algebrite

test_tensor = -> run_test [ "[[a]]", "[[a]]", # --------------------------------- # basic parsing, promotion and printout # --------------------------------- "[[1,0],[0,0]]", "[[1,0],[0,0]]", # --------------------------------- # basic rank and shape checks # --------------------------------- # in general, the trick to count # rank (i.e. dimensions) is to count the # number of nested brackets # and the trick to determine the shape # is to count the commas proceeding # from the outermost to the # inner-most brackets. "rank(a)", "0", "rank([a,b,c])", "1", "shape([a,b,c])", "[3]", "rank([[a,b,c]])", "2", # traditional matrix 1x3 # i.e. one row three columns # i.e. row vector "shape([[a,b,c]])", "[1,3]", "rank([[a],[b],[c]])", "2", # traditional matrix 3x1 # i.e. one columns three rows # i.e. column vector "shape([[a],[b],[c]])", "[3,1]", "rank([[[a,b,c]]])", "3", "shape([[[a,b,c]]])", "[1,1,3]", "rank([[[a],[b],[c]]])", "3", "shape([[[a],[b],[c]]])", "[1,3,1]", "rank([[[a]],[[b]],[[c]]])", "3", "shape([[[a]],[[b]],[[c]]])", "[3,1,1]", # --------------------------------- # check tensor promotion # --------------------------------- "a=[1,2,3]", "", "rank(a)", "1", "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]]", # ------------------------------------------------------- # parsing, assigments and invokations calisthenics # mixes [] used for a) tensor building and b) tensor indexing # and mixes () used for a) function declarations # b) function invokation and c) precedence # Nests functions and matrices inside one another. # ------------------------------------------------------- # -------------------- "f(x) = x + 1", "", "a=[1,f,3]", "", "a[2]", "function (x) -> x+1", "a[f(1)]", "function (x) -> x+1", "a[a[f(1)](1)]", "function (x) -> x+1", "a[2](9)", "10", "a[f(1)](f(8))", "10", "a[a[f(1)](1)](a[f(1)](8))", "10", # -------------------- "g(x) = x + 1", "", "f() = [1,g,3]", "", "a=[1,f,3]", "", "a[2]()[2](7)", "8", # -------------------- "g(x) = x + 1", "", "f() = [[1,g,3],[0,0,0],[0,0,0]]", "", "a=[1,f,3]", "", "a[2]()[1][2](8)", "9", "(a[2]())[1][2](8)", "9", "((a[2]())[1])[2](8)", "9", "(((a[2]())[1])[2])(8)", "9", "(((a[a[1]+a[1]]())[a[1]])[a[1]+a[1]])(8)", "9", "f()[1][2](8)", "9", "f()[a[1]][a[1]+a[1]](8)", "9", # -------------------- "g(x) = transpose(x)", "", "f() = [[1,g,3],[0,0,0],[0,0,0]]", "", "a=[1,f,3]", "", "a[2]()[1][2]([[1,2,3,4]])", "[[1],[2],[3],[4]]", # -------------------- "unit(x)", "unit(x)", "unit(3)", "[[1,0,0],[0,1,0],[0,0,1]]", "unit(1)", "[[1]]", # cleanup "a=quote(a)", "", "b=quote(b)", "", "c=quote(c)", "", "f=quote(f)", "", "g=quote(g)", "", ]