+++ /dev/null
-let
-
-type vec = array of int
-type vector = {dim : int, d : vec}
-
-type mat = array of vector
-type matrix = {x : int, y : int, d : mat}
-
-function vectorCreate(n : int) : vector =
- vector{dim = n, d = vec[n] of 0}
-
-function vectorLiftedAdd(X : vector, Y : vector) : vector =
- let var tmp : vector := vectorCreate(X.dim)
- in for i := 0 to X.dim do
- tmp.d[i] := X.d[i] + Y.d[i];
- tmp
- end
-
-function vectorLiftedMul(X : vector, Y : vector) : vector =
- let var tmp : vector := vectorCreate(X.dim)
- in for i := 0 to X.dim do
- tmp.d[i] := X.d[i] * Y.d[i];
- tmp
- end
-
-function vectorInProduct(X : vector, Y : vector) : int =
- let var tmp : int := 0
- in for i := 0 to X.dim do
- tmp := tmp + X.d[i] * Y.d[i];
- tmp
- end
-
-
-
-function matrixCreate(n : int, m : int) : matrix =
- let var tmp := matrix{x = n, y = m, d = mat[n] of nil}
- in for i := 0 to n do
- tmp.d[i] := vectorCreate(m);
- tmp
- end
-
-function matrixRow(A : matrix, i : int) : vector =
- A.d[i]
-
-function matrixCol(A : matrix, j : int) : vector =
- let var tmp := vectorCreate(A.y)
- in for i := 0 to A.y do
- tmp.d[i] := A.d[i].d[j];
- tmp
- end
-
-function matrixTranspose(A : matrix) : matrix =
- let var tmp := matrixCreate(A.y, A.x)
- in for i := 0 to A.x do
- for j := 0 to A.y do
- tmp.d[j].d[i] := A.d[i].d[j];
- tmp
- end
-
-function matrixLiftedAdd(A : matrix, B : matrix) : matrix =
- let var tmp := matrixCreate(A.x, A.y)
- in if A.x <> B.x | A.y <> B.y then exit(1)
- else for i := 0 to A.x do
- for j := 0 to A.y do
- tmp.d[i].d[j] := A.d[i].d[j] + B.d[i].d[j];
- tmp
- end
-
-function matrixLiftedMul(A : matrix, B : matrix) : matrix =
- let var tmp := matrixCreate(A.x, A.y)
- in if A.x <> B.x | A.y <> B.y then exit(1)
- else for i := 0 to A.x do
- for j := 0 to A.y do
- tmp.d[i].d[j] := A.d[i].d[j] * B.d[i].d[j];
- tmp
- end
-
-function matrixMul(A : matrix, B : matrix) : matrix =
- let var tmp := matrixCreate(A.x, B.y)
- in if A.y <> B.x then exit(1)
- else for i := 0 to A.x do
- for j := 0 to B.y do
- tmp.d[i].d[j] := vectorInProduct(matrixRow(A,i), matrixCol(B,j));
- tmp
- end
-
-function createDiagMat(X : vector) : matrix =
- let var tmp := matrixCreate(X.dim, X.dim)
- in for i := 0 to X.dim do
- tmp.d[i].d[i] := X.d[i];
- tmp
- end
-
-/* matrixMul(A, B) where B is a diagonal matrix, which can be represented
- by a vector
-*/
-
-function matrixMulDiag(A : matrix, X : vector) : matrix =
- let var tmp := matrixCreate(A.x, A.y)
- in if A.y <> X.dim then exit(1)
- else for i := 0 to A.x do
- for j := 0 to A.y do
- tmp.d[i].d[j] := A.d[i].d[j] * X.d[j];
- tmp
- end
-
-/* Challenge: matrixMul(A, createDiagMat(X)) == matrixMulDiag(A, X)
-i.e., derive the rhs from the lhs by specialization
-
-What are the laws involved?
-
-Challenge: matrixMul(A, create5shapeMatrix(a,b,c,d,e)) == efficient algorithm
-
-*/
-
-in
-
- /* matrixLiftedAdd(matrixCreate(8),matrixCreate(8)) */
-
- matrixMul(A, createDiagMat(X))
-
-end
\ No newline at end of file