570 lines
16 KiB
C
570 lines
16 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 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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/* 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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/* Table of constant values */
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static doublereal c_b4 = 1.;
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static doublereal c_b5 = 0.;
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static integer c__1 = 1;
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/* > \brief \b DLARF1F applies an elementary reflector to a general rectangular */
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/* matrix assuming v(1) = 1. */
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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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/* > Download DLARF1F + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarf1f
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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/dlarf1f
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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/dlarf1f
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.f"> */
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/* > [TXT]</a> */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DLARF1F( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) */
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/* CHARACTER SIDE */
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/* INTEGER INCV, LDC, M, N */
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/* DOUBLE PRECISION TAU */
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/* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) */
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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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/* > DLARF1F applies a real elementary reflector H to a real m by n matrix */
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/* > C, from either the left or the right. H is represented in the form */
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/* > */
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/* > H = I - tau * v * v**T */
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/* > */
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/* > where tau is a real scalar and v is a real vector. */
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/* > */
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/* > If tau = 0, then H is taken to be the unit matrix. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] SIDE */
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/* > \verbatim */
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/* > SIDE is CHARACTER*1 */
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/* > = 'L': form H * C */
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/* > = 'R': form C * H */
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/* > \endverbatim */
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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 C. */
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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 C. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] V */
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/* > \verbatim */
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/* > V is DOUBLE PRECISION array, dimension */
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/* > (1 + (M-1)*abs(INCV)) if SIDE = 'L' */
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/* > or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */
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/* > The vector v in the representation of H. V is not used if */
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/* > TAU = 0. V(1) is not referenced or modified. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] INCV */
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/* > \verbatim */
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/* > INCV is INTEGER */
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/* > The increment between elements of v. INCV <> 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TAU */
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/* > \verbatim */
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/* > TAU is DOUBLE PRECISION */
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/* > The value tau in the representation of H. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] C */
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/* > \verbatim */
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/* > C is DOUBLE PRECISION array, dimension (LDC,N) */
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/* > On entry, the m by n matrix C. */
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/* > On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
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/* > or C * H if SIDE = 'R'. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDC */
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/* > \verbatim */
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/* > LDC is INTEGER */
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/* > The leading dimension of the array C. LDC >= f2cmax(1,M). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] WORK */
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/* > \verbatim */
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/* > WORK is DOUBLE PRECISION array, dimension */
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/* > (N) if SIDE = 'L' */
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/* > or (M) if SIDE = 'R' */
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/* > \endverbatim */
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/* To take advantage of the fact that v(1) = 1, we do the following */
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/* v = [ 1 v_2 ]**T */
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/* If SIDE='L' */
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/* |-----| */
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/* | C_1 | */
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/* C =| C_2 | */
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/* |-----| */
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/* C_1\in\mathbb{R}^{1\times n}, C_2\in\mathbb{R}^{m-1\times n} */
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/* So we compute: */
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/* C = HC = (I - \tau vv**T)C */
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/* = C - \tau vv**T C */
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/* w = C**T v = [ C_1**T C_2**T ] [ 1 v_2 ]**T */
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/* = C_1**T + C_2**T v ( DGEMM then DAXPY ) */
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/* C = C - \tau vv**T C */
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/* = C - \tau vw**T */
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/* Giving us C_1 = C_1 - \tau w**T ( DAXPY ) */
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/* and */
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/* C_2 = C_2 - \tau v_2w**T ( DGER ) */
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/* If SIDE='R' */
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/* C = [ C_1 C_2 ] */
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/* C_1\in\mathbb{R}^{m\times 1}, C_2\in\mathbb{R}^{m\times n-1} */
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/* So we compute: */
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/* C = CH = C(I - \tau vv**T) */
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/* = C - \tau Cvv**T */
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/* w = Cv = [ C_1 C_2 ] [ 1 v_2 ]**T */
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/* = C_1 + C_2v_2 ( DGEMM then DAXPY ) */
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/* C = C - \tau Cvv**T */
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/* = C - \tau wv**T */
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/* Giving us C_1 = C_1 - \tau w ( DAXPY ) */
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/* and */
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/* C_2 = C_2 - \tau wv_2**T ( DGER ) */
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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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/* > \ingroup larf */
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/* ===================================================================== */
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/* Subroutine */ int dlarf1f_(char *side, integer *m, integer *n, doublereal *
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v, integer *incv, doublereal *tau, doublereal *c__, integer *ldc,
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doublereal *work)
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{
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/* System generated locals */
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integer c_dim1, c_offset, i__1;
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doublereal d__1;
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/* Local variables */
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integer i__;
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logical applyleft;
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extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *), dscal_(integer *, doublereal *, doublereal *, integer
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*);
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *);
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integer lastc;
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extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *);
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integer lastv;
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extern integer iladlc_(integer *, integer *, doublereal *, integer *),
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iladlr_(integer *, integer *, doublereal *, integer *);
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/* -- LAPACK auxiliary routine -- */
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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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/* ===================================================================== */
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/* Parameter adjustments */
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|
--v;
|
|
c_dim1 = *ldc;
|
|
c_offset = 1 + c_dim1;
|
|
c__ -= c_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
applyleft = lsame_(side, "L");
|
|
lastv = 1;
|
|
lastc = 0;
|
|
if (*tau != 0.) {
|
|
/* Set up variables for scanning V. LASTV begins pointing to the end */
|
|
/* of V. */
|
|
if (applyleft) {
|
|
lastv = *m;
|
|
} else {
|
|
lastv = *n;
|
|
}
|
|
if (*incv > 0) {
|
|
i__ = (lastv - 1) * *incv + 1;
|
|
} else {
|
|
i__ = 1;
|
|
}
|
|
/* Look for the last non-zero row in V. */
|
|
/* Since we are assuming that V(1) = 1, and it is not stored, so we */
|
|
/* shouldn't access it. */
|
|
while(lastv > 1 && v[i__] == 0.) {
|
|
--lastv;
|
|
i__ -= *incv;
|
|
}
|
|
if (applyleft) {
|
|
/* Scan for the last non-zero column in C(1:lastv,:). */
|
|
lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
|
|
} else {
|
|
/* Scan for the last non-zero row in C(:,1:lastv). */
|
|
lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
|
|
}
|
|
}
|
|
if (lastc == 0) {
|
|
return 0;
|
|
}
|
|
if (applyleft) {
|
|
|
|
/* Form H * C */
|
|
|
|
/* Check if lastv = 1. This means v = 1, So we just need to comp */
|
|
/* C := HC = (1-\tau)C. */
|
|
if (lastv == 1) {
|
|
|
|
/* C(1,1:lastc) := ( 1 - tau ) * C(1,1:lastc) */
|
|
|
|
d__1 = 1. - *tau;
|
|
dscal_(&lastc, &d__1, &c__[c_offset], ldc);
|
|
} else {
|
|
|
|
/* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) */
|
|
|
|
/* w(1:lastc,1) := C(2:lastv,1:lastc)**T * v(2:lastv,1) */
|
|
i__1 = lastv - 1;
|
|
dgemv_("Transpose", &i__1, &lastc, &c_b4, &c__[c_dim1 + 2], ldc, &
|
|
v[*incv + 1], incv, &c_b5, &work[1], &c__1);
|
|
/* w(1:lastc,1) += C(1,1:lastc)**T * v(1,1) = C(1,1:lastc)**T */
|
|
daxpy_(&lastc, &c_b4, &c__[c_offset], ldc, &work[1], &c__1);
|
|
|
|
/* C(1:lastv,1:lastc) := C(...) - tau * v(1:lastv,1) * w(1:lastc,1)**T */
|
|
|
|
/* C(1, 1:lastc) := C(...) - tau * v(1,1) * w(1:lastc,1)**T */
|
|
/* = C(...) - tau * w(1:lastc,1)**T */
|
|
d__1 = -(*tau);
|
|
daxpy_(&lastc, &d__1, &work[1], &c__1, &c__[c_offset], ldc);
|
|
/* C(2:lastv,1:lastc) := C(...) - tau * v(2:lastv,1)*w(1:last */
|
|
i__1 = lastv - 1;
|
|
d__1 = -(*tau);
|
|
dger_(&i__1, &lastc, &d__1, &v[*incv + 1], incv, &work[1], &c__1,
|
|
&c__[c_dim1 + 2], ldc);
|
|
}
|
|
} else {
|
|
|
|
/* Form C * H */
|
|
|
|
/* Check if n = 1. This means v = 1, so we just need to compute */
|
|
/* C := CH = C(1-\tau). */
|
|
if (lastv == 1) {
|
|
|
|
/* C(1:lastc,1) := ( 1 - tau ) * C(1:lastc,1) */
|
|
|
|
d__1 = 1. - *tau;
|
|
dscal_(&lastc, &d__1, &c__[c_offset], &c__1);
|
|
} else {
|
|
|
|
/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */
|
|
|
|
/* w(1:lastc,1) := C(1:lastc,2:lastv) * v(2:lastv,1) */
|
|
i__1 = lastv - 1;
|
|
dgemv_("No transpose", &lastc, &i__1, &c_b4, &c__[(c_dim1 << 1) +
|
|
1], ldc, &v[*incv + 1], incv, &c_b5, &work[1], &c__1);
|
|
/* w(1:lastc,1) += C(1:lastc,1) v(1,1) = C(1:lastc,1) */
|
|
daxpy_(&lastc, &c_b4, &c__[c_offset], &c__1, &work[1], &c__1);
|
|
|
|
/* C(1:lastc,1:lastv) := C(...) - tau * w(1:lastc,1) * v(1:lastv,1)**T */
|
|
|
|
/* C(1:lastc,1) := C(...) - tau * w(1:lastc,1) * v(1,1)** */
|
|
/* = C(...) - tau * w(1:lastc,1) */
|
|
d__1 = -(*tau);
|
|
daxpy_(&lastc, &d__1, &work[1], &c__1, &c__[c_offset], &c__1);
|
|
/* C(1:lastc,2:lastv) := C(...) - tau * w(1:lastc,1) * v(2:la */
|
|
i__1 = lastv - 1;
|
|
d__1 = -(*tau);
|
|
dger_(&lastc, &i__1, &d__1, &work[1], &c__1, &v[*incv + 1], incv,
|
|
&c__[(c_dim1 << 1) + 1], ldc);
|
|
}
|
|
}
|
|
return 0;
|
|
|
|
/* End of DLARF1F */
|
|
|
|
} /* dlarf1f_ */
|
|
|