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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. | ||
| # | ||
| #------------------------------------------------------------- | ||
|
|
||
| # Computes the matrix square root B of a matrix A, such that | ||
| # A = B %*% B. | ||
| # | ||
| # INPUT: | ||
| # ------------------------------------------------------------------------------ | ||
| # A Input Matrix A | ||
| # S Strategy (COMMON .. java-based commons-math, DML) | ||
| # ------------------------------------------------------------------------------ | ||
| # | ||
| # OUTPUT: | ||
| # ------------------------------------------------------------------------------ | ||
| # B Output Matrix B | ||
| # ------------------------------------------------------------------------------ | ||
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| m_sqrtMatrix = function(Matrix[Double] A, String S) | ||
| return(Matrix[Double] B) | ||
| { | ||
| if (S == "COMMON") { | ||
| B = sqrtMatrixJava(A) | ||
| } else if (S == "DML") { | ||
| N = nrow(A); | ||
| D = ncol(A); | ||
|
|
||
| #check that matrix is square | ||
| if (D != N){ | ||
| stop("matrixSqrt Input Error: matrix not square!") | ||
| } | ||
|
|
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| # Any non singualar square matrix has a square root | ||
| isDiag = isDiagonal(A) | ||
| if(isDiag) { | ||
| B = sqrtDiagMatrix(A); | ||
| } else { | ||
| [eValues, eVectors] = eigen(A); | ||
|
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| hasNonNegativeEigenValues = (sum(eValues >= 0) == length(eValues)); | ||
|
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| if(!hasNonNegativeEigenValues) { | ||
| stop("matrixSqrt exec Error: matrix has imaginary square root"); | ||
| } | ||
|
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| isSymmetric = sum(A == t(A)) == length(A); | ||
| allEigenValuesUnique = length(eValues) == length(unique(eValues)); | ||
|
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| if(allEigenValuesUnique | isSymmetric) { | ||
| # calculate X = VDV^(-1) -> S = sqrt(D) -> sqrt_x = VSV^(-1) | ||
| sqrtD = sqrtDiagMatrix(diag(eValues)); | ||
| V_Inv = inv(eVectors); | ||
| B = eVectors %*% sqrtD %*% V_Inv; | ||
| } else { | ||
| #formular: (Denman–Beavers iteration) | ||
| Y = A | ||
| #identity matrix | ||
| Z = diag(matrix(1.0, rows=N, cols=1)) | ||
|
|
||
| for (x in 1:100) { | ||
| Y_new = (1 / 2) * (Y + inv(Z)) | ||
| Z_new = (1 / 2) * (Z + inv(Y)) | ||
| Y = Y_new | ||
| Z = Z_new | ||
| } | ||
| B = Y | ||
| } | ||
| } | ||
| } else { | ||
| stop("Error: Unknown strategy for matrix square root.") | ||
| } | ||
| } | ||
|
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| # assumes square and diagonal matrix | ||
| sqrtDiagMatrix = function(Matrix[Double] X) | ||
| return(Matrix[Double] sqrt_x) | ||
| { | ||
| N = nrow(X); | ||
|
|
||
| #check if identity matrix | ||
| is_identity = sum(diag(diag(X)) == X)==length(X) | ||
| & sum(diag(X) == matrix(1,nrow(X),1))==nrow(X); | ||
|
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||
| if(is_identity) | ||
| sqrt_x = X; | ||
| else | ||
| sqrt_x = diag(sqrt(diag(X))); | ||
| } | ||
|
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| isDiagonal = function (Matrix[Double] X) | ||
| return(boolean diagonal) | ||
| { | ||
| #all cells should be the same to be diagonal | ||
| diagonal = sum(diag(diag(X)) == X) == length(X); | ||
| } | ||
|
|
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