wehub-resource-sync
504 lines
15 KiB
C++
504 lines
15 KiB
C++
/* ******************************************************************************
|
|
*
|
|
*
|
|
* 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.
|
|
*
|
|
* See the NOTICE file distributed with this work for additional
|
|
* information regarding copyright ownership.
|
|
* 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 11.01.2018
|
|
//
|
|
#include <helpers/MmulHelper.h>
|
|
#include <helpers/hhColPivQR.h>
|
|
#include <helpers/jacobiSVD.h>
|
|
#if NOT_EXCLUDED(svd)
|
|
namespace sd {
|
|
namespace ops {
|
|
namespace helpers {
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
JacobiSVD<T>::JacobiSVD(NDArray& matrix, const bool calcU, const bool calcV, const bool fullUV)
|
|
: _m(matrix.dataType(), matrix.getContext(), true),
|
|
_s(matrix.dataType(), matrix.getContext(), true),
|
|
_u(matrix.dataType(), matrix.getContext(), true),
|
|
_v(matrix.dataType(), matrix.getContext(), true) {
|
|
if (matrix.rankOf() != 2 || matrix.isScalar())
|
|
THROW_EXCEPTION("ops::helpers::JacobiSVD constructor: input array must be 2D matrix !");
|
|
|
|
_rows = static_cast<int>(matrix.sizeAt(0));
|
|
_cols = static_cast<int>(matrix.sizeAt(1));
|
|
_diagSize = math::sd_min<int>(_rows, _cols);
|
|
|
|
_calcU = calcU;
|
|
_calcV = calcV;
|
|
_fullUV = fullUV;
|
|
|
|
std::vector<LongType> sShape = {_diagSize,1};
|
|
_s = NDArray(matrix.ordering(),sShape, matrix.dataType(), matrix.getContext());
|
|
|
|
if (_calcU) {
|
|
std::vector<LongType> rowsShape = {_rows,_rows};
|
|
std::vector<LongType> rowsShape2 = {_rows,_diagSize};
|
|
if (_fullUV)
|
|
_u = NDArray(matrix.ordering(), rowsShape, matrix.dataType(), matrix.getContext());
|
|
else
|
|
_u = NDArray(matrix.ordering(), rowsShape2, matrix.dataType(), matrix.getContext());
|
|
} else {
|
|
std::vector<LongType> rowsShape = {_rows, 1};
|
|
_u = NDArray(matrix.ordering(), rowsShape, matrix.dataType(), matrix.getContext());
|
|
}
|
|
if (_calcV) {
|
|
if (_fullUV) {
|
|
std::vector<LongType> colsShape = {_cols, _cols};
|
|
_v = NDArray(matrix.ordering(), colsShape, matrix.dataType(), matrix.getContext());
|
|
}
|
|
else {
|
|
std::vector<LongType> shape = {_cols, _diagSize};
|
|
_v = NDArray(matrix.ordering(),shape, matrix.dataType(), matrix.getContext());
|
|
}
|
|
} else {
|
|
std::vector<LongType> vShape = {_cols, 1};
|
|
_v = NDArray(matrix.ordering(), vShape, matrix.dataType(), matrix.getContext());
|
|
}
|
|
std::vector<LongType> mShape = {_diagSize, _diagSize};
|
|
_m = NDArray(matrix.ordering(), mShape, matrix.dataType(), matrix.getContext());
|
|
|
|
|
|
evalData(matrix);
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
void JacobiSVD<T>::mulRotationOnLeft(const int i, const int j, NDArray& block, NDArray& rotation) {
|
|
if (i < j) {
|
|
if (j + 1 > block.sizeAt(0))
|
|
THROW_EXCEPTION(
|
|
"ops::helpers::JacobiSVD mulRotationOnLeft: second arguments is out of array row range !");
|
|
|
|
NDArray *tempPtr = block({i, j + 1, j - i, 0, 0, 0}, true, true);
|
|
NDArray temp = *tempPtr;
|
|
NDArray *tempAssignResult = mmul(rotation, temp);
|
|
temp.assign(tempAssignResult);
|
|
delete tempAssignResult;
|
|
delete tempPtr;
|
|
|
|
} else {
|
|
if (j + 1 > block.sizeAt(0) || i + 1 > block.sizeAt(0))
|
|
THROW_EXCEPTION(
|
|
"ops::helpers::JacobiSVD mulRotationOnLeft: some or both integer arguments are out of array row range !");
|
|
|
|
std::vector<LongType> tempShape = {2, block.sizeAt(1)};
|
|
NDArray temp(block.ordering(),tempShape, block.dataType(), block.getContext());
|
|
|
|
NDArray *row1Ptr = block({i, i + 1, 0, 0}, true);
|
|
NDArray row1 = *row1Ptr;
|
|
|
|
NDArray *row2Ptr = block({j, j + 1, 0, 0}, true);
|
|
NDArray row2 = *row2Ptr;
|
|
|
|
NDArray *rowTemp1Ptr = temp({0, 1, 0, 0}, true);
|
|
NDArray rowTemp1 = *rowTemp1Ptr;
|
|
|
|
NDArray *rowTemp2Ptr = temp({1, 2, 0, 0}, true);
|
|
NDArray rowTemp2 = *rowTemp2Ptr;
|
|
|
|
rowTemp1.assign(&row1);
|
|
rowTemp2.assign(&row2);
|
|
NDArray *tempAssignResult = mmul(rotation, temp);
|
|
temp.assign(tempAssignResult);
|
|
delete tempAssignResult;
|
|
row1.assign(&rowTemp1);
|
|
row2.assign(&rowTemp2);
|
|
|
|
delete row1Ptr;
|
|
delete row2Ptr;
|
|
delete rowTemp1Ptr;
|
|
delete rowTemp2Ptr;
|
|
}
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
void JacobiSVD<T>::mulRotationOnRight(const int i, const int j, NDArray& block, NDArray& rotation) {
|
|
if (i < j) {
|
|
if (j + 1 > block.sizeAt(1))
|
|
THROW_EXCEPTION(
|
|
"ops::helpers::JacobiSVD mulRotationOnRight: second argument is out of array column range !");
|
|
|
|
NDArray *tempPtr = block({0, 0, 0, i, j + 1, j - i}, true, true);
|
|
NDArray temp = *tempPtr;
|
|
NDArray *tempAssignResult = mmul(temp, rotation);
|
|
temp.assign(tempAssignResult);
|
|
delete tempAssignResult;
|
|
delete tempPtr;
|
|
} else {
|
|
if (j + 1 > block.sizeAt(1) || i + 1 > block.sizeAt(1))
|
|
THROW_EXCEPTION(
|
|
"ops::helpers::JacobiSVD mulRotationOnRight: some or both integer arguments are out of array column range !");
|
|
|
|
std::vector<LongType> tempShape = {block.sizeAt(0), 2};
|
|
NDArray temp(block.ordering(), tempShape, block.dataType(), block.getContext());
|
|
|
|
NDArray *col1Ptr = block({0, 0, i, i + 1}, true);
|
|
NDArray col1 = *col1Ptr;
|
|
|
|
NDArray *col2Ptr = block({0, 0, j, j + 1}, true);
|
|
NDArray col2 = *col2Ptr;
|
|
|
|
NDArray *colTemp1Ptr = temp({0, 0, 0, 1}, true);
|
|
NDArray colTemp1 = *colTemp1Ptr;
|
|
|
|
NDArray *colTemp2Ptr = temp({0, 0, 1, 2}, true);
|
|
NDArray colTemp2 = *colTemp2Ptr;
|
|
|
|
colTemp1.assign(&col1);
|
|
colTemp2.assign(&col2);
|
|
NDArray *tempAssignResult = mmul(temp, rotation);
|
|
temp.assign(tempAssignResult);
|
|
delete tempAssignResult;
|
|
col1.assign(&colTemp1);
|
|
col2.assign(&colTemp2);
|
|
|
|
delete col1Ptr;
|
|
delete col2Ptr;
|
|
delete colTemp1Ptr;
|
|
delete colTemp2Ptr;
|
|
}
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
bool JacobiSVD<T>::isBlock2x2NotDiag(NDArray& block, int p, int q, T& maxElem) {
|
|
std::vector<LongType> shape = {2, 2};
|
|
NDArray rotation(_m.ordering(), shape, _m.dataType(), _m.getContext());
|
|
|
|
T n = math::sd_sqrt<T, T>(block.t<T>(p, p) * block.t<T>(p, p) + block.t<T>(q, p) * block.t<T>(q, p));
|
|
|
|
const T almostZero = DataTypeUtils::min_positive<T>();
|
|
const T precision = DataTypeUtils::eps<T>();
|
|
|
|
if (n == (T)0.f) {
|
|
block.r<T>(p, p) = (T)0;
|
|
block.r<T>(q, p) = (T)0;
|
|
} else {
|
|
T v = block.t<T>(p, p) / n;
|
|
|
|
rotation.r<T>(0, 0) = rotation.r<T>(1, 1) = v;
|
|
|
|
v = block.t<T>(q, p) / n;
|
|
rotation.r<T>(0, 1) = v;
|
|
|
|
rotation.r<T>(1, 0) = -rotation.template t<T>(0, 1);
|
|
mulRotationOnLeft(p, q, block, rotation);
|
|
NDArray *rotT = rotation.transpose();
|
|
if (_calcU) mulRotationOnRight(p, q, _u, *rotT);
|
|
delete rotT;
|
|
}
|
|
|
|
maxElem =
|
|
math::sd_max<T>(maxElem, math::sd_max<T>(math::sd_abs<T,T>(block.t<T>(p, p)), math::sd_abs<T,T>(block.t<T>(q, q))));
|
|
T threshold = math::sd_max<T>(almostZero, precision * maxElem);
|
|
|
|
return math::sd_abs<T,T>(block.t<T>(p, q)) > threshold || math::sd_abs<T,T>(block.t<T>(q, p)) > threshold;
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
bool JacobiSVD<T>::createJacobiRotation(const T& x, const T& y, const T& z, NDArray& rotation) {
|
|
T denom = (T)(2.f) * math::sd_abs<T,T>(y);
|
|
|
|
if (denom < DataTypeUtils::min_positive<T>()) {
|
|
rotation.r<T>(0, 0) = rotation.r<T>(1, 1) = (T)1.f;
|
|
rotation.r<T>(0, 1) = rotation.r<T>(1, 0) = (T)0.f;
|
|
|
|
return false;
|
|
} else {
|
|
T tau = (x - z) / denom;
|
|
T w = math::sd_sqrt<T, T>(tau * tau + (T)1.f);
|
|
T t;
|
|
|
|
if (tau > (T)0.)
|
|
t = (T)1.f / (tau + w);
|
|
else
|
|
t = (T)1.f / (tau - w);
|
|
|
|
T sign = t > (T)0. ? (T)1.f : (T)-1.f;
|
|
|
|
T cos = (T)1.f / math::sd_sqrt<T, T>(t * t + (T)1.f);
|
|
T sin = -sign * (y / math::sd_abs<T,T>(y)) * math::sd_abs<T,T>(t) * cos;
|
|
|
|
rotation.r<T>(0, 1) = sin;
|
|
rotation.r<T>(1, 0) = -sin;
|
|
rotation.r<T>(0, 0) = rotation.r<T>(1, 1) = cos;
|
|
|
|
return true;
|
|
}
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
void JacobiSVD<T>::createJacobiRotationGivens(const T& p, const T& q, NDArray& rotation) {
|
|
T cos, sin;
|
|
|
|
if (q == (T)0) {
|
|
cos = p < (T)0 ? (T)-1 : (T)1;
|
|
sin = (T)0;
|
|
} else if (p == (T)0) {
|
|
cos = (T)0;
|
|
sin = q < (T)0 ? (T)1 : (T)-1;
|
|
} else if (math::sd_abs<T,T>(p) > math::sd_abs<T,T>(q)) {
|
|
T t = q / p;
|
|
T u = math::sd_sqrt<T, T>((T)1 + t * t);
|
|
if (p < (T)0) u = -u;
|
|
cos = (T)1 / u;
|
|
sin = -t * cos;
|
|
} else {
|
|
T t = p / q;
|
|
T u = math::sd_sqrt<T, T>((T)1 + t * t);
|
|
if (q < (T)0) u = -u;
|
|
sin = -(T)1 / u;
|
|
cos = -t * sin;
|
|
}
|
|
|
|
rotation.r<T>(0, 1) = sin;
|
|
rotation.r<T>(1, 0) = -sin;
|
|
rotation.r<T>(0, 0) = rotation.r<T>(1, 1) = cos;
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
void JacobiSVD<T>::svd2x2(NDArray& block, int p, int q, NDArray& left, NDArray& right) {
|
|
std::vector<LongType> shape = {2, 2};
|
|
NDArray m(block.ordering(), shape, block.dataType(), block.getContext());
|
|
m.r<T>(0, 0) = block.t<T>(p, p);
|
|
m.r<T>(0, 1) = block.t<T>(p, q);
|
|
m.r<T>(1, 0) = block.t<T>(q, p);
|
|
m.r<T>(1, 1) = block.t<T>(q, q);
|
|
|
|
NDArray rotation(block.ordering(),shape, block.dataType(), block.getContext());
|
|
T t = m.t<T>(0, 0) + m.t<T>(1, 1);
|
|
T d = m.t<T>(1, 0) - m.t<T>(0, 1);
|
|
|
|
if (math::sd_abs<T,T>(d) < DataTypeUtils::min<T>()) {
|
|
rotation.r<T>(0, 0) = rotation.r<T>(1, 1) = (T)1;
|
|
rotation.r<T>(0, 1) = rotation.r<T>(1, 0) = (T)0;
|
|
} else {
|
|
T u = t / d;
|
|
T tmp = math::sd_sqrt<T, T>((T)1.f + u * u);
|
|
rotation.r<T>(0, 0) = rotation.r<T>(1, 1) = u / tmp;
|
|
rotation.r<T>(0, 1) = (T)1.f / tmp;
|
|
rotation.r<T>(1, 0) = -rotation.t<T>(0, 1);
|
|
}
|
|
NDArray *mAssignResult = mmul(rotation, m);
|
|
m.assign(mAssignResult);
|
|
delete mAssignResult;
|
|
|
|
createJacobiRotation(m.t<T>(0, 0), m.t<T>(0, 1), m.t<T>(1, 1), right);
|
|
NDArray *rightT = right.transpose();
|
|
NDArray *leftAssignResult = mmul(rotation, *rightT);
|
|
left.assign(leftAssignResult);
|
|
delete leftAssignResult;
|
|
delete rightT;
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
void JacobiSVD<T>::evalData(NDArray& matrix) {
|
|
const T precision = (T)2.f * DataTypeUtils::eps<T>();
|
|
const T almostZero = DataTypeUtils::min_positive<T>();
|
|
|
|
auto* scaleResult = matrix.reduceNumber(reduce::AMax);
|
|
T scale = scaleResult->template t<T>(0);
|
|
delete scaleResult;
|
|
if (scale < (T)1.f) scale = (T)1.f;
|
|
|
|
if (_rows > _cols) {
|
|
NDArray *scaled = matrix / scale;
|
|
HHcolPivQR qr(*scaled);
|
|
delete scaled;
|
|
NDArray qrRef = *qr._qr;
|
|
|
|
NDArray *mAssignPtr = qrRef({0, _cols, 0, _cols});
|
|
NDArray mAssign = *mAssignPtr;
|
|
_m.assign(&mAssign);
|
|
delete mAssignPtr;
|
|
|
|
_m.fillAsTriangular<T>(0., 0, 0, _m, 'l',false);
|
|
|
|
HHsequence hhSeg(qr._qr, qr._coeffs, 'u');
|
|
|
|
if (_fullUV)
|
|
hhSeg.applyTo(&_u);
|
|
else if (_calcU) {
|
|
_u.setIdentity();
|
|
hhSeg.mulLeft(&_u);
|
|
}
|
|
|
|
|
|
if (_calcV) _v.assign(qr._permut);
|
|
} else if (_rows < _cols) {
|
|
NDArray *matrixT = matrix.transpose();
|
|
NDArray *scaled = (*matrixT) / scale;
|
|
HHcolPivQR qr(*scaled);
|
|
delete scaled;
|
|
NDArray qrRef = *qr._qr;
|
|
|
|
NDArray *mAssignPtr = qrRef({0, _rows, 0, _rows});
|
|
NDArray mAssign = *mAssignPtr;
|
|
_m.assign(&mAssign);
|
|
delete mAssignPtr;
|
|
|
|
_m.fillAsTriangular<T>(0., 0, 0, _m, 'l',false);
|
|
_m.transposei();
|
|
|
|
HHsequence hhSeg(qr._qr, qr._coeffs, 'u'); // type = 'u' is not mistake here !
|
|
|
|
if (_fullUV)
|
|
hhSeg.applyTo(&_v);
|
|
else if (_calcV) {
|
|
_v.setIdentity();
|
|
hhSeg.mulLeft(&_v);
|
|
}
|
|
|
|
|
|
if (_calcU) _u.assign(qr._permut);
|
|
|
|
delete matrixT;
|
|
} else {
|
|
NDArray *mAssignPtr = matrix({0, _diagSize, 0, _diagSize});
|
|
NDArray *mAssignDiv = (*mAssignPtr) / scale;
|
|
_m.assign(mAssignDiv);
|
|
delete mAssignDiv;
|
|
delete mAssignPtr;
|
|
|
|
if (_calcU) _u.setIdentity();
|
|
|
|
if (_calcV) _v.setIdentity();
|
|
}
|
|
|
|
|
|
T maxDiagElem = static_cast<T>(0.);
|
|
for (int i = 0; i < _diagSize; ++i) {
|
|
T current = math::sd_abs<T,T>(_m.t<T>(i, i));
|
|
if (maxDiagElem < current) maxDiagElem = current;
|
|
}
|
|
|
|
bool stop = false;
|
|
|
|
while (!stop) {
|
|
stop = true;
|
|
|
|
for (int p = 1; p < _diagSize; ++p) {
|
|
for (int q = 0; q < p; ++q) {
|
|
T threshold = math::sd_max<T>(almostZero, precision * maxDiagElem);
|
|
|
|
if (math::sd_abs<T,T>(_m.t<T>(p, q)) > threshold || math::sd_abs<T,T>(_m.t<T>(q, p)) > threshold) {
|
|
stop = false;
|
|
|
|
std::vector<LongType> shape = {2, 2};
|
|
NDArray rotLeft(_m.ordering(), shape, _m.dataType(), _m.getContext());
|
|
NDArray rotRight(_m.ordering(), shape, _m.dataType(), _m.getContext());
|
|
svd2x2(_m, p, q, rotLeft, rotRight);
|
|
|
|
mulRotationOnLeft(p, q, _m, rotLeft);
|
|
NDArray *rotLeftTranspose = rotLeft.transpose();
|
|
if (_calcU) mulRotationOnRight(p, q, _u, *rotLeftTranspose);
|
|
|
|
mulRotationOnRight(p, q, _m, rotRight);
|
|
|
|
if (_calcV) mulRotationOnRight(p, q, _v, rotRight);
|
|
|
|
maxDiagElem = math::sd_max<T>(
|
|
maxDiagElem, math::sd_max<T>(math::sd_abs<T,T>(_m.t<T>(p, p)), math::sd_abs<T,T>(_m.t<T>(q, q))));
|
|
|
|
delete rotLeftTranspose;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
for (int i = 0; i < _diagSize; ++i) {
|
|
_s.r<T>(i) = math::sd_abs<T,T>(_m.t<T>(i, i));
|
|
|
|
if (_calcU && _m.t<T>(i, i) < (T)0.) {
|
|
NDArray *tempPtr = _u({0, 0, i, i + 1}, true);
|
|
NDArray temp = *tempPtr;
|
|
temp.applyTransform(transform::Neg, &temp, nullptr);
|
|
delete tempPtr;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
_s *= scale;
|
|
for (int i = 0; i < _diagSize; i++) {
|
|
NDArray *sSlicePtr = _s({i, -1, 0, 0});
|
|
NDArray sSlice = *sSlicePtr;
|
|
|
|
NDArray *indexNum = sSlice.indexReduceNumber(indexreduce::IndexMax, nullptr);
|
|
int pos = indexNum->template e<int>(0);
|
|
auto* maxResult = sSlice.reduceNumber(reduce::Max);
|
|
T maxSingVal = maxResult->template t<T>(0);
|
|
delete maxResult;
|
|
|
|
delete sSlicePtr;
|
|
delete indexNum;
|
|
|
|
if (maxSingVal == (T)0.) break;
|
|
|
|
if (pos) {
|
|
pos += i;
|
|
|
|
math::sd_swap<T>(_s.r<T>(i), _s.r<T>(pos));
|
|
|
|
if (_calcU) {
|
|
NDArray *temp1Ptr = _u({0, 0, pos, pos + 1}, true);
|
|
NDArray temp1 = *temp1Ptr;
|
|
|
|
NDArray *temp2Ptr = _u({0, 0, i, i + 1}, true);
|
|
NDArray temp2 = *temp2Ptr;
|
|
|
|
temp1.swapUnsafe(temp2);
|
|
|
|
delete temp1Ptr;
|
|
delete temp2Ptr;
|
|
}
|
|
|
|
if (_calcV) {
|
|
NDArray *temp1Ptr = _v({0, 0, pos, pos + 1}, true);
|
|
NDArray temp1 = *temp1Ptr;
|
|
|
|
NDArray *temp2Ptr = _v({0, 0, i, i + 1}, true);
|
|
NDArray temp2 = *temp2Ptr;
|
|
|
|
temp1.swapUnsafe(temp2);
|
|
|
|
delete temp1Ptr;
|
|
delete temp2Ptr;
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
BUILD_SINGLE_TEMPLATE( class JacobiSVD, , SD_FLOAT_TYPES);
|
|
|
|
} // namespace helpers
|
|
} // namespace ops
|
|
} // namespace sd
|
|
|
|
#endif
|