cavis/libnd4j/include/helpers/householder.h

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/*******************************************************************************
* Copyright (c) 2015-2018 Skymind, Inc.
*
* This program and the accompanying materials are made available under the
* terms of the Apache License, Version 2.0 which is available at
* https://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.
*
* SPDX-License-Identifier: Apache-2.0
******************************************************************************/
//
// Created by Yurii Shyrma on 18.12.2017.
//
#ifndef LIBND4J_HOUSEHOLDER_H
#define LIBND4J_HOUSEHOLDER_H
#include "array/NDArray.h"
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namespace sd {
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namespace ops {
namespace helpers {
template <typename T>
class Householder {
public:
/**
* this method calculates Householder matrix P = identity_matrix - coeff * w * w^T
* P * x = [normX, 0, 0 , 0, ...]
* coeff - scalar
* w = [1, w1, w2, w3, ...]
* w = u / u0
* u = x - |x|*e0
* u0 = x0 - |x|
* e0 = [1, 0, 0 , 0, ...]
*
* x - input vector, remains unaffected
*/
static NDArray evalHHmatrix(const NDArray& x);
/**
* this method evaluates data required for calculation of Householder matrix P = identity_matrix - coeff * w * w^T
* P * x = [normX, 0, 0 , 0, ...]
* coeff - scalar
* w = [1, w1, w2, w3, ...]
* w = u / u0
* u = x - |x|*e0
* u0 = x0 - |x|
* e0 = [1, 0, 0 , 0, ...]
*
* x - input vector, remains unaffected
* tail - the essential part of the vector w: [w1, w2, w3, ...]
* normX - this scalar is the first non-zero element in vector resulting from Householder transformation -> (P*x)
* coeff - scalar, scaling factor in Householder matrix formula
*/
static void evalHHmatrixData(const NDArray& x, NDArray& tail, T& coeff, T& normX);
static void evalHHmatrixDataI(const NDArray& x, T& coeff, T& normX);
/**
* this method mathematically multiplies input matrix on Householder from the left P * matrix
*
* matrix - input matrix
* tail - the essential part of the Householder vector w: [w1, w2, w3, ...]
* coeff - scalar, scaling factor in Householder matrix formula
*/
static void mulLeft(NDArray& matrix, const NDArray& tail, const T coeff);
/**
* this method mathematically multiplies input matrix on Householder from the right matrix * P
*
* matrix - input matrix
* tail - the essential part of the Householder vector w: [w1, w2, w3, ...]
* coeff - scalar, scaling factor in Householder matrix formula
*/
static void mulRight(NDArray& matrix, const NDArray& tail, const T coeff);
};
// /**
// * this function reduce given matrix to upper bidiagonal form (in-place operation), matrix must satisfy following condition rows >= cols
// *
// * matrix - input 2D matrix to be reduced to upper bidiagonal from
// */
// template <typename T>
// void biDiagonalizeUp(NDArray& matrix);
// /**
// * given a matrix [m,n], this function computes its singular value decomposition matrix = u * s * v^T
// *
// * matrix - input 2D matrix to decompose, [m, n]
// * u - unitary matrix containing left singular vectors of input matrix, [m, m]
// * s - diagonal matrix with singular values of input matrix (non-negative) on the diagonal sorted in decreasing order,
// * actually the mathematically correct dimension of s is [m, n], however for memory saving we work with s as vector [1, p], where p is smaller among m and n
// * v - unitary matrix containing right singular vectors of input matrix, [n, n]
// * calcUV - if true then u and v will be computed, in opposite case function works significantly faster
// * fullUV - if false then only p (p is smaller among m and n) first columns of u and v will be calculated and their dimensions in this case are [m, p] and [n, p]
// *
// */
// void svd(const NDArray& matrix, NDArray& u, NDArray& s, NDArray& v, const bool calcUV = false, const bool fullUV = false)
}
}
}
#endif //LIBND4J_HOUSEHOLDER_H