/*******************************************************************************
* 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 <helpers/MmulHelper.h>
#include <array/NDArrayFactory.h>
#include <graph/Status.h>
#include <execution/Threads.h>
#include <execution/Threads.h>
namespace sd {
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++) {
math::nd4j_swap(matrix->t<T>(theFirst, i), matrix->t<T>(theSecond, i));
}
}
BUILD_SINGLE_TEMPLATE(template void swapRows_, (NDArray* matrix, int theFirst, int theSecond), FLOAT_TYPES);
template <typename T>
static void swapRows(T* matrixBuf, Nd4jLong const* matrixShape, Nd4jLong theFirst, Nd4jLong theSecond) {
if (theFirst != theSecond) {
auto n = shape::sizeAt(matrixShape, -1);
auto loop = PRAGMA_THREADS_FOR {
for (auto i = start; i < stop; i++) {
Nd4jLong theFirstPos[] = {theFirst, i};
Nd4jLong theSecondPos[] = {theSecond, i};
auto theFirstIndex = shape::getOffset(matrixShape, theFirstPos, 0);
auto theSecondIndex = shape::getOffset(matrixShape, theSecondPos, 0);
math::nd4j_swap(matrixBuf[theFirstIndex], matrixBuf[theSecondIndex]);
}
};
samediff::Threads::parallel_tad(loop, 0, n, 1);
}
}
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->setIdentity();
if (inputMatrix->isIdentityMatrix()) return;
auto invertDiagonals = PRAGMA_THREADS_FOR {
for (int i = start; i < stop; i += increment)
invertedMatrix->t<T>(i, i) /= inputMatrix->t<T>(i, i);
};
auto invertSubDiagonals = PRAGMA_THREADS_FOR {
for (int i = start; i < stop; i += increment)
invertedMatrix->t<T>(i, i - 1) -= (inputMatrix->t<T>(i, i - 1) * invertedMatrix->t<T>(i - 1, i - 1) / inputMatrix->t<T>(i, i));
};
samediff::Threads::parallel_for(invertDiagonals, 0, n, 1);
samediff::Threads::parallel_for(invertSubDiagonals, 1, n, 1);
// PRAGMA_OMP_PARALLEL_FOR_SIMD
for (int i = 1; i < n; i++) {
for (int j = 0; j < i - 1 ; j++)
for (int k = 0; k < i; 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 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;
}
auto invertDiagonals = PRAGMA_THREADS_FOR {
for (auto i = start; i < stop; i += increment)
invertedMatrix->t<T>(i, i) /= inputMatrix->t<T>(i, i);
};
//PRAGMA_OMP_PARALLEL_FOR_IF(n > Environment::getInstance()->elementwiseThreshold())
auto invertUpDiagonals = PRAGMA_THREADS_FOR {
for (auto i = start; i < stop; i += increment)
invertedMatrix->t<T>(i, i + 1) -= (inputMatrix->t<T>(i, i + 1) * invertedMatrix->t<T>(i + 1, i + 1) /
inputMatrix->t<T>(i, i));
};
samediff::Threads::parallel_for(invertDiagonals, 0, n, 1);
samediff::Threads::parallel_for(invertUpDiagonals, 0, n - 1, 1);
// PRAGMA_OMP_PARALLEL_FOR_SIMD
for (auto i = n - 2; i >= 0; i--) {
for (auto j = i + 2; j < n; j++)
for (auto 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, typename I>
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, context);
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 (sd::math::nd4j_abs(compoundMatrix.t<T>(rowCounter, i)) > pivotValue) {
pivotValue = sd::math::nd4j_abs(compoundMatrix.t<T>(rowCounter, i));
pivot = rowCounter;
}
}
if( pivotValue > DataTypeUtils::min<T>()) {
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) {
auto permutaionVector = NDArrayFactory::create('c', {rowNum}, DataTypeUtils::fromT<I>(), input->getContext());
for (auto i = 0; i < rowNum; i++) {
for (auto j = 0; j < columnNum; j++) {
if (permutationMatrix.t<T>(i, j) != 0) {
permutaionVector.template t<I>(i) = j;
}
}
}
if (permutationMatrix.isSameShape(permutation))
permutation->assign(permutationMatrix);
else if (permutation->isSameShape(permutaionVector)) {
permutation->assign(permutaionVector);
}
}
return determinant;
}
BUILD_DOUBLE_TEMPLATE(template NDArray lup_, (LaunchContext *context, NDArray* input, NDArray* output, NDArray* permutation), FLOAT_TYPES, INDEXING_TYPES);
/*
* lu decomposition with naive algorithm with partial pivoting
* */
template <typename T, typename I>
static I argmaxCol(I column, T* compoundBuffer, Nd4jLong const* compoundShape) {
auto rowNum = shape::sizeAt(compoundShape, 0);
Nd4jLong xInitial[] = {column, column};
auto xInitialIndex = shape::getOffset(compoundShape, xInitial, 0);
auto maxValue = T(0); //sd::math::nd4j_abs(compoundBuffer[xInitialIndex]);
auto result = -1;
//auto loop = PRAGMA_THREADS_FOR {
auto start = column, stop = rowNum, increment = 1;
for (auto rowCounter = start; rowCounter < stop; rowCounter++) {
Nd4jLong xPos[] = {rowCounter, column};
auto xIndex = shape::getOffset(compoundShape, xPos, 0);
if (sd::math::nd4j_abs(compoundBuffer[xIndex]) > maxValue) {
maxValue = sd::math::nd4j_max(maxValue, sd::math::nd4j_abs(compoundBuffer[xIndex]));
result = rowCounter;
}
}
//};
//samediff::Threads::parallel_for(loop, column, rowNum, 1);
return result;
}
template <typename T>
void processColumns(int currentRow, int rowNum, T* compoundBuf, Nd4jLong const* compoundShape) {
Nd4jLong xDiag[] = {currentRow, currentRow};
auto diagIndex = shape::getOffset(compoundShape, xDiag, 0);
auto loop = PRAGMA_THREADS_FOR {
for (auto j = start; j < stop; j++) {
Nd4jLong xRow[] = {j, currentRow};
auto rowIndex = shape::getOffset(compoundShape, xRow, 0);
compoundBuf[rowIndex] /= compoundBuf[diagIndex]; //output->t<T>(i, i);
for (int k = currentRow + 1; k < rowNum; k++) {
Nd4jLong yRow[] = {j, k};
Nd4jLong yCol[] = {currentRow, k};
auto rowIndexY = shape::getOffset(compoundShape, yRow, 0);
auto colIndex = shape::getOffset(compoundShape, yCol, 0);
compoundBuf[rowIndexY] -= compoundBuf[rowIndex] * compoundBuf[colIndex];
}
}
};
samediff::Threads::parallel_tad(loop, currentRow + 1, rowNum, 1);
}
template <typename T>
static void doolitleLU(LaunchContext* context, NDArray* compound, Nd4jLong rowNum) {
auto input = compound->dup();
compound->nullify();
// Decomposing matrix into Upper and Lower
// triangular matrix
for (auto i = 0; i < rowNum; i++) {
// Upper Triangular
for (auto k = i; k < rowNum; k++) {
// Summation of L(i, j) * U(j, k)
int sum = 0;
for (int j = 0; j < i; j++)
sum += compound->t<T>(i,j) * compound->t<T>(j,k);
// Evaluating U(i, k)
compound->t<T>(i, k) = input.t<T>(i, k) - sum;
}
// Lower Triangular
for (int k = i + 1; k < rowNum; k++) {
// Summation of L(k, j) * U(j, i)
int sum = 0;
for (int j = 0; j < i; j++)
sum += compound->t<T>(k,j) * compound->t<T>(j, i);
// Evaluating L(k, i)
compound->t<T>(k, i) = (input.t<T>(k, i) - sum) / compound->t<T>(i,i);
}
}
}
template <typename T, typename I>
static void luNN_(LaunchContext *context, NDArray* compound, NDArray* permutation, Nd4jLong rowNum) {
//const int rowNum = compound->rows();
// const int columnNum = output->columns();
if (permutation) { // LUP algorithm
permutation->linspace(0);
auto permutationBuf = permutation->bufferAsT<I>(); //dataBuffer()->primaryAsT<I>();
auto compoundBuf = compound->bufferAsT<T>();
auto compoundShape = compound->shapeInfo();
auto permutationShape = permutation->shapeInfo();
for (auto i = 0; i < rowNum - 1; i++) {
auto pivotIndex = argmaxCol(i, compoundBuf, compoundShape);
if (pivotIndex < 0) {
throw std::runtime_error("helpers::luNN_: input matrix is singular.");
}
math::nd4j_swap(permutationBuf[shape::getIndexOffset(i, permutationShape)],
permutationBuf[shape::getIndexOffset(pivotIndex, permutationShape)]);
swapRows(compoundBuf, compoundShape, i, pivotIndex);
processColumns(i, rowNum, compoundBuf, compoundShape);
}
}
else { // Doolitle algorithm with LU decomposition
doolitleLU<T>(context, compound, rowNum);
}
}
template <typename T, typename I>
static void lu_(LaunchContext * context, NDArray* input, NDArray* output, NDArray* permutationVectors) {
auto n = input->sizeAt(-1);
output->assign(input); // fill up output tensor with zeros
ResultSet outputs = output->allTensorsAlongDimension({-2, -1});
ResultSet permutations;
if (permutationVectors)
permutations = permutationVectors->allTensorsAlongDimension({-1});
auto loop = PRAGMA_THREADS_FOR {
for (auto i = start; i < stop; i++) {
luNN_<T, I>(context, outputs.at(i), permutationVectors?permutations.at(i):nullptr, n);
}
};
samediff::Threads::parallel_for(loop, 0, outputs.size(), 1);
}
void lu(LaunchContext *context, NDArray* input, NDArray* output, NDArray* permutation) {
BUILD_DOUBLE_SELECTOR(input->dataType(), permutation?permutation->dataType():DataType::INT32, lu_, (context, input, output, permutation), FLOAT_TYPES, INDEXING_TYPES);
}
// BUILD_DOUBLE_TEMPLATE(template NDArray lu_, (LaunchContext *context, NDArray* input, NDArray* output, NDArray* permutation), FLOAT_TYPES, INDEXING_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, int>(context, &matrix, (NDArray*)nullptr, (NDArray*)nullptr));
}
return Status::OK();
}
int determinant(sd::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, int>(context, &matrix, (NDArray*)nullptr, (NDArray*)nullptr);
if (det.e<T>(0) != 0.f)
output->p(e, sd::math::nd4j_log<T,T>(sd::math::nd4j_abs(det.t<T>(0))));
}
return ND4J_STATUS_OK;
}
int logAbsDeterminant(sd::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, int>(context, &matrix, &compound, &permutation).template e<T>(0);
// FIXME: and how this is going to work on float16?
if (sd::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);
sd::MmulHelper::mmul(&matrix, &upperMatrix, &compound, 1.0, 0.0);
sd::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();
}
template <typename T>
static int lowerInverse_(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);
// auto batchLoop = PRAGMA_THREADS_FOR {
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 = T(1.f);
for (auto i = 0; i < n; i++) {
det *= matrix. template t<T>(i, i);
}
// FIXME: and how this is going to work on float16?
if (sd::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.nullify();
invertLowerMatrix(&matrix, &lowerMatrix);
for (int k = e * n2, row = 0; k < (e + 1) * n2; k++) {
output->t<T>(k) = lowerMatrix.template t<T>(row++);
}
}
return Status::OK();
}
template <typename T>
static int upperInverse_(LaunchContext *context, NDArray* input, NDArray* output) {
auto n = input->sizeAt(-1);
auto n2 = n * n;
output->nullify(); // fill up output tensor with zeros
// auto matrix = NDArrayFactory::create('c', {n, n}, DataTypeUtils::fromT<T>(), context); //, block.getWorkspace());
// auto lowerMatrix = NDArrayFactory::create('c', {n, n}, DataTypeUtils::fromT<T>(), context);
// auto upperMatrix = NDArrayFactory::create('c', {n, n}, DataTypeUtils::fromT<T>(), context);
auto inputPart = input->allTensorsAlongDimension({-2, -1});
auto outputPart = output->allTensorsAlongDimension({-2, -1});
auto totalCount = outputPart.size(); //lengthOf() / n2;
for (int e = 0; e < totalCount; e++) {
invertUpperMatrix(inputPart.at(e), outputPart.at(e));
}
return Status::OK();
}
int inverse(sd::LaunchContext * context, NDArray* input, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), return inverse_, (context, input, output), FLOAT_TYPES);
}
int lowerInverseFunctor(sd::LaunchContext * context, NDArray* input, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), return lowerInverse_, (context, input, output), FLOAT_TYPES);
}
int upperInverseFunctor(sd::LaunchContext * context, NDArray* input, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), return upperInverse_, (context, input, output), FLOAT_TYPES);
}
template <typename T>
static bool checkCholeskyInput_(sd::LaunchContext * context, NDArray const* input) {
//std::unique_ptr<NDArray> matrix(NDArrayFactory::create_('c', {n, n}, input->dataType())); //, block.getWorkspace());
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 (sd::math::nd4j_abs(thisMatrix->e<T>(r, c) - lastMatrixList.at(i)->e<T>(c,r)) > DataTypeUtils::min<T>()) 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(sd::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, sd::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(sd::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) {
auto tempOutput = input->dup();
int res = cholesky_<T>(context, input, &tempOutput, false);
if (res != ND4J_STATUS_OK)
return res;
auto n = input->sizeAt(-1);
auto totalCount = output->lengthOf();
std::vector<T> d(n);
ResultSet matricies = tempOutput.allTensorsAlongDimension({input->rankOf()-2, input->rankOf() - 1});
for (Nd4jLong e = 0; e < totalCount; e++) {
for (size_t i = 0; i < n; ++i)
output->t<T>(e) += sd::math::nd4j_log<T,T>(sd::math::nd4j_pow<T,T,T>(matricies.at(e)->t<T>(i, i), T(2)));
}
return ND4J_STATUS_OK;
}
int logdetFunctor(sd::LaunchContext * context, NDArray* input, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), return logdetFunctor_, (context, input, output), FLOAT_TYPES);
}
int lup(sd::LaunchContext * context, NDArray* input, NDArray* compound, NDArray* permutation) {
BUILD_DOUBLE_SELECTOR(input->dataType(), permutation->dataType(), lup_, (context, input, compound, permutation), FLOAT_NATIVE, INDEXING_TYPES);
return Status::OK();
}
}
}
}