eigenmath/tensor.cpp

913 lines
14 KiB
C++

#include "stdafx.h"
#include "defs.h"
static void promote_tensor(void);
static int compatible(U *, U *);
//-----------------------------------------------------------------------------
//
// Called from the "eval" module to evaluate tensor elements.
//
// p1 points to the tensor operand.
//
//-----------------------------------------------------------------------------
void
eval_tensor(void)
{
int i, ndim, nelem;
U **a, **b;
//---------------------------------------------------------------------
//
// create a new tensor for the result
//
//---------------------------------------------------------------------
nelem = p1->u.tensor->nelem;
ndim = p1->u.tensor->ndim;
p2 = alloc_tensor(nelem);
p2->u.tensor->ndim = ndim;
for (i = 0; i < ndim; i++)
p2->u.tensor->dim[i] = p1->u.tensor->dim[i];
//---------------------------------------------------------------------
//
// b = eval(a)
//
//---------------------------------------------------------------------
a = p1->u.tensor->elem;
b = p2->u.tensor->elem;
for (i = 0; i < nelem; i++) {
push(a[i]);
eval();
b[i] = pop();
}
//---------------------------------------------------------------------
//
// push the result
//
//---------------------------------------------------------------------
push(p2);
promote_tensor();
check_tensor();
}
//-----------------------------------------------------------------------------
//
// Add tensors
//
// Input: Operands on stack
//
// Output: Result on stack
//
//-----------------------------------------------------------------------------
void
tensor_plus_tensor(void)
{
int i, ndim, nelem;
U **a, **b, **c;
save();
p2 = pop();
p1 = pop();
// are the dimension lists equal?
ndim = p1->u.tensor->ndim;
if (ndim != p2->u.tensor->ndim) {
push(nil);
restore();
return;
}
for (i = 0; i < ndim; i++)
if (p1->u.tensor->dim[i] != p2->u.tensor->dim[i]) {
push(nil);
restore();
return;
}
// create a new tensor for the result
nelem = p1->u.tensor->nelem;
p3 = alloc_tensor(nelem);
p3->u.tensor->ndim = ndim;
for (i = 0; i < ndim; i++)
p3->u.tensor->dim[i] = p1->u.tensor->dim[i];
// c = a + b
a = p1->u.tensor->elem;
b = p2->u.tensor->elem;
c = p3->u.tensor->elem;
for (i = 0; i < nelem; i++) {
push(a[i]);
push(b[i]);
add();
c[i] = pop();
}
// push the result
push(p3);
check_tensor();
restore();
}
//-----------------------------------------------------------------------------
//
// careful not to reorder factors
//
//-----------------------------------------------------------------------------
void
tensor_times_scalar(void)
{
int i, ndim, nelem;
U **a, **b;
save();
p2 = pop();
p1 = pop();
ndim = p1->u.tensor->ndim;
nelem = p1->u.tensor->nelem;
p3 = alloc_tensor(nelem);
p3->u.tensor->ndim = ndim;
for (i = 0; i < ndim; i++)
p3->u.tensor->dim[i] = p1->u.tensor->dim[i];
a = p1->u.tensor->elem;
b = p3->u.tensor->elem;
for (i = 0; i < nelem; i++) {
push(a[i]);
push(p2);
multiply();
b[i] = pop();
}
push(p3);
restore();
}
void
scalar_times_tensor(void)
{
int i, ndim, nelem;
U **a, **b;
save();
p2 = pop();
p1 = pop();
ndim = p2->u.tensor->ndim;
nelem = p2->u.tensor->nelem;
p3 = alloc_tensor(nelem);
p3->u.tensor->ndim = ndim;
for (i = 0; i < ndim; i++)
p3->u.tensor->dim[i] = p2->u.tensor->dim[i];
a = p2->u.tensor->elem;
b = p3->u.tensor->elem;
for (i = 0; i < nelem; i++) {
push(p1);
push(a[i]);
multiply();
b[i] = pop();
}
push(p3);
restore();
}
int
is_square_matrix(U *p)
{
if (istensor(p) && p->u.tensor->ndim == 2 && p->u.tensor->dim[0] == p->u.tensor->dim[1])
return 1;
else
return 0;
}
//-----------------------------------------------------------------------------
//
// compute the adjunct of tos
//
//-----------------------------------------------------------------------------
void
adj(void)
{
int i, j, n;
save();
p1 = pop();
if (!is_square_matrix(p1)) {
push_symbol(ADJ);
push(p1);
list(2);
restore();
return;
}
n = p1->u.tensor->dim[0];
p2 = alloc_tensor(n * n);
p2->u.tensor->ndim = 2;
p2->u.tensor->dim[0] = n;
p2->u.tensor->dim[1] = n;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++) {
cofactor(p1, n, i, j);
p2->u.tensor->elem[n * j + i] = pop(); /* transpose */
}
push(p2);
restore();
}
void
cofactor(U *p, int n, int row, int col)
{
int i, j;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
if (i != row && j != col)
push(p->u.tensor->elem[n * i + j]);
determinant(n - 1);
if ((row + col) % 2)
negate();
}
//-----------------------------------------------------------------------------
//
// transpose tos-2 along indices tos-1 and tos
//
//-----------------------------------------------------------------------------
void
transpose(void)
{
int i, j, k, l, m, ndim, nelem, t;
int ai[MAXDIM], an[MAXDIM];
U **a, **b;
save();
p3 = pop();
p2 = pop();
p1 = pop();
if (!istensor(p1))
goto dont_evaluate;
ndim = p1->u.tensor->ndim;
nelem = p1->u.tensor->nelem;
push(p2);
l = pop_integer();
push(p3);
m = pop_integer();
if (l < 1 || l > ndim || m < 1 || m > ndim)
goto dont_evaluate;
l--;
m--;
p2 = alloc_tensor(nelem);
p2->u.tensor->ndim = ndim;
for (i = 0; i < ndim; i++)
p2->u.tensor->dim[i] = p1->u.tensor->dim[i];
p2->u.tensor->dim[l] = p1->u.tensor->dim[m];
p2->u.tensor->dim[m] = p1->u.tensor->dim[l];
a = p1->u.tensor->elem;
b = p2->u.tensor->elem;
for (i = 0; i < ndim; i++) {
ai[i] = 0;
an[i] = p1->u.tensor->dim[i];
}
//---------------------------------------------------------------------
//
// copy elements from a to b
//
//---------------------------------------------------------------------
for (i = 0; i < nelem; i++) {
t = ai[l]; ai[l] = ai[m]; ai[m] = t;
t = an[l]; an[l] = an[m]; an[m] = t;
k = 0;
for (j = 0; j < ndim; j++)
k = (k * an[j]) + ai[j];
t = ai[l]; ai[l] = ai[m]; ai[m] = t;
t = an[l]; an[l] = an[m]; an[m] = t;
b[k] = a[i];
for (j = ndim - 1; j >= 0; j--) {
if (++ai[j] < an[j])
break;
ai[j] = 0;
}
}
push(p2);
restore();
return;
dont_evaluate:
push_symbol(TRANSPOSE);
push(p1);
push(p2);
push(p3);
list(4);
restore();
}
#if 0
//-----------------------------------------------------------------------------
//
// tos-3 tensor
//
// tos-2 index
//
// tos-1 index
//
//-----------------------------------------------------------------------------
void
contract(void)
{
int h, i, j, k, l, m, n, ndim, nelem;
int ai[MAXDIM], an[MAXDIM];
U **a, **b;
save();
p3 = pop();
p2 = pop();
p1 = pop();
if (!istensor(p1))
goto out;
ndim = p1->u.tensor->ndim;
push(p2);
l = pop_integer();
push(p3);
m = pop_integer();
if (l < 1 || l > ndim || m < 1 || m > ndim)
goto out;
if (l == m)
goto out;
l--;
m--;
n = p1->u.tensor->dim[l];
if (n != p1->u.tensor->dim[m])
goto out;
//---------------------------------------------------------------------
//
// nelem is the number of elements in "b"
//
//---------------------------------------------------------------------
nelem = 1;
for (i = 0; i < ndim; i++)
if (i != l && i != m)
nelem *= p1->u.tensor->dim[i];
p2 = alloc_tensor(nelem);
p2->u.tensor->ndim = ndim - 2;
j = 0;
for (i = 0; i < ndim; i++)
if (i != l && i != m)
p2->u.tensor->dim[j++] = p1->u.tensor->dim[i];
a = p1->u.tensor->elem;
b = p2->u.tensor->elem;
for (i = 0; i < ndim; i++) {
ai[i] = 0;
an[i] = p1->u.tensor->dim[i];
}
for (i = 0; i < nelem; i++) {
push(_zero);
for (j = 0; j < n; j++) {
ai[l] = j;
ai[m] = j;
h = 0;
for (k = 0; k < ndim; k++)
h = (h * an[k]) + ai[k];
push(a[h]);
add();
}
b[i] = pop();
for (j = ndim - 1; j >= 0; j--) {
if (j == l || j == m)
continue;
if (++ai[j] < an[j])
break;
ai[j] = 0;
}
}
if (nelem == 1) {
push(b[0]);
restore();
return;
}
push(p2);
check_tensor();
restore();
return;
out: push(_contract);
push(p1);
push(p2);
push(p3);
list(4);
restore();
}
#endif
//-----------------------------------------------------------------------------
//
// gradient of tensor
//
//-----------------------------------------------------------------------------
void
d_tensor_tensor(void)
{
int i, j, ndim, nelem;
U **a, **b, **c;
ndim = p1->u.tensor->ndim;
nelem = p1->u.tensor->nelem;
if (ndim + 1 >= MAXDIM)
goto dont_evaluate;
p3 = alloc_tensor(nelem * p2->u.tensor->nelem);
p3->u.tensor->ndim = ndim + 1;
for (i = 0; i < ndim; i++)
p3->u.tensor->dim[i] = p1->u.tensor->dim[i];
p3->u.tensor->dim[ndim] = p2->u.tensor->dim[0];
a = p1->u.tensor->elem;
b = p2->u.tensor->elem;
c = p3->u.tensor->elem;
for (i = 0; i < nelem; i++) {
for (j = 0; j < p2->u.tensor->nelem; j++) {
push(a[i]);
push(b[j]);
derivative();
c[i * p2->u.tensor->nelem + j] = pop();
}
}
push(p3);
check_tensor();
return;
dont_evaluate:
push_symbol(DERIVATIVE);
push(p1);
push(p2);
list(3);
}
//-----------------------------------------------------------------------------
//
// gradient of scalar
//
//-----------------------------------------------------------------------------
void
d_scalar_tensor(void)
{
int i;
U **a, **b;
p3 = alloc_tensor(p2->u.tensor->nelem);
p3->u.tensor->ndim = 1;
p3->u.tensor->dim[0] = p2->u.tensor->dim[0];
a = p2->u.tensor->elem;
b = p3->u.tensor->elem;
for (i = 0; i < p2->u.tensor->nelem; i++) {
push(p1);
push(a[i]);
derivative();
b[i] = pop();
}
push(p3);
check_tensor();
}
//-----------------------------------------------------------------------------
//
// Derivative of tensor
//
//-----------------------------------------------------------------------------
void
d_tensor_scalar(void)
{
int i;
U **a, **b;
p3 = alloc_tensor(p1->u.tensor->nelem);
p3->u.tensor->ndim = p1->u.tensor->ndim;
for (i = 0; i < p1->u.tensor->ndim; i++)
p3->u.tensor->dim[i] = p1->u.tensor->dim[i];
a = p1->u.tensor->elem;
b = p3->u.tensor->elem;
for (i = 0; i < p1->u.tensor->nelem; i++) {
push(a[i]);
push(p2);
derivative();
b[i] = pop();
}
push(p3);
check_tensor();
}
int
compare_tensors(U *p1, U *p2)
{
int i;
if (p1->u.tensor->ndim < p2->u.tensor->ndim)
return -1;
if (p1->u.tensor->ndim > p2->u.tensor->ndim)
return 1;
for (i = 0; i < p1->u.tensor->ndim; i++) {
if (p1->u.tensor->dim[i] < p2->u.tensor->dim[i])
return -1;
if (p1->u.tensor->dim[i] > p2->u.tensor->dim[i])
return 1;
}
for (i = 0; i < p1->u.tensor->nelem; i++) {
if (equal(p1->u.tensor->elem[i], p2->u.tensor->elem[i]))
continue;
if (lessp(p1->u.tensor->elem[i], p2->u.tensor->elem[i]))
return -1;
else
return 1;
}
return 0;
}
#if 0
// complex conjugate of tensor
void
conj_tensor(void)
{
int i;
U **a, **b;
p3 = alloc_tensor(p1->u.tensor->nelem);
p3->u.tensor->ndim = p1->u.tensor->ndim;
for (i = 0; i < p1->u.tensor->ndim; i++)
p3->u.tensor->dim[i] = p1->u.tensor->dim[i];
a = p1->u.tensor->elem;
b = p3->u.tensor->elem;
for (i = 0; i < p1->u.tensor->nelem; i++) {
push(a[i]);
sconj();
b[i] = pop();
}
push(p3);
}
#endif
//-----------------------------------------------------------------------------
//
// Replace zero tensor with scalar zero
//
// Input: Tensor on stack
//
// Output: Result on stack
//
//-----------------------------------------------------------------------------
void
check_tensor(void)
{
int i, n;
U **a;
if (!istensor(stack[tos - 1]))
return;
n = stack[tos - 1]->u.tensor->nelem;
a = stack[tos - 1]->u.tensor->elem;
for (i = 0; i < n; i++)
if (!iszero(a[i]))
return;
stack[tos - 1] = _zero;
}
//-----------------------------------------------------------------------------
//
// Raise a tensor to a power
//
// Input: p1 tensor
//
// p2 exponent
//
// Output: Result on stack
//
//-----------------------------------------------------------------------------
void
power_tensor(void)
{
int i, k, n;
// first and last dims must be equal
k = p1->u.tensor->ndim - 1;
if (p1->u.tensor->dim[0] != p1->u.tensor->dim[k]) {
push_symbol(POWER);
push(p1);
push(p2);
list(3);
return;
}
push(p2);
n = pop_integer();
if (n == (int) 0x80000000) {
push_symbol(POWER);
push(p1);
push(p2);
list(3);
return;
}
if (n == 0) {
if (p1->u.tensor->ndim != 2)
stop("power(tensor,0) with tensor rank not equal to 2");
n = p1->u.tensor->dim[0];
p1 = alloc_tensor(n * n);
p1->u.tensor->ndim = 2;
p1->u.tensor->dim[0] = n;
p1->u.tensor->dim[1] = n;
for (i = 0; i < n; i++)
p1->u.tensor->elem[n * i + i] = _one;
push(p1);
return;
}
if (n < 0) {
n = -n;
push(p1);
inv();
p1 = pop();
}
push(p1);
for (i = 1; i < n; i++) {
push(p1);
inner();
if (iszero(stack[tos - 1]))
break;
}
}
void
copy_tensor(void)
{
int i;
save();
p1 = pop();
p2 = alloc_tensor(p1->u.tensor->nelem);
p2->u.tensor->ndim = p1->u.tensor->ndim;
for (i = 0; i < p1->u.tensor->ndim; i++)
p2->u.tensor->dim[i] = p1->u.tensor->dim[i];
for (i = 0; i < p1->u.tensor->nelem; i++)
p2->u.tensor->elem[i] = p1->u.tensor->elem[i];
push(p2);
restore();
}
// Tensors with elements that are also tensors get promoted to a higher rank.
static void
promote_tensor(void)
{
int i, j, k, nelem, ndim;
save();
p1 = pop();
if (!istensor(p1)) {
push(p1);
restore();
return;
}
p2 = p1->u.tensor->elem[0];
for (i = 1; i < p1->u.tensor->nelem; i++)
if (!compatible(p2, p1->u.tensor->elem[i]))
stop("Cannot promote tensor due to inconsistent tensor components.");
if (!istensor(p2)) {
push(p1);
restore();
return;
}
ndim = p1->u.tensor->ndim + p2->u.tensor->ndim;
if (ndim > MAXDIM)
stop("tensor rank > 24");
nelem = p1->u.tensor->nelem * p2->u.tensor->nelem;
p3 = alloc_tensor(nelem);
p3->u.tensor->ndim = ndim;
for (i = 0; i < p1->u.tensor->ndim; i++)
p3->u.tensor->dim[i] = p1->u.tensor->dim[i];
for (j = 0; j < p2->u.tensor->ndim; j++)
p3->u.tensor->dim[i + j] = p2->u.tensor->dim[j];
k = 0;
for (i = 0; i < p1->u.tensor->nelem; i++) {
p2 = p1->u.tensor->elem[i];
for (j = 0; j < p2->u.tensor->nelem; j++)
p3->u.tensor->elem[k++] = p2->u.tensor->elem[j];
}
push(p3);
restore();
}
static int
compatible(U *p, U *q)
{
int i;
if (!istensor(p) && !istensor(q))
return 1;
if (!istensor(p) || !istensor(q))
return 0;
if (p->u.tensor->ndim != q->u.tensor->ndim)
return 0;
for (i = 0; i < p->u.tensor->ndim; i++)
if (p->u.tensor->dim[i] != q->u.tensor->dim[i])
return 0;
return 1;
}
static char *s[] = {
"#test_tensor",
"a=(1,2,3)",
"",
"b=(4,5,6)",
"",
"c=(7,8,9)",
"",
"rank((a,b,c))",
"2",
"(a,b,c)",
"((1,2,3),(4,5,6),(7,8,9))",
"a=quote(a)",
"",
"b=quote(b)",
"",
"c=quote(c)",
"",
};
void
test_tensor(void)
{
test(__FILE__, s, sizeof s / sizeof (char *));
}