realroot_doc 0.1.1
Functions
mmx::vct Namespace Reference

Functions

Function Documentation

void mmx::vct::accconv ( C *  r,
int  str,
const C *  a,
unsigned  na,
int  sta,
const C *  b,
unsigned  nb,
int  stb 
)

standard convolution loop, do not initialize r.

Parameters:
rbase address of the result.
strincrement for r.
abase address of first operand.
nanumber of coefficients for a.
staincrement for a.
bbase address of second operand.
nbnumber of coefficients for a.
stbincrement for b.

Definition at line 277 of file tensor_vctops.hpp.

Referenced by conv().

  {
    C * er;
    const C * ea, * eb;
    for ( ea = a; ea != a + na*sta; ea += sta, r += str )
      for ( er = r, eb = b; eb != b + nb*stb; eb += stb, er += str )
        *er += *ea**eb;
  };
void mmx::vct::accmax ( A &  mx,
const B *  v,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 192 of file tensor_vctops.hpp.

Referenced by max().

  {
    const B * p;
    for (  p = v; p != v+n*s; p += s )
      if ( mx < *p ) mx = *p;
  };
void mmx::vct::accmin ( A &  mn,
B const *  v,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 177 of file tensor_vctops.hpp.

Referenced by min().

  {
    const B * p;
    for ( p = v; p != v + n*s; p += s ) 
      if ( mn > *p ) mn = *p;
  };
void mmx::vct::conv ( C *  r,
unsigned  nr,
int  str,
const C *  a,
unsigned  na,
int  sta,
const C *  b,
unsigned  nb,
int  stb 
)

truncated convolution loop:

Parameters:
rbase address of the result.
nrnumber of coefficients wanted.
strincrement for r.
abase address of first operand.
nanumber of coefficients for a.
staincrement for a.
bbase address of second operand.
nbnumber of coefficients for a. stb increment for b.

Definition at line 229 of file tensor_vctops.hpp.

References min().

  {
    if ( na < nb ) { conv(r,nr,str,b,nb,stb,a,na,sta); return; };
    int k, l;
    C * er;
    const C * ea, * eb, * eeb, * eea;
    er = r; 
    eb = b;
    
    for ( er = r, eb = b, k = 0; k < std::min(nb,nr); k ++, er += str, eb += stb )
      for ( eeb = eb, ea = a, *er = 0, l = 0; 
            l <= k; 
            *er += *ea**eeb, l ++, eeb -= stb, ea += sta ) ;
    
    for ( ; k < std::min(na,nr) ; k ++,   er += str )
      for ( *er = 0, 
              l = k-nb+1, eeb = b +(nb-1)*stb , ea = a + l*sta; 
            l <= k; 
            *er+= *ea**eeb,
              l ++, eeb -= stb, ea += sta ) ;
    
    for ( ; k < nr; k ++,  er += str )
      for ( *er = 0, 
              l = k-nb+1, eeb = b+(nb-1)*stb,  ea = a + l*sta; 
            l < na; 
            *er += *ea**eeb, 
              l ++, eeb -= stb, ea += sta ) ;
  };
void mmx::vct::conv ( C *  r,
int  str,
const C *  a,
unsigned  na,
int  sta,
const C *  b,
unsigned  nb,
int  stb 
)

standard convolution loop.

Parameters:
rbase address of the result.
strincrement for r.
abase address of first operand.
nanumber of coefficients for a.
staincrement for a.
bbase address of second operand.
nbnumber of coefficients for a.
stbincrement for b.

Definition at line 300 of file tensor_vctops.hpp.

References accconv().

  {
    C * er;
    for ( er = r; er != r + (na+nb-1)*str; *er++ = 0 ) ;
    accconv(r,str,a,na,sta,b,nb,stb);
  };
void mmx::vct::copy ( A *  a,
const B *  b,
unsigned  n,
int  sa,
int  sb 
) [inline]

Definition at line 146 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != a + n*sa; *ea = *b, ea += sa, b += sb ) ;
  };
void mmx::vct::copy ( A *  a,
const B *  b,
unsigned  n 
) [inline]

Definition at line 140 of file tensor_vctops.hpp.

Referenced by mmx::tensor::binoms(), and mmerge().

  {
    std::copy(b,b+n,a) ;
  };
void mmx::vct::decasteljau ( C *  c,
unsigned  n,
const I &  i,
int  s = 1 
)

Definition at line 459 of file tensor_vctops.hpp.

{
  C *ec, *p;
  for ( ec = c + (n-1)*s; ec != c; ec -= s )
    for ( p = c; p != ec; p += s )
      *p = (1.0-i)**p+i**(p+s) ;
};
void mmx::vct::dhorner ( O &  p,
O &  dp,
C const *const  c,
unsigned  n,
const I &  t,
int  s = 1 
) [inline]

Definition at line 468 of file tensor_vctops.hpp.

{ 
  p = c[n-1], dp  = 0.0; 
  for ( int j = (n-2)*s; j >=0; dp=dp*t+p, p=p*t+c[j], j -= s ) ; 
};
void mmx::vct::diff ( C *  dst,
C const *const  src,
unsigned  sz,
int  st = 1 
) [inline]

Definition at line 453 of file tensor_vctops.hpp.

{ 
  for ( unsigned i = 0; i < sz-1; dst[i*st] = (i+1)*src[(i+1)*st], i++ ) ; 
};
void mmx::vct::fill ( C *  a,
unsigned  n,
int  s,
const C &  x 
)

Definition at line 152 of file tensor_vctops.hpp.

Referenced by binary_sleeve_subdivision< K >::barre(), mmx::tensor::clear(), mmx::realroot::fill_data(), mmx::linear::LUinverse(), mcrossp(), mdotp(), eenv::monoms_print(), msimplify(), and pmmul().

  {
    for ( C * pa = a; pa != a+n*s; *pa = x, pa += s ) ;
  };
void mmx::vct::hhorner ( O &  o,
C const *const  c,
unsigned  n,
const I &  i,
const I &  i0,
int  s = 1 
) [inline]

Definition at line 436 of file tensor_vctops.hpp.

Referenced by mmx::tensor::hevalm(), and hhorner().

{ 
  o = O(c[(n-1)*s]);
  for ( int p = (n-2)*s; p >= 0; o *= i, o +=  O(c[p])*i0, p -= s ) ; 
};
texp::sup<C,I>::T mmx::vct::hhorner ( C const *const  c,
unsigned  n,
const I &  i,
const I &  i0,
int  s = 1 
) [inline]

Definition at line 444 of file tensor_vctops.hpp.

References hhorner().

{ 
  typename texp::ringof<C,I>::T o(0);
  hhorner(o,c,n,i,i0,s) ; 
  return o; 
};
void mmx::vct::horner ( O &  o,
C const *const  c,
unsigned  n,
const I &  i,
int  s = 1 
) [inline]

Definition at line 420 of file tensor_vctops.hpp.

Referenced by horner().

{ 
  o = O(0);
  for ( int p = (n-1)*s; p != 0; o +=  as<O>(c[p]), o *= i, p -= s ) ; 
  o+= as<O>(c[0]); 
};
texp::sup<C,I>::T mmx::vct::horner ( C const *const  c,
unsigned  n,
const I &  i,
int  s = 1 
) [inline]

Definition at line 428 of file tensor_vctops.hpp.

References horner().

{ 
  typename texp::ringof<C,I>::T o(0);
  horner(o,c,n,i,s); 
  return o; 
};
void mmx::vct::icopy ( A *  a,
unsigned *  aadd,
unsigned  nadd,
const B *  b 
) [inline]

Definition at line 158 of file tensor_vctops.hpp.

Referenced by mmx::tensor::add(), mmx::tensor::extend(), and mmx::tensor::sub().

  {
    for ( unsigned * ea = aadd; ea != aadd + nadd; a[*ea++] = *b++ ) ;
  };
void mmx::vct::inverses ( A *  a,
A *  ea 
)

Definition at line 476 of file tensor_vctops.hpp.

Referenced by mmx::tensor::ibinoms().

{ for ( ;a != ea; *a++ = 1/(*a) ) ; };
void mmx::vct::ipadd ( A *  a,
unsigned *  aadd,
unsigned  nadd,
const B *  b 
) [inline]

Definition at line 164 of file tensor_vctops.hpp.

Referenced by mmx::tensor::add(), and mmx::tensor::waddm().

  {
    for ( unsigned * ea = aadd; ea != aadd + nadd; a[*ea++] += *b++ ) ;
  };
void mmx::vct::ipsub ( A *  a,
unsigned *  aadd,
unsigned  nadd,
const B *  b 
) [inline]

Definition at line 170 of file tensor_vctops.hpp.

Referenced by mmx::tensor::sub(), and mmx::tensor::wsubm().

  {
    for ( unsigned * ea = aadd; ea != aadd + nadd; a[*ea++] -= *b++ ) ;
  };
real_t mmx::vct::max ( real_t const *  src,
int  sz,
int  st = 1 
)

Definition at line 488 of file tensor_vctops.hpp.

    {
      real_t r = src[0];
      for ( int p = st; p != sz*st; p += st ) if ( r < src[p] ) r = src[p];    
      return r;
    };
void mmx::vct::max ( A &  mx,
B const *  v,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 200 of file tensor_vctops.hpp.

References accmax().

  {
    mx = v[0];
    accmax(mx,v,n,s) ;
  };
real_t mmx::vct::min ( real_t const *  src,
int  sz,
int  st = 1 
)

Definition at line 480 of file tensor_vctops.hpp.

    {
      real_t r = src[0];
      for ( int p = st; p != sz*st; p += st ) if ( r > src[p] ) r = src[p];    
      return r;
    };
void mmx::vct::min ( A &  mn,
B const *  v,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 185 of file tensor_vctops.hpp.

References accmin().

Referenced by conv().

  {
    mn = v[0];
    accmin(mn,v+s,n-1,s) ;
  };
void mmx::vct::minmax ( C &  m,
C &  M,
const C *  a,
unsigned  n,
unsigned  s = 1 
) [inline]
Parameters:
mminimum value.
Mmaximum value.
abase address of coefficients.
numberof coefficients.
incrementused to access a.

Definition at line 317 of file tensor_vctops.hpp.

  {
    for ( const C * e = a + n*s-s, m = M = *e; a < e; a += 2*s )
      {
        if ( *a > *(a+s) )
          {
            if ( *a > M ) M = *a; 
            if ( *(a+s) < m ) m = *(a+s) ;
          }
        else 
          {
            if ( *a > M ) M = *a;
            if ( *(a+s) < m ) m = *(a+s) ;
          };
      };
  };
unsigned mmx::vct::mmerge ( C *  r,
const C *  a,
const C *  b,
unsigned  na,
unsigned  nb 
) [inline]

Definition at line 335 of file tensor_vctops.hpp.

References copy().

  {
    C * er(r);
    const C * ea(a), * eb(b);
    a += na;
    b += nb;
    for (;;)
      {
        while( ea < a && *ea < *eb ) *er++ = *ea++;
        if (  ea == a ) { std::copy(eb,b,er) ; break; };
        if ( *ea == *eb ) { *er++ = *ea++; eb++;};
        while( eb < b && *eb < *ea ) *er++ = *eb++;
        if (  eb == b ) { std::copy(ea,a,er); break; };
        if ( *eb == *ea ) { *er++ = *eb++; ea++;};
      };
    return er-r;
  };
void mmx::vct::mmerge ( C *  r,
int  str,
const C *  a,
unsigned  na,
int  sta,
const C *  b,
unsigned  nb,
int  stb 
) [inline]

Definition at line 355 of file tensor_vctops.hpp.

  {
    C * er(r);
    const C * ea(a), * eb(b);
    
    a += na*sta;
    b += nb*stb;
    
    for (;;)
      {
        for (;ea != a && *ea < *eb; *er = *ea, er += str, ea += sta ) ;
        
        if (  ea == a ) 
          { 
            for ( ; eb != b; *er = *eb, er += str, eb += stb ) ;
            break;
          };
        
        if ( *ea == *eb ) 
          { 
            *er = *ea;
            er += str;
            ea += sta;
            eb += stb;
          };
        
        for (;eb != b && *eb < *ea; *er = *eb, er += str, eb += stb ) ;

        if (  eb == b ) 
          { 
            for ( ; ea != a; *er = *ea, er += str, ea += sta ) ;
            break;
          };
        
        if ( *eb == *ea ) 
          { 
            *er = *eb;
            er += str;
            eb += stb;
            ea += sta;
          };
      };
    return (er - r)/str;
  };
void mmx::vct::padd ( A *  a,
const B *  b,
unsigned  sz,
int  sta = 1,
int  stb = 1 
) [inline]

Definition at line 13 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a+sz*sta; *ea += *b , ea += sta, b += stb ) {}
  };
void mmx::vct::padd ( A *  a,
const B *  b,
const C *  c,
unsigned  sz,
int  sta = 1,
int  stb = 1,
int  stc = 1 
) [inline]

Definition at line 19 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a+sz*sta; *ea = *b+*c, ea += sta, b += stb, c += stc ) ;
  };
void mmx::vct::pdiv ( A *  a,
const B *  b,
const C *  c,
unsigned  sz,
int  sta = 1,
int  stb = 1,
int  stc = 1 
) [inline]

Definition at line 56 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a+sz*sta; *ea = *b/(*c), ea += sta, b += stb, c += stc ) ; 
  };
void mmx::vct::pdiv ( A *  a,
const B *  b,
unsigned  sz,
int  sta = 1,
int  stb = 1 
) [inline]

Definition at line 50 of file tensor_vctops.hpp.

Referenced by mmx::tensor::uscale().

  { 
    for ( A * ea = a; ea != a+sz*sta; *ea /= *b, ea += sta, b += stb ) ; 
  };
void mmx::vct::pmul ( A *  a,
const B *  b,
int  sz,
int  sta = 1,
int  stb = 1 
) [inline]

Definition at line 38 of file tensor_vctops.hpp.

Referenced by mmx::tensor::binoms(), and mmx::tensor::scale().

  { 
    for ( A * ea = a; ea != a+sz*sta; *ea *= *b, ea += sta, b += stb ) ; 
  };
void mmx::vct::pmul ( A *  a,
const B *  b,
const C *  c,
unsigned  sz,
int  sta = 1,
int  stb = 1,
int  stc = 1 
) [inline]

Definition at line 44 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a+sz*sta; *ea = *b**c, ea += sta, b += stb, c += stc ) ; 
  };
void mmx::vct::print ( const A *  p,
unsigned  n,
int  st = 1,
std::ostream &  o = std::cout 
) [inline]

Definition at line 206 of file tensor_vctops.hpp.

  {
    const A * i;
    o << "[ ";
    for ( i = p; i != p + (n-1)*st; i += st )
      o << *i << ", ";
    o << *i << " ]";
  };
void mmx::vct::psub ( A *  a,
const B *  b,
unsigned  sz,
int  sta = 1,
int  stb = 1 
) [inline]

Definition at line 26 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a+sz*sta; *ea -= *b, ea += sta, b += stb ) ; 
  };
void mmx::vct::psub ( A *  a,
const B *  b,
const C *  c,
unsigned  sz,
int  sta = 1,
int  stb = 1,
int  stc = 1 
) [inline]

Definition at line 32 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a+sz*sta; *ea = *b-*c, ea += sta, b += stb, c += stc ) ; 
  };
void mmx::vct::scadd ( A *  a,
const B &  b,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 62 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a + n*s; *a += b, ea += s ) ;
  };
void mmx::vct::scadd ( A *  a,
const B *  b,
const C &  c,
unsigned  n,
int  sa = 1,
int  sb = 1 
) [inline]

Definition at line 68 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != a + n*sa; *ea = *b + c, ea += sa, b += sb ) ;
  };
static void mmx::vct::scale ( C *  p,
const C &  s,
unsigned  n,
int  is = 1 
) [static]

Definition at line 413 of file tensor_vctops.hpp.

  {
    C pw = s;
    for (C * cp = p + is; cp != p + n * is; *cp *= pw, pw *= s, cp += is) ;
  };
void mmx::vct::scdiv ( A *  a,
const C &  c,
const B *  b,
unsigned  n,
int  sa = 1,
int  sb = 1 
) [inline]

Definition at line 134 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != a + n*sa; *ea = c/(*b), ea += sa, b += sb ) ;
  }
void mmx::vct::scdiv ( A *  a,
const B *  b,
const C &  c,
unsigned  n,
int  sa = 1,
int  sb = 1 
) [inline]

Definition at line 128 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != a + n*sa; *ea = *b/c, ea += sa, b += sb ) ;
  }
void mmx::vct::scdiv ( const B &  b,
A *  a,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 122 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != a+n*s; *ea = b/(*ea), ea += s ) ;
  };
void mmx::vct::scdiv ( A *  a,
const B &  b,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 116 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a+n*s; *ea /= b, ea += s ) ;
  }
void mmx::vct::scmul ( A *  a,
const B &  b,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 98 of file tensor_vctops.hpp.

Referenced by mmx::tensor::mdiff().

  { 
    for ( A * ea = a; ea != a+n*s; *ea *= b, ea += s ) ;
  }
void mmx::vct::scmul ( A *  a,
const A *  _a,
const B *  b,
const C &  c 
) [inline]

Definition at line 110 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != _a; *ea++ = *b++*c ) ;
  }
void mmx::vct::scmul ( A *  a,
const B *  b,
const C &  c,
unsigned  n,
int  sa = 1,
int  sb = 1 
) [inline]

Definition at line 104 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != a + n*sa; *ea = *b*c, ea += sa, b += sb ) ;
  }
void mmx::vct::scsub ( A *  a,
const B &  b,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 74 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a + n*s; *ea -= b, ea += s ) ;
  };
void mmx::vct::scsub ( A *  a,
const B *  b,
const C &  c,
unsigned  n,
int  sa = 1,
int  sb = 1 
) [inline]

Definition at line 86 of file tensor_vctops.hpp.

  { 
    for ( A * ea = a; ea != a+n*sa; *ea = *b-c, ea += sa, b += sb ) ;
  }
void mmx::vct::scsub ( A *  a,
const B &  b,
const C *  c,
unsigned  n,
int  sa = 1,
int  sb = 1 
) [inline]

Definition at line 92 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != a+n*sa; *ea = c-*b, ea += sa, b += sb ) ;
  };
void mmx::vct::scsub ( const B &  b,
A *  a,
unsigned  n,
int  s = 1 
) [inline]

Definition at line 80 of file tensor_vctops.hpp.

  {
    for ( A * ea = a; ea != a+n*s;  *ea = b-*ea, ea += s ) ;
  }
static void mmx::vct::shift ( C *  p,
const C &  c,
unsigned  n,
int  is = 1 
) [static]

Definition at line 405 of file tensor_vctops.hpp.

  {
    int j, k, s;
    for (s = n, j = 0; j <= s - 2; j++)
      for (k = s - 2; k >= j; p[k * is] += c * p[k * is + is], k--) ;
  };