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cavis/libnd4j/include/ops/declarable/helpers/cpu/lup.cpp

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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
******************************************************************************/
//
// @author raver119@gmail.com
//
#include <ops/declarable/helpers/top_k.h>
#include <MmulHelper.h>
#include <NDArrayFactory.h>
#include <Status.h>
namespace nd4j {
namespace ops {
namespace helpers {
template <typename T>
static void swapRows_(NDArray* matrix, int theFirst, int theSecond) {
if (theFirst != theSecond)
for (int i = 0; i < matrix->columns(); i++) {
T e0 = matrix->e<T>(theFirst, i);
T e1 = matrix->e<T>(theSecond, i);
matrix->p<T>(theFirst, i, e1);
matrix->p<T>(theSecond, i, e0);
}
}
BUILD_SINGLE_TEMPLATE(template void swapRows_, (NDArray* matrix, int theFirst, int theSecond), FLOAT_TYPES);
void swapRows(NDArray* matrix, int theFirst, int theSecond) {
BUILD_SINGLE_SELECTOR(matrix->dataType(), swapRows_, (matrix, theFirst, theSecond), FLOAT_TYPES);
}
template <typename T>
static void invertLowerMatrix_(NDArray* inputMatrix, NDArray* invertedMatrix) {
int n = inputMatrix->rows();
invertedMatrix->assign(0.f);
// PRAGMA_OMP_PARALLEL_FOR_IF(n > Environment::getInstance()->elementwiseThreshold())
for (int i = 0; i < n; i++)
invertedMatrix->p(i, i, 1.0f);
if (inputMatrix->isIdentityMatrix()) return;
//PRAGMA_OMP_PARALLEL_FOR_IF(n > Environment::getInstance()->elementwiseThreshold())
for (int i = 1; i < n; i++)
invertedMatrix->t<T>(i, i - 1) = -inputMatrix->t<T>(i, i - 1);
//PRAGMA_OMP_PARALLEL_FOR_SIMD
for (int i = 2; i < n; i++) {
for (int j = i - 2; j > -1; --j)
for (int k = 0; k < i; k++)
invertedMatrix->t<T>(i, j) -= (invertedMatrix->t<T>(k, j) * inputMatrix->t<T>(i, k));
}
}
BUILD_SINGLE_TEMPLATE(template void invertLowerMatrix_, (NDArray* inputMatrix, NDArray* invertedMatrix);, FLOAT_TYPES);
void invertLowerMatrix(NDArray* inputMatrix, NDArray* invertedMatrix) {
BUILD_SINGLE_SELECTOR(inputMatrix->dataType(), invertLowerMatrix_, (inputMatrix, invertedMatrix), FLOAT_TYPES);
}
template <typename T>
static void _invertUpperMatrix(NDArray* inputMatrix, NDArray* invertedMatrix) {
int n = inputMatrix->rows();
invertedMatrix->setIdentity();
if (inputMatrix->isIdentityMatrix()) { // the inverse for I is I
return;
}
//PRAGMA_OMP_PARALLEL_FOR_IF(n > Environment::getInstance()->elementwiseThreshold())
for (int i = 0; i < n; i++)
invertedMatrix->t<T>(i, i) /= inputMatrix->t<T>(i, i);
//PRAGMA_OMP_PARALLEL_FOR_IF(n > Environment::getInstance()->elementwiseThreshold())
for (int i = 0; i < n - 1; i++)
invertedMatrix->t<T>(i, i + 1) -= (inputMatrix->t<T>(i, i + 1) * invertedMatrix->t<T>(i + 1, i + 1) / inputMatrix->t<T>(i, i));
// PRAGMA_OMP_PARALLEL_FOR_SIMD
for (int i = n - 2; i > - 1; i--) {
for (int j = i + 2; j < n; j++)
for (int k = i; k < n; k++)
invertedMatrix->t<T>(i, j) -= ((invertedMatrix->t<T>(k, j) * inputMatrix->t<T>(i, k) / inputMatrix->t<T>(i, i)));
}
}
BUILD_SINGLE_TEMPLATE(template void _invertUpperMatrix, (NDArray* inputMatrix, NDArray* invertedMatrix);, FLOAT_TYPES);
void invertUpperMatrix(NDArray* inputMatrix, NDArray* invertedMatrix) {
BUILD_SINGLE_SELECTOR(inputMatrix->dataType(), _invertUpperMatrix, (inputMatrix, invertedMatrix), FLOAT_TYPES);
}
template <typename T>
static NDArray lup_(LaunchContext *context, NDArray* input, NDArray* compound, NDArray* permutation) {
const int rowNum = input->rows();
const int columnNum = input->columns();
NDArray determinant = NDArrayFactory::create<T>(1.f);
NDArray compoundMatrix = *input; // copy
NDArray permutationMatrix(input, false, context); // has same shape as input and contiguous strides
permutationMatrix.setIdentity();
T pivotValue; // = T(0.0);
int pivot; // = -1;
int swapCount = 0;
for(int i = 0; i < rowNum; i++ ) {
pivotValue = T(0.0);
pivot = -1;
//PRAGMA_OMP_PARALLEL_FOR //_ARGS(firstprivate(pivot,pivotValue))
for(int rowCounter = i; rowCounter < rowNum; rowCounter++ ) {
if (nd4j::math::nd4j_abs(compoundMatrix.t<T>(rowCounter, i)) > pivotValue) {
pivotValue = nd4j::math::nd4j_abs(compoundMatrix.t<T>(rowCounter, i));
pivot = rowCounter;
}
}
if( pivotValue > T(0.00001)) {
swapRows(&compoundMatrix, pivot, i);
swapRows(&permutationMatrix, pivot, i);
if (pivot != i)
swapCount++;
for( int j = i + 1; j < rowNum; j++ ) {
compoundMatrix.t<T>(j, i) /= compoundMatrix.t<T>(i, i);
//PRAGMA_OMP_PARALLEL_FOR
for( int k = i + 1; k < rowNum; k++ ) {
compoundMatrix.t<T>(j, k) -= compoundMatrix.t<T>(j, i) * compoundMatrix.t<T>(i, k);
}
}
}
}
for (int e = 0; e < rowNum; e++) {
// nd4j_printf("Compound matrix diag %i %f.\n", e, (*compoundMatrix)(e, e));
determinant *= compoundMatrix.e<T>(e, e);
}
if (swapCount % 2) determinant = -determinant;
if (compound != nullptr)
compound->assign(compoundMatrix);
if (permutation != nullptr)
permutation->assign(permutationMatrix);
return determinant;
}
BUILD_SINGLE_TEMPLATE(template NDArray lup_, (LaunchContext *context, NDArray* input, NDArray* output, NDArray* permutation), FLOAT_TYPES);
template <typename T>
static int determinant_(LaunchContext *context, NDArray* input, NDArray* output) {
Nd4jLong n = input->sizeAt(-1);
Nd4jLong n2 = n * n;
auto matrix = NDArrayFactory::create(input->ordering(), {n, n}, input->dataType(), context); //, block.getWorkspace());
for (int e = 0; e < output->lengthOf(); e++) {
for (int k = e * n2, row = 0; k < (e + 1) * n2; ++k, ++row)
matrix.p(row, input->e<T>(k));
output->p(e, lup_<T>(context, &matrix, (NDArray*)nullptr, (NDArray*)nullptr));
}
return Status::OK();
}
int determinant(nd4j::LaunchContext * context, NDArray* input, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), return determinant_, (context, input, output), FLOAT_TYPES);
}
template <typename T>
int logAbsDeterminant_(LaunchContext *context, NDArray* input, NDArray* output) {
Nd4jLong n = input->sizeAt(-1);
Nd4jLong n2 = n * n;
NDArray matrix = NDArrayFactory::create(input->ordering(), {n, n}, input->dataType(), context); //, block.getWorkspace());
for (int e = 0; e < output->lengthOf(); e++) {
for (int k = e * n2, row = 0; k < (e + 1) * n2; ++k, ++row) {
matrix.p(row, input->e<T>(k));
}
NDArray det = lup_<T>(context, &matrix, (NDArray*)nullptr, (NDArray*)nullptr);
if (det.e<T>(0) != 0.f)
output->p(e, nd4j::math::nd4j_log<T,T>(nd4j::math::nd4j_abs(det.t<T>(0))));
}
return ND4J_STATUS_OK;
}
int logAbsDeterminant(nd4j::LaunchContext * context, NDArray* input, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), return logAbsDeterminant_, (context, input, output), FLOAT_TYPES);
}
template <typename T>
static int inverse_(LaunchContext *context, NDArray* input, NDArray* output) {
auto n = input->sizeAt(-1);
auto n2 = n * n;
auto totalCount = output->lengthOf() / n2;
output->assign(0.f); // fill up output tensor with zeros
auto matrix = NDArrayFactory::create('c', {n, n}, DataTypeUtils::fromT<T>(), context); //, block.getWorkspace());
auto compound = NDArrayFactory::create('c', {n, n}, DataTypeUtils::fromT<T>(), context); //, block.getWorkspace());
auto permutation = NDArrayFactory::create('c', {n, n}, DataTypeUtils::fromT<T>(), context);
auto lowerMatrix = NDArrayFactory::create('c', {n, n}, DataTypeUtils::fromT<T>(), context);
auto upperMatrix = NDArrayFactory::create('c', {n, n}, DataTypeUtils::fromT<T>(), context);
for (int e = 0; e < totalCount; e++) {
if (e)
matrix.assign(0.f);
for (int k = e * n2, row = 0; k < (e + 1) * n2; k++) {
matrix.p(row++, input->e<T>(k));
}
T det = lup_<T>(context, &matrix, &compound, &permutation).template e<T>(0);
// FIXME: and how this is going to work on float16?
if (nd4j::math::nd4j_abs<T>(det) < T(0.000001)) {
nd4j_printf("matrix_inverse: The matrix %i has no inverse due determinant is %lf. Quiting...\n", e, det);
matrix.printIndexedBuffer("Wrong matrix");
return ND4J_STATUS_VALIDATION;
}
lowerMatrix.setIdentity(); // set up U to identity matrix
for (int k = 1; k < n; k++) { // and then put all values under main diagonal on to it
for (int j = 0; j < k; j++)
lowerMatrix.template t<T>(k, j) = compound.template t<T>(k, j);
}
upperMatrix.setIdentity(); // set up U to identity matrix
for (int k = 0; k < n; k++) { // and then put all values under main diagonal on to it
for (int j = k; j < n; j++)
upperMatrix.template t<T>(k, j) = compound.template e<T>(k, j);
}
invertUpperMatrix(&upperMatrix, &matrix);
invertLowerMatrix(&lowerMatrix, &upperMatrix);
nd4j::MmulHelper::mmul(&matrix, &upperMatrix, &compound, 1.0, 0.0);
nd4j::MmulHelper::mmul(&compound, &permutation, &matrix, 1.0, 0.0);
for (int k = e * n2, row = 0; k < (e + 1) * n2; k++) {
output->t<T>(k) = matrix.template t<T>(row++);
}
}
return Status::OK();
}
int inverse(nd4j::LaunchContext * context, NDArray* input, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), return inverse_, (context, input, output), FLOAT_TYPES);
}
template <typename T>
static bool checkCholeskyInput_(nd4j::LaunchContext * context, NDArray const* input) {
//std::unique_ptr<NDArray> matrix(NDArrayFactory::create_('c', {n, n}, input->dataType())); //, block.getWorkspace());
std::unique_ptr<ResultSet> lastMatrixList(input->allTensorsAlongDimension({input->rankOf() - 2, input->rankOf()-1}));
for (size_t i = 0; i < lastMatrixList->size(); i++) {
auto thisMatrix = lastMatrixList->at(i);
// check for symmetric
for (Nd4jLong r = 0; r < thisMatrix->rows(); r++)
for (Nd4jLong c = 0; c < thisMatrix->columns(); c++)
if (nd4j::math::nd4j_abs(thisMatrix->e<T>(r, c) - lastMatrixList->at(i)->e<T>(c,r)) > T(1.e-6f)) return false;
NDArray output = NDArrayFactory::create<T>(0., context);
if (ND4J_STATUS_OK != determinant(context, thisMatrix, &output)) return false;
if (output.e<T>(0) <= T(0)) return 0;
NDArray reversedMatrix(*thisMatrix);
if (ND4J_STATUS_OK != inverse(context, thisMatrix, &reversedMatrix)) return false;
if (ND4J_STATUS_OK != determinant(context, &reversedMatrix, &output)) return false;
if (output.e<T>(0) <= T(0)) return 0;
}
return true;
}
bool checkCholeskyInput(nd4j::LaunchContext * context, NDArray const* input) {
BUILD_SINGLE_SELECTOR(input->dataType(), return checkCholeskyInput_, (context, input), FLOAT_TYPES);
}
template <typename T>
int cholesky_(LaunchContext *context, NDArray* input, NDArray* output, bool inplace) {
auto n = input->sizeAt(-1);
auto n2 = n * n;
auto totalCount = output->lengthOf() / n2;
if (!inplace)
output->assign(0.f); // fill up output tensor with zeros only inplace=false
std::unique_ptr<NDArray> matrix(NDArrayFactory::create_('c', {n, n}, input->dataType(), context)); //, block.getWorkspace());
std::unique_ptr<NDArray> lowerMatrix(NDArrayFactory::create_('c',{n, n}, input->dataType(), context));
for (int e = 0; e < totalCount; e++) {
// fill up matrix
for (int k = e * n2, l = 0; k < (e + 1) * n2; k++) {
matrix->p(l++, input->e<T>(k));
}
//if (e) // from the second loop need to zero matrix
lowerMatrix->assign(0.f);
for (Nd4jLong col = 0; col < n; col++) {
for (Nd4jLong row = 0; row < col; row++) {
T rowSum = 0;
for (Nd4jLong k = 0; k < row; ++k)
rowSum += (lowerMatrix->e<T>(col, k) * lowerMatrix->e<T>(row, k));
lowerMatrix->p(col, row, (matrix->e<T>(row, col) - rowSum) / lowerMatrix->e<double>(row, row));
}
T diagonalSum = 0;
for (Nd4jLong k = 0; k < col; ++k)
diagonalSum += lowerMatrix->e<T>(col, k) * lowerMatrix->e<T>(col, k);
lowerMatrix->p(col, col, nd4j::math::nd4j_sqrt<T, T>(matrix->e<T>(col, col) - diagonalSum));
//nd4j_printf("%i: ", col);
//lowerMatrix->printIndexedBuffer("Lower matrix");
}
for (int k = e * n2, l = 0; k < (e + 1) * n2; k++) {
output->p(k, lowerMatrix->e<T>(l++));
}
}
return ND4J_STATUS_OK;
}
int cholesky(nd4j::LaunchContext * context, NDArray* input, NDArray* output, bool inplace) {
BUILD_SINGLE_SELECTOR(input->dataType(), return cholesky_, (context, input, output, inplace), FLOAT_TYPES);
}
template <typename T>
int logdetFunctor_(LaunchContext *context, NDArray* input, NDArray* output) {
std::unique_ptr<NDArray> tempOutput(input->dup());
int res = cholesky_<T>(context, input, tempOutput.get(), false);
if (res != ND4J_STATUS_OK)
return res;
auto n = input->sizeAt(-1);
auto totalCount = output->lengthOf();
std::vector<T> d(n);
std::unique_ptr<ResultSet> matricies(tempOutput->allTensorsAlongDimension({input->rankOf()-2, input->rankOf() - 1}));
std::unique_ptr<ResultSet> inputMatricies(input->allTensorsAlongDimension({input->rankOf()-2, input->rankOf() - 1}));
for (Nd4jLong e = 0; e < totalCount; e++) {
//d[0] = inputMatricies->at(e)->t<T>(0, 0);
for (size_t i = 0; i < n; ++i) {
output->t<T>(e) += nd4j::math::nd4j_log<T,T>(nd4j::math::nd4j_pow<T,T,T>(matricies->at(e)->t<T>(i, i), T(2)));
}
}
return ND4J_STATUS_OK;
}
int logdetFunctor(nd4j::LaunchContext * context, NDArray* input, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), return logdetFunctor_, (context, input, output), FLOAT_TYPES);
}
}
}
}
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