algebrite/sources/inner.coffee

Computer Algebra System in Coffeescript

# Do the inner product of tensors.



Eval_inner = ->
	p1 = cdr(p1)
	push(car(p1))
	Eval()
	p1 = cdr(p1)
	while (iscons(p1))
		push(car(p1))
		Eval()
		inner()
		p1 = cdr(p1)

inner = ->
	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
inner_f = ->

	i = 0
	n = p1.tensor.dim[p1.tensor.ndim - 1]

	if (n != p2.tensor.dim[0])
		debugger
		stop("inner: tensor dimension check")

	ndim = p1.tensor.ndim + p2.tensor.ndim - 2

	if (ndim > MAXDIM)
		stop("inner: rank of result exceeds maximum")

	a = p1.tensor.elem
	b = p2.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 in [0...(p1.tensor.ndim - 1)]
		ak *= p1.tensor.dim[i]

	bk = 1
	for i in [1...p2.tensor.ndim]
		bk *= p2.tensor.dim[i]

	p3 = alloc_tensor(ak * bk)

	c = p3.tensor.elem

	# new method copied from ginac http://www.ginac.de/
	for i in [0...ak]
		for j in [0...n]
			if (iszero(a[i * n + j]))
				continue
			for k in [0...bk]
				push(a[i * n + j])
				push(b[j * bk + k])
				multiply()
				push(c[i * bk + k])
				add()
				c[i * bk + k] = pop()

	#---------------------------------------------------------------------
	#
	#	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.tensor.elem[0])
	else
		p3.tensor.ndim = ndim
		j = 0
		for i in [0...(p1.tensor.ndim - 1)]
			p3.tensor.dim[i] = p1.tensor.dim[i]
		j = p1.tensor.ndim - 1
		for i in [0...(p2.tensor.ndim - 1)]
			p3.tensor.dim[j + i] = p2.tensor.dim[i + 1]
		push(p3)