algebrite

### contract ===================================================================== Tags ---- scripting, JS, internal, treenode, general concept Parameters ---------- a,i,j General description ------------------- Contract across tensor indices i.e. returns "a" summed over indices i and j. If i and j are omitted then 1 and 2 are used. contract(m) is equivalent to the trace of matrix m. ### Eval_contract = -> push(cadr(p1)) Eval() if (cddr(p1) == symbol(NIL)) push_integer(1) push_integer(2) else push(caddr(p1)) Eval() push(cadddr(p1)) Eval() contract() contract = -> save() yycontract() restore() yycontract = -> h = 0 i = 0 j = 0 k = 0 l = 0 m = 0 n = 0 ndim = 0 nelem = 0 ai = [] an = [] p3 = pop() p2 = pop() p1 = pop() if (!istensor(p1)) if (!isZeroAtomOrTensor(p1)) stop("contract: tensor expected, 1st arg is not a tensor") push(zero) return push(p2) l = pop_integer() push(p3) m = pop_integer() ndim = p1.tensor.ndim if (l < 1 || l > ndim || m < 1 || m > ndim || l == m \ || p1.tensor.dim[l - 1] != p1.tensor.dim[m - 1]) stop("contract: index out of range") l-- m-- n = p1.tensor.dim[l] # nelem is the number of elements in "b" nelem = 1 for i in [0...ndim] if (i != l && i != m) nelem *= p1.tensor.dim[i] #console.log "nelem:" + nelem p2 = alloc_tensor(nelem) #console.log "p2:" + p2 p2.tensor.ndim = ndim - 2 j = 0 for i in [0...ndim] if (i != l && i != m) p2.tensor.dim[j++] = p1.tensor.dim[i] a = p1.tensor.elem b = p2.tensor.elem #console.log "a: " + a #console.log "b: " + b for i in [0...ndim] ai[i] = 0 an[i] = p1.tensor.dim[i] for i in [0...nelem] push(zero) for j in [0...n] ai[l] = j ai[m] = j h = 0 for k in [0...ndim] h = (h * an[k]) + ai[k] push(a[h]) #console.log "a[h]: " + a[h] add() #console.log "tos: " + stack[tos-1] b[i] = pop() #console.log "b[i]: " + b[i] for j in [(ndim - 1)..0] if (j == l || j == m) continue if (++ai[j] < an[j]) break ai[j] = 0 if (nelem == 1) push(b[0]) else push(p2) #console.log "returning: " + stack[tos-1]