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/**
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
// Matrix factorization using macros.
// Build the matrices first using the build_matrix.mrql query
Mmatrix = source(binary,"tmp/Xmatrix.bin");
Hmatrix = source(binary,"tmp/Ymatrix.bin");
Wmatrix = source(binary,"tmp/Zmatrix.bin");
macro transpose ( X ) {
select (x,j,i)
from (x,i,j) in X
};
// matrix multiplication:
macro multiply ( X, Y ) {
select (sum(z),i,j)
from (x,i,k) in X, (y,k,j) in Y, z = x*y
group by (i,j)
};
// cell-wise multiplication:
macro Cmult ( X, Y ) {
select ( x*y, i, j )
from (x,i,j) in X, (y,i,j) in Y
};
// cell-wise division:
macro Cdiv ( X, Y ) {
select ( x/y, i, j )
from (x,i,j) in X, (y,i,j) in Y
};
// Gaussian non-negative matrix factorization (from SystemML paper)
macro factorize ( V, Hinit, Winit ) {
repeat (H,W) = (Hinit,Winit)
step ( Cmult(H,Cdiv(multiply(transpose(W),V),multiply(transpose(W),multiply(W,H)))),
Cmult(W,Cdiv(multiply(V,transpose(H)),multiply(W,multiply(H,transpose(H))))) )
limit 4
};
let (X1,X2) = factorize(Mmatrix,Hmatrix,Wmatrix)
in multiply(X1,transpose(X2));