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354 | #include "moab/FindPtFuncs.h"
/*--------------------------------------------------------------------------
Matrix-Matrix Multiplication
mxm_ab (A,na,B,nb,C,nc) :
gives C = A B where A is na x nb, B is nb x nc, C is na x nc
a := r | c to indicate A is in row- or column- major format
b := r | c to indicate B is in row- or column- major format
C is always column-major
--------------------------------------------------------------------------*/
static void mxm_cc( const realType* A, unsigned na, const realType* B, unsigned nb, realType* C, unsigned nc )
{
unsigned i, j, k;
realType* Ccol = C;
const realType* Bcol = B;
for( j = 0; j < nc; ++j, Ccol += na, Bcol += nb )
{
const realType* Acol = A;
for( i = 0; i < na; ++i )
Ccol[i] = 0;
for( k = 0; k < nb; ++k, Acol += na )
for( i = 0; i < na; ++i )
Ccol[i] += Acol[i] * Bcol[k];
}
}
static void mxm_rc( const realType* A, unsigned na, const realType* B, unsigned nb, realType* C, unsigned nc )
{
unsigned i, j, k;
realType* Ccol = C;
const realType* Bcol = B;
for( j = 0; j < nc; ++j, Ccol += na, Bcol += nb )
{
const realType* Arow = A;
for( i = 0; i < na; ++i, Arow += nb )
{
Ccol[i] = 0;
for( k = 0; k < nb; ++k )
Ccol[i] += Arow[k] * Bcol[k];
}
}
}
static void mxm_cr( const realType* A, unsigned na, const realType* B, unsigned nb, realType* C, unsigned nc )
{
unsigned i, j, k;
const realType *Acol = A, *Brow = B;
for( i = 0; i < na * nc; ++i )
C[i] = 0;
for( k = 0; k < nb; ++k, Acol += na, Brow += nc )
{
realType* Ccol = C;
for( j = 0; j < nc; ++j, Ccol += na )
for( i = 0; i < na; ++i )
Ccol[i] += Acol[i] * Brow[j];
}
}
/*
static void mxm_rr(const realType *A, unsigned na,
const realType *B, unsigned nb,
realType *C, unsigned nc)
{
unsigned i,j,k;
realType *Ccol = C;
const realType *Bcol = B;
for(j=0;j<nc;++j,Ccol+=na,++Bcol) {
const realType *Arow = A;
for(i=0;i<na;++i,Arow+=nb) {
const realType *Bkj = Bcol;
Ccol[i]=0.0;
for(k=0;k<nb;++k,Bkj+=nc)
Ccol[i] += Arow[k] * *Bkj;
}
}
}
*/
/*--------------------------------------------------------------------------
Matrix-Vector Multiplication
mxv_f (y,ny,A,x,nx) :
gives y = A x where A is ny x nx
f := r | c to indicate A is in row- or column- major format
--------------------------------------------------------------------------*/
static void mxv_c( realType* y, unsigned ny, const realType* A, const realType* x, unsigned nx )
{
realType *yp = y, *y_end = y + ny;
const realType* x_end = x + nx;
realType xk = *x;
do
{
*yp++ = *A++ * xk;
} while( yp != y_end );
for( ++x; x != x_end; ++x )
{
xk = *x;
yp = y;
do
{
*yp++ += *A++ * xk;
} while( yp != y_end );
}
}
static void mxv_r( realType* y, unsigned ny, const realType* A, const realType* x, unsigned nx )
{
realType* y_end = y + ny;
const realType* x_end = x + nx;
do
{
const realType* xp = x;
realType sum = *A++ * *xp++;
while( xp != x_end )
{
sum += *A++ * *xp++;
}
*y++ = sum;
} while( y != y_end );
}
/*--------------------------------------------------------------------------
Vector-Vector Multiplication
inner (u,v,n) : inner product
--------------------------------------------------------------------------*/
/* precondition: n>=1 */
static realType inner( const realType* u, const realType* v, unsigned n )
{
const realType* u_end = u + n;
realType sum = *u++ * *v++;
while( u != u_end )
{
sum += *u++ * *v++;
}
return sum;
}
/*--------------------------------------------------------------------------
1-,2-,3-d Tensor Application
the 3d case:
tensor_f3(R,mr,nr, S,ms,ns, T,mt,nt, u,v, work1,work2)
gives v = [ R (x) S (x) T ] u
where R is mr x nr, S is ms x ns, T is mt x nt,
each in row- or column-major format according to f := r | c
u is nr x ns x nt in column-major format (inner index is r)
v is mr x ms x mt in column-major format (inner index is r)
--------------------------------------------------------------------------*/
void tensor_c1( const realType* R, unsigned mr, unsigned nr, const realType* u, realType* v )<--- The function 'tensor_c1' is never used.
{
mxv_c( v, mr, R, u, nr );
}
void tensor_r1( const realType* R, unsigned mr, unsigned nr, const realType* u, realType* v )<--- The function 'tensor_r1' is never used.
{
mxv_r( v, mr, R, u, nr );
}
/* W holds mr*ns reals */
void tensor_c2( const realType* R,<--- The function 'tensor_c2' is never used.
unsigned mr,
unsigned nr,
const realType* S,
unsigned ms,
unsigned ns,
const realType* u,
realType* v,
realType* W )
{
mxm_cc( R, mr, u, nr, W, ns );
mxm_cr( W, mr, S, ns, v, ms );
}
/* W holds mr*ns reals */
void tensor_r2( const realType* R,<--- The function 'tensor_r2' is never used.
unsigned mr,
unsigned nr,
const realType* S,
unsigned ms,
unsigned ns,
const realType* u,
realType* v,
realType* W )
{
mxm_rc( R, mr, u, nr, W, ns );
mxm_cc( W, mr, S, ns, v, ms );
}
/* W holds mr*ns*nt reals,
Z holds mr*ms*nt reals */
void tensor_c3( const realType* R,<--- The function 'tensor_c3' is never used.
unsigned mr,
unsigned nr,
const realType* S,
unsigned ms,
unsigned ns,
const realType* T,
unsigned mt,
unsigned nt,
const realType* u,
realType* v,
realType* W,
realType* Z )
{
unsigned n, mrns = mr * ns, mrms = mr * ms;
realType* Zp = Z;
mxm_cc( R, mr, u, nr, W, ns * nt );
for( n = 0; n < nt; ++n, W += mrns, Zp += mrms )
mxm_cr( W, mr, S, ns, Zp, ms );
mxm_cr( Z, mrms, T, nt, v, mt );
}
/* W holds mr*ns*nt reals,
Z holds mr*ms*nt reals */
void tensor_r3( const realType* R,<--- The function 'tensor_r3' is never used.
unsigned mr,
unsigned nr,
const realType* S,
unsigned ms,
unsigned ns,
const realType* T,
unsigned mt,
unsigned nt,
const realType* u,
realType* v,
realType* W,
realType* Z )
{
unsigned n, mrns = mr * ns, mrms = mr * ms;
realType* Zp = Z;
mxm_rc( R, mr, u, nr, W, ns * nt );
for( n = 0; n < nt; ++n, W += mrns, Zp += mrms )
mxm_cc( W, mr, S, ns, Zp, ms );
mxm_cc( Z, mrms, T, nt, v, mt );
}
/*--------------------------------------------------------------------------
1-,2-,3-d Tensor Application of Row Vectors (for Interpolation)
the 3d case:
v = tensor_i3(Jr,nr, Js,ns, Jt,nt, u, work)
same effect as tensor_r3(Jr,1,nr, Js,1,ns, Jt,1,nt, u,&v, work1,work2):
gives v = [ Jr (x) Js (x) Jt ] u
where Jr, Js, Jt are row vectors (interpolation weights)
u is nr x ns x nt in column-major format (inner index is r)
v is a scalar
--------------------------------------------------------------------------*/
realType tensor_i1( const realType* Jr, unsigned nr, const realType* u )
{
return inner( Jr, u, nr );
}
/* work holds ns reals */
realType tensor_i2( const realType* Jr,
unsigned nr,
const realType* Js,
unsigned ns,
const realType* u,
realType* work )
{
mxv_r( work, ns, u, Jr, nr );
return inner( Js, work, ns );
}
/* work holds ns*nt + nt reals */
realType tensor_i3( const realType* Jr,
unsigned nr,
const realType* Js,
unsigned ns,
const realType* Jt,
unsigned nt,
const realType* u,
realType* work )
{
realType* work2 = work + nt;
mxv_r( work2, ns * nt, u, Jr, nr );
mxv_r( work, nt, work2, Js, ns );
return inner( Jt, work, nt );
}
/*--------------------------------------------------------------------------
1-,2-,3-d Tensor Application of Row Vectors
for simultaneous Interpolation and Gradient computation
the 3d case:
v = tensor_ig3(Jr,Dr,nr, Js,Ds,ns, Jt,Dt,nt, u,g, work)
gives v = [ Jr (x) Js (x) Jt ] u
g_0 = [ Dr (x) Js (x) Jt ] u
g_1 = [ Jr (x) Ds (x) Jt ] u
g_2 = [ Jr (x) Js (x) Dt ] u
where Jr,Dr,Js,Ds,Jt,Dt are row vectors
(interpolation & derivative weights)
u is nr x ns x nt in column-major format (inner index is r)
v is a scalar, g is an array of 3 reals
--------------------------------------------------------------------------*/
realType tensor_ig1( const realType* Jr, const realType* Dr, unsigned nr, const realType* u, realType* g )
{
*g = inner( Dr, u, nr );
return inner( Jr, u, nr );
}
/* work holds 2*ns reals */
realType tensor_ig2( const realType* Jr,
const realType* Dr,
unsigned nr,
const realType* Js,
const realType* Ds,
unsigned ns,
const realType* u,
realType* g,
realType* work )
{
realType *a = work, *ar = a + ns;
mxv_r( a, ns, u, Jr, nr );
mxv_r( ar, ns, u, Dr, nr );
g[0] = inner( Js, ar, ns );
g[1] = inner( Ds, a, ns );
return inner( Js, a, ns );
}
/* work holds 2*ns*nt + 3*ns reals */
realType tensor_ig3( const realType* Jr,
const realType* Dr,
unsigned nr,
const realType* Js,
const realType* Ds,
unsigned ns,
const realType* Jt,
const realType* Dt,
unsigned nt,
const realType* u,
realType* g,
realType* work )
{
unsigned nsnt = ns * nt;
realType *a = work, *ar = a + nsnt, *b = ar + nsnt, *br = b + ns, *bs = br + ns;
mxv_r( a, nsnt, u, Jr, nr );
mxv_r( ar, nsnt, u, Dr, nr );
mxv_r( b, nt, a, Js, ns );
mxv_r( br, nt, ar, Js, ns );
mxv_r( bs, nt, a, Ds, ns );
g[0] = inner( Jt, br, nt );
g[1] = inner( Jt, bs, nt );
g[2] = inner( Dt, b, nt );
return inner( Jt, b, nt );
}
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