1391 lines
38 KiB
C
1391 lines
38 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 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZLARFB + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfb.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfb.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, */
|
|
/* T, LDT, C, LDC, WORK, LDWORK ) */
|
|
|
|
/* CHARACTER DIRECT, SIDE, STOREV, TRANS */
|
|
/* INTEGER K, LDC, LDT, LDV, LDWORK, M, N */
|
|
/* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), */
|
|
/* $ WORK( LDWORK, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZLARFB applies a complex block reflector H or its transpose H**H to a */
|
|
/* > complex M-by-N matrix C, from either the left or the right. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] SIDE */
|
|
/* > \verbatim */
|
|
/* > SIDE is CHARACTER*1 */
|
|
/* > = 'L': apply H or H**H from the Left */
|
|
/* > = 'R': apply H or H**H from the Right */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TRANS */
|
|
/* > \verbatim */
|
|
/* > TRANS is CHARACTER*1 */
|
|
/* > = 'N': apply H (No transpose) */
|
|
/* > = 'C': apply H**H (Conjugate transpose) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] DIRECT */
|
|
/* > \verbatim */
|
|
/* > DIRECT is CHARACTER*1 */
|
|
/* > Indicates how H is formed from a product of elementary */
|
|
/* > reflectors */
|
|
/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */
|
|
/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] STOREV */
|
|
/* > \verbatim */
|
|
/* > STOREV is CHARACTER*1 */
|
|
/* > Indicates how the vectors which define the elementary */
|
|
/* > reflectors are stored: */
|
|
/* > = 'C': Columnwise */
|
|
/* > = 'R': Rowwise */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix C. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix C. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > The order of the matrix T (= the number of elementary */
|
|
/* > reflectors whose product defines the block reflector). */
|
|
/* > If SIDE = 'L', M >= K >= 0; */
|
|
/* > if SIDE = 'R', N >= K >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] V */
|
|
/* > \verbatim */
|
|
/* > V is COMPLEX*16 array, dimension */
|
|
/* > (LDV,K) if STOREV = 'C' */
|
|
/* > (LDV,M) if STOREV = 'R' and SIDE = 'L' */
|
|
/* > (LDV,N) if STOREV = 'R' and SIDE = 'R' */
|
|
/* > See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDV */
|
|
/* > \verbatim */
|
|
/* > LDV is INTEGER */
|
|
/* > The leading dimension of the array V. */
|
|
/* > If STOREV = 'C' and SIDE = 'L', LDV >= f2cmax(1,M); */
|
|
/* > if STOREV = 'C' and SIDE = 'R', LDV >= f2cmax(1,N); */
|
|
/* > if STOREV = 'R', LDV >= K. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] T */
|
|
/* > \verbatim */
|
|
/* > T is COMPLEX*16 array, dimension (LDT,K) */
|
|
/* > The triangular K-by-K matrix T in the representation of the */
|
|
/* > block reflector. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. LDT >= K. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] C */
|
|
/* > \verbatim */
|
|
/* > C is COMPLEX*16 array, dimension (LDC,N) */
|
|
/* > On entry, the M-by-N matrix C. */
|
|
/* > On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDC */
|
|
/* > \verbatim */
|
|
/* > LDC is INTEGER */
|
|
/* > The leading dimension of the array C. LDC >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (LDWORK,K) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDWORK */
|
|
/* > \verbatim */
|
|
/* > LDWORK is INTEGER */
|
|
/* > The leading dimension of the array WORK. */
|
|
/* > If SIDE = 'L', LDWORK >= f2cmax(1,N); */
|
|
/* > if SIDE = 'R', LDWORK >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2013 */
|
|
|
|
/* > \ingroup complex16OTHERauxiliary */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The shape of the matrix V and the storage of the vectors which define */
|
|
/* > the H(i) is best illustrated by the following example with n = 5 and */
|
|
/* > k = 3. The elements equal to 1 are not stored; the corresponding */
|
|
/* > array elements are modified but restored on exit. The rest of the */
|
|
/* > array is not used. */
|
|
/* > */
|
|
/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
|
|
/* > */
|
|
/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */
|
|
/* > ( v1 1 ) ( 1 v2 v2 v2 ) */
|
|
/* > ( v1 v2 1 ) ( 1 v3 v3 ) */
|
|
/* > ( v1 v2 v3 ) */
|
|
/* > ( v1 v2 v3 ) */
|
|
/* > */
|
|
/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
|
|
/* > */
|
|
/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */
|
|
/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */
|
|
/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */
|
|
/* > ( 1 v3 ) */
|
|
/* > ( 1 ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zlarfb_(char *side, char *trans, char *direct, char *
|
|
storev, integer *m, integer *n, integer *k, doublecomplex *v, integer
|
|
*ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer *
|
|
ldc, doublecomplex *work, integer *ldwork)
|
|
{
|
|
/* System generated locals */
|
|
integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
|
|
work_offset, i__1, i__2, i__3, i__4, i__5;
|
|
doublecomplex z__1, z__2;
|
|
|
|
/* Local variables */
|
|
integer i__, j;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *), zcopy_(integer *, doublecomplex *,
|
|
integer *, doublecomplex *, integer *), ztrmm_(char *, char *,
|
|
char *, char *, integer *, integer *, doublecomplex *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *), zlacgv_(integer *, doublecomplex *,
|
|
integer *);
|
|
char transt[1];
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* June 2013 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Quick return if possible */
|
|
|
|
/* Parameter adjustments */
|
|
v_dim1 = *ldv;
|
|
v_offset = 1 + v_dim1 * 1;
|
|
v -= v_offset;
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
c_dim1 = *ldc;
|
|
c_offset = 1 + c_dim1 * 1;
|
|
c__ -= c_offset;
|
|
work_dim1 = *ldwork;
|
|
work_offset = 1 + work_dim1 * 1;
|
|
work -= work_offset;
|
|
|
|
/* Function Body */
|
|
if (*m <= 0 || *n <= 0) {
|
|
return;
|
|
}
|
|
|
|
if (lsame_(trans, "N")) {
|
|
*(unsigned char *)transt = 'C';
|
|
} else {
|
|
*(unsigned char *)transt = 'N';
|
|
}
|
|
|
|
if (lsame_(storev, "C")) {
|
|
|
|
if (lsame_(direct, "F")) {
|
|
|
|
/* Let V = ( V1 ) (first K rows) */
|
|
/* ( V2 ) */
|
|
/* where V1 is unit lower triangular. */
|
|
|
|
if (lsame_(side, "L")) {
|
|
|
|
/* Form H * C or H**H * C where C = ( C1 ) */
|
|
/* ( C2 ) */
|
|
|
|
/* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) */
|
|
|
|
/* W := C1**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
|
|
&c__1);
|
|
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
|
|
/* L10: */
|
|
}
|
|
|
|
/* W := W * V1 */
|
|
|
|
ztrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b1,
|
|
&v[v_offset], ldv, &work[work_offset], ldwork);
|
|
if (*m > *k) {
|
|
|
|
/* W := W + C2**H * V2 */
|
|
|
|
i__1 = *m - *k;
|
|
zgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
|
|
&c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 +
|
|
v_dim1], ldv, &c_b1, &work[work_offset], ldwork);
|
|
}
|
|
|
|
/* W := W * T**H or W * T */
|
|
|
|
ztrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork);
|
|
|
|
/* C := C - V * W**H */
|
|
|
|
if (*m > *k) {
|
|
|
|
/* C2 := C2 - V2 * W**H */
|
|
|
|
i__1 = *m - *k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
|
|
&z__1, &v[*k + 1 + v_dim1], ldv, &work[
|
|
work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1]
|
|
, ldc);
|
|
}
|
|
|
|
/* W := W * V1**H */
|
|
|
|
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k,
|
|
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
|
|
|
|
/* C1 := C1 - W**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = j + i__ * c_dim1;
|
|
i__4 = j + i__ * c_dim1;
|
|
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
|
|
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
|
|
z__2.i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L20: */
|
|
}
|
|
/* L30: */
|
|
}
|
|
|
|
} else if (lsame_(side, "R")) {
|
|
|
|
/* Form C * H or C * H**H where C = ( C1 C2 ) */
|
|
|
|
/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
|
|
|
|
/* W := C1 */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
|
|
work_dim1 + 1], &c__1);
|
|
/* L40: */
|
|
}
|
|
|
|
/* W := W * V1 */
|
|
|
|
ztrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b1,
|
|
&v[v_offset], ldv, &work[work_offset], ldwork);
|
|
if (*n > *k) {
|
|
|
|
/* W := W + C2 * V2 */
|
|
|
|
i__1 = *n - *k;
|
|
zgemm_("No transpose", "No transpose", m, k, &i__1, &c_b1,
|
|
&c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 +
|
|
v_dim1], ldv, &c_b1, &work[work_offset], ldwork);
|
|
}
|
|
|
|
/* W := W * T or W * T**H */
|
|
|
|
ztrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork);
|
|
|
|
/* C := C - W * V**H */
|
|
|
|
if (*n > *k) {
|
|
|
|
/* C2 := C2 - W * V2**H */
|
|
|
|
i__1 = *n - *k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", m, &i__1, k,
|
|
&z__1, &work[work_offset], ldwork, &v[*k + 1 +
|
|
v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1],
|
|
ldc);
|
|
}
|
|
|
|
/* W := W * V1**H */
|
|
|
|
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k,
|
|
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
|
|
|
|
/* C1 := C1 - W */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * c_dim1;
|
|
i__4 = i__ + j * c_dim1;
|
|
i__5 = i__ + j * work_dim1;
|
|
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
|
|
i__4].i - work[i__5].i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Let V = ( V1 ) */
|
|
/* ( V2 ) (last K rows) */
|
|
/* where V2 is unit upper triangular. */
|
|
|
|
if (lsame_(side, "L")) {
|
|
|
|
/* Form H * C or H**H * C where C = ( C1 ) */
|
|
/* ( C2 ) */
|
|
|
|
/* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) */
|
|
|
|
/* W := C2**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
|
|
work_dim1 + 1], &c__1);
|
|
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
|
|
/* L70: */
|
|
}
|
|
|
|
/* W := W * V2 */
|
|
|
|
ztrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b1,
|
|
&v[*m - *k + 1 + v_dim1], ldv, &work[work_offset],
|
|
ldwork);
|
|
if (*m > *k) {
|
|
|
|
/* W := W + C1**H * V1 */
|
|
|
|
i__1 = *m - *k;
|
|
zgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
|
|
&c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &
|
|
c_b1, &work[work_offset], ldwork);
|
|
}
|
|
|
|
/* W := W * T**H or W * T */
|
|
|
|
ztrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork);
|
|
|
|
/* C := C - V * W**H */
|
|
|
|
if (*m > *k) {
|
|
|
|
/* C1 := C1 - V1 * W**H */
|
|
|
|
i__1 = *m - *k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
|
|
&z__1, &v[v_offset], ldv, &work[work_offset],
|
|
ldwork, &c_b1, &c__[c_offset], ldc);
|
|
}
|
|
|
|
/* W := W * V2**H */
|
|
|
|
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k,
|
|
&c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[
|
|
work_offset], ldwork);
|
|
|
|
/* C2 := C2 - W**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = *m - *k + j + i__ * c_dim1;
|
|
i__4 = *m - *k + j + i__ * c_dim1;
|
|
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
|
|
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
|
|
z__2.i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L80: */
|
|
}
|
|
/* L90: */
|
|
}
|
|
|
|
} else if (lsame_(side, "R")) {
|
|
|
|
/* Form C * H or C * H**H where C = ( C1 C2 ) */
|
|
|
|
/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
|
|
|
|
/* W := C2 */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
|
|
j * work_dim1 + 1], &c__1);
|
|
/* L100: */
|
|
}
|
|
|
|
/* W := W * V2 */
|
|
|
|
ztrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b1,
|
|
&v[*n - *k + 1 + v_dim1], ldv, &work[work_offset],
|
|
ldwork);
|
|
if (*n > *k) {
|
|
|
|
/* W := W + C1 * V1 */
|
|
|
|
i__1 = *n - *k;
|
|
zgemm_("No transpose", "No transpose", m, k, &i__1, &c_b1,
|
|
&c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, &
|
|
work[work_offset], ldwork)
|
|
;
|
|
}
|
|
|
|
/* W := W * T or W * T**H */
|
|
|
|
ztrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork);
|
|
|
|
/* C := C - W * V**H */
|
|
|
|
if (*n > *k) {
|
|
|
|
/* C1 := C1 - W * V1**H */
|
|
|
|
i__1 = *n - *k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", m, &i__1, k,
|
|
&z__1, &work[work_offset], ldwork, &v[v_offset],
|
|
ldv, &c_b1, &c__[c_offset], ldc);
|
|
}
|
|
|
|
/* W := W * V2**H */
|
|
|
|
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", m, k,
|
|
&c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[
|
|
work_offset], ldwork);
|
|
|
|
/* C2 := C2 - W */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + (*n - *k + j) * c_dim1;
|
|
i__4 = i__ + (*n - *k + j) * c_dim1;
|
|
i__5 = i__ + j * work_dim1;
|
|
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
|
|
i__4].i - work[i__5].i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L110: */
|
|
}
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
|
|
|
|
} else if (lsame_(storev, "R")) {
|
|
|
|
if (lsame_(direct, "F")) {
|
|
|
|
/* Let V = ( V1 V2 ) (V1: first K columns) */
|
|
/* where V1 is unit upper triangular. */
|
|
|
|
if (lsame_(side, "L")) {
|
|
|
|
/* Form H * C or H**H * C where C = ( C1 ) */
|
|
/* ( C2 ) */
|
|
|
|
/* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) */
|
|
|
|
/* W := C1**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
|
|
&c__1);
|
|
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
|
|
/* L130: */
|
|
}
|
|
|
|
/* W := W * V1**H */
|
|
|
|
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k,
|
|
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
|
|
if (*m > *k) {
|
|
|
|
/* W := W + C2**H * V2**H */
|
|
|
|
i__1 = *m - *k;
|
|
zgemm_("Conjugate transpose", "Conjugate transpose", n, k,
|
|
&i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[(*k
|
|
+ 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset]
|
|
, ldwork);
|
|
}
|
|
|
|
/* W := W * T**H or W * T */
|
|
|
|
ztrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork);
|
|
|
|
/* C := C - V**H * W**H */
|
|
|
|
if (*m > *k) {
|
|
|
|
/* C2 := C2 - V2**H * W**H */
|
|
|
|
i__1 = *m - *k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("Conjugate transpose", "Conjugate transpose", &
|
|
i__1, n, k, &z__1, &v[(*k + 1) * v_dim1 + 1], ldv,
|
|
&work[work_offset], ldwork, &c_b1, &c__[*k + 1 +
|
|
c_dim1], ldc);
|
|
}
|
|
|
|
/* W := W * V1 */
|
|
|
|
ztrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b1,
|
|
&v[v_offset], ldv, &work[work_offset], ldwork);
|
|
|
|
/* C1 := C1 - W**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = j + i__ * c_dim1;
|
|
i__4 = j + i__ * c_dim1;
|
|
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
|
|
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
|
|
z__2.i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L140: */
|
|
}
|
|
/* L150: */
|
|
}
|
|
|
|
} else if (lsame_(side, "R")) {
|
|
|
|
/* Form C * H or C * H**H where C = ( C1 C2 ) */
|
|
|
|
/* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) */
|
|
|
|
/* W := C1 */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
|
|
work_dim1 + 1], &c__1);
|
|
/* L160: */
|
|
}
|
|
|
|
/* W := W * V1**H */
|
|
|
|
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", m, k,
|
|
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
|
|
if (*n > *k) {
|
|
|
|
/* W := W + C2 * V2**H */
|
|
|
|
i__1 = *n - *k;
|
|
zgemm_("No transpose", "Conjugate transpose", m, k, &i__1,
|
|
&c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k
|
|
+ 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset]
|
|
, ldwork);
|
|
}
|
|
|
|
/* W := W * T or W * T**H */
|
|
|
|
ztrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork);
|
|
|
|
/* C := C - W * V */
|
|
|
|
if (*n > *k) {
|
|
|
|
/* C2 := C2 - W * V2 */
|
|
|
|
i__1 = *n - *k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "No transpose", m, &i__1, k, &z__1,
|
|
&work[work_offset], ldwork, &v[(*k + 1) * v_dim1
|
|
+ 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1],
|
|
ldc);
|
|
}
|
|
|
|
/* W := W * V1 */
|
|
|
|
ztrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b1,
|
|
&v[v_offset], ldv, &work[work_offset], ldwork);
|
|
|
|
/* C1 := C1 - W */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * c_dim1;
|
|
i__4 = i__ + j * c_dim1;
|
|
i__5 = i__ + j * work_dim1;
|
|
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
|
|
i__4].i - work[i__5].i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L170: */
|
|
}
|
|
/* L180: */
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Let V = ( V1 V2 ) (V2: last K columns) */
|
|
/* where V2 is unit lower triangular. */
|
|
|
|
if (lsame_(side, "L")) {
|
|
|
|
/* Form H * C or H**H * C where C = ( C1 ) */
|
|
/* ( C2 ) */
|
|
|
|
/* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) */
|
|
|
|
/* W := C2**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
|
|
work_dim1 + 1], &c__1);
|
|
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
|
|
/* L190: */
|
|
}
|
|
|
|
/* W := W * V2**H */
|
|
|
|
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k,
|
|
&c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
|
|
work_offset], ldwork);
|
|
if (*m > *k) {
|
|
|
|
/* W := W + C1**H * V1**H */
|
|
|
|
i__1 = *m - *k;
|
|
zgemm_("Conjugate transpose", "Conjugate transpose", n, k,
|
|
&i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset],
|
|
ldv, &c_b1, &work[work_offset], ldwork);
|
|
}
|
|
|
|
/* W := W * T**H or W * T */
|
|
|
|
ztrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork);
|
|
|
|
/* C := C - V**H * W**H */
|
|
|
|
if (*m > *k) {
|
|
|
|
/* C1 := C1 - V1**H * W**H */
|
|
|
|
i__1 = *m - *k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("Conjugate transpose", "Conjugate transpose", &
|
|
i__1, n, k, &z__1, &v[v_offset], ldv, &work[
|
|
work_offset], ldwork, &c_b1, &c__[c_offset], ldc);
|
|
}
|
|
|
|
/* W := W * V2 */
|
|
|
|
ztrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b1,
|
|
&v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
|
|
work_offset], ldwork);
|
|
|
|
/* C2 := C2 - W**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = *m - *k + j + i__ * c_dim1;
|
|
i__4 = *m - *k + j + i__ * c_dim1;
|
|
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
|
|
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
|
|
z__2.i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L200: */
|
|
}
|
|
/* L210: */
|
|
}
|
|
|
|
} else if (lsame_(side, "R")) {
|
|
|
|
/* Form C * H or C * H**H where C = ( C1 C2 ) */
|
|
|
|
/* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) */
|
|
|
|
/* W := C2 */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
|
|
j * work_dim1 + 1], &c__1);
|
|
/* L220: */
|
|
}
|
|
|
|
/* W := W * V2**H */
|
|
|
|
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k,
|
|
&c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
|
|
work_offset], ldwork);
|
|
if (*n > *k) {
|
|
|
|
/* W := W + C1 * V1**H */
|
|
|
|
i__1 = *n - *k;
|
|
zgemm_("No transpose", "Conjugate transpose", m, k, &i__1,
|
|
&c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &
|
|
c_b1, &work[work_offset], ldwork);
|
|
}
|
|
|
|
/* W := W * T or W * T**H */
|
|
|
|
ztrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork);
|
|
|
|
/* C := C - W * V */
|
|
|
|
if (*n > *k) {
|
|
|
|
/* C1 := C1 - W * V1 */
|
|
|
|
i__1 = *n - *k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "No transpose", m, &i__1, k, &z__1,
|
|
&work[work_offset], ldwork, &v[v_offset], ldv, &
|
|
c_b1, &c__[c_offset], ldc)
|
|
;
|
|
}
|
|
|
|
/* W := W * V2 */
|
|
|
|
ztrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b1,
|
|
&v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
|
|
work_offset], ldwork);
|
|
|
|
/* C1 := C1 - W */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + (*n - *k + j) * c_dim1;
|
|
i__4 = i__ + (*n - *k + j) * c_dim1;
|
|
i__5 = i__ + j * work_dim1;
|
|
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
|
|
i__4].i - work[i__5].i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L230: */
|
|
}
|
|
/* L240: */
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZLARFB */
|
|
|
|
} /* zlarfb_ */
|
|
|