T( k ) ) */
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/* > */
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/* > where */
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/* > */
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/* > T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ), */
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/* > ( 0 ) */
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/* > ( z( k ) ) */
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/* > */
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/* > tau is a scalar and z( k ) is an ( n - m ) element vector. */
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/* > tau and z( k ) are chosen to annihilate the elements of the kth row */
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/* > of X. */
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/* > */
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/* > The scalar tau is returned in the kth element of TAU and the vector */
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/* > u( k ) in the kth row of A, such that the elements of z( k ) are */
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/* > in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in */
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/* > the upper triangular part of A. */
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/* > */
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/* > Z is given by */
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/* > */
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/* > Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ void dtzrqf_(integer *m, integer *n, doublereal *a, integer *
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lda, doublereal *tau, integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2;
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doublereal d__1;
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/* Local variables */
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extern /* Subroutine */ void dger_(integer *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *);
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integer i__, k;
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extern /* Subroutine */ void dgemv_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *), dcopy_(integer *,
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doublereal *, integer *, doublereal *, integer *), daxpy_(integer
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*, doublereal *, doublereal *, integer *, doublereal *, integer *)
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;
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integer m1;
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extern /* Subroutine */ void dlarfg_(integer *, doublereal *, doublereal *,
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integer *, doublereal *);
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extern int xerbla_(char *, integer *, ftnlen);
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/* -- LAPACK computational routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* December 2016 */
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/* ===================================================================== */
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/* Test the input parameters. */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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--tau;
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/* Function Body */
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*info = 0;
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if (*m < 0) {
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*info = -1;
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} else if (*n < *m) {
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*info = -2;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -4;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DTZRQF", &i__1, 6);
|
|
return;
|
|
}
|
|
|
|
/* Perform the factorization. */
|
|
|
|
if (*m == 0) {
|
|
return;
|
|
}
|
|
if (*m == *n) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
tau[i__] = 0.;
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
/* Computing MIN */
|
|
i__1 = *m + 1;
|
|
m1 = f2cmin(i__1,*n);
|
|
for (k = *m; k >= 1; --k) {
|
|
|
|
/* Use a Householder reflection to zero the kth row of A. */
|
|
/* First set up the reflection. */
|
|
|
|
i__1 = *n - *m + 1;
|
|
dlarfg_(&i__1, &a[k + k * a_dim1], &a[k + m1 * a_dim1], lda, &tau[
|
|
k]);
|
|
|
|
if (tau[k] != 0. && k > 1) {
|
|
|
|
/* We now perform the operation A := A*P( k ). */
|
|
|
|
/* Use the first ( k - 1 ) elements of TAU to store a( k ), */
|
|
/* where a( k ) consists of the first ( k - 1 ) elements of */
|
|
/* the kth column of A. Also let B denote the first */
|
|
/* ( k - 1 ) rows of the last ( n - m ) columns of A. */
|
|
|
|
i__1 = k - 1;
|
|
dcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &tau[1], &c__1);
|
|
|
|
/* Form w = a( k ) + B*z( k ) in TAU. */
|
|
|
|
i__1 = k - 1;
|
|
i__2 = *n - *m;
|
|
dgemv_("No transpose", &i__1, &i__2, &c_b8, &a[m1 * a_dim1 +
|
|
1], lda, &a[k + m1 * a_dim1], lda, &c_b8, &tau[1], &
|
|
c__1);
|
|
|
|
/* Now form a( k ) := a( k ) - tau*w */
|
|
/* and B := B - tau*w*z( k )**T. */
|
|
|
|
i__1 = k - 1;
|
|
d__1 = -tau[k];
|
|
daxpy_(&i__1, &d__1, &tau[1], &c__1, &a[k * a_dim1 + 1], &
|
|
c__1);
|
|
i__1 = k - 1;
|
|
i__2 = *n - *m;
|
|
d__1 = -tau[k];
|
|
dger_(&i__1, &i__2, &d__1, &tau[1], &c__1, &a[k + m1 * a_dim1]
|
|
, lda, &a[m1 * a_dim1 + 1], lda);
|
|
}
|
|
/* L20: */
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DTZRQF */
|
|
|
|
} /* dtzrqf_ */
|
|
|