eigenmath/inner.cpp

195 lines
3.6 KiB
C++

// Do the inner product of tensors.
#include "stdafx.h"
#include "defs.h"
static void inner_f(void);
void
eval_inner(void)
{
p1 = cdr(p1);
push(car(p1));
eval();
p1 = cdr(p1);
while (iscons(p1)) {
push(car(p1));
eval();
inner();
p1 = cdr(p1);
}
}
void
inner(void)
{
save();
p2 = pop();
p1 = pop();
if (istensor(p1) && istensor(p2))
inner_f();
else {
push(p1);
push(p2);
if (istensor(p1))
tensor_times_scalar();
else if (istensor(p2))
scalar_times_tensor();
else
multiply();
}
restore();
}
// inner product of tensors p1 and p2
static void
inner_f(void)
{
int ak, bk, i, j, k, n, ndim;
U **a, **b, **c;
n = p1->u.tensor->dim[p1->u.tensor->ndim - 1];
if (n != p2->u.tensor->dim[0])
stop("inner: tensor dimension check");
ndim = p1->u.tensor->ndim + p2->u.tensor->ndim - 2;
if (ndim > MAXDIM)
stop("inner: rank of result exceeds maximum");
a = p1->u.tensor->elem;
b = p2->u.tensor->elem;
//---------------------------------------------------------------------
//
// ak is the number of rows in tensor A
//
// bk is the number of columns in tensor B
//
// Example:
//
// A[3][3][4] B[4][4][3]
//
// 3 3 ak = 3 * 3 = 9
//
// 4 3 bk = 4 * 3 = 12
//
//---------------------------------------------------------------------
ak = 1;
for (i = 0; i < p1->u.tensor->ndim - 1; i++)
ak *= p1->u.tensor->dim[i];
bk = 1;
for (i = 1; i < p2->u.tensor->ndim; i++)
bk *= p2->u.tensor->dim[i];
p3 = alloc_tensor(ak * bk);
c = p3->u.tensor->elem;
// new method copied from ginac
#if 1
for (i = 0; i < ak; i++) {
for (j = 0; j < n; j++) {
if (iszero(a[i * n + j]))
continue;
for (k = 0; k < bk; k++) {
push(a[i * n + j]);
push(b[j * bk + k]);
multiply();
push(c[i * bk + k]);
add();
c[i * bk + k] = pop();
}
}
}
#else
for (i = 0; i < ak; i++) {
for (j = 0; j < bk; j++) {
push(_zero);
for (k = 0; k < n; k++) {
push(a[i * n + k]);
push(b[k * bk + j]);
multiply();
add();
}
c[i * bk + j] = pop();
}
}
#endif
//---------------------------------------------------------------------
//
// Note on understanding "k * bk + j"
//
// k * bk because each element of a column is bk locations apart
//
// + j because the beginnings of all columns are in the first bk
// locations
//
// Example: n = 2, bk = 6
//
// b111 <- 1st element of 1st column
// b112 <- 1st element of 2nd column
// b113 <- 1st element of 3rd column
// b121 <- 1st element of 4th column
// b122 <- 1st element of 5th column
// b123 <- 1st element of 6th column
//
// b211 <- 2nd element of 1st column
// b212 <- 2nd element of 2nd column
// b213 <- 2nd element of 3rd column
// b221 <- 2nd element of 4th column
// b222 <- 2nd element of 5th column
// b223 <- 2nd element of 6th column
//
//---------------------------------------------------------------------
if (ndim == 0)
push(p3->u.tensor->elem[0]);
else {
p3->u.tensor->ndim = ndim;
for (i = 0; i < p1->u.tensor->ndim - 1; i++)
p3->u.tensor->dim[i] = p1->u.tensor->dim[i];
j = i;
for (i = 0; i < p2->u.tensor->ndim - 1; i++)
p3->u.tensor->dim[j + i] = p2->u.tensor->dim[i + 1];
push(p3);
}
}
static char *s[] = {
"inner(a,b)",
"a*b",
"inner(a,(b1,b2))",
"(a*b1,a*b2)",
"inner((a1,a2),b)",
"(a1*b,a2*b)",
"inner(((a11,a12),(a21,a22)),(x1,x2))",
"(a11*x1+a12*x2,a21*x1+a22*x2)",
"inner((1,2),(3,4))",
"11",
"inner(inner((1,2),((3,4),(5,6))),(7,8))",
"219",
"inner((1,2),inner(((3,4),(5,6)),(7,8)))",
"219",
"inner((1,2),((3,4),(5,6)),(7,8))",
"219",
};
void
test_inner(void)
{
test(__FILE__, s, sizeof s / sizeof (char *));
}