cavis/libnd4j/include/helpers/cpu/jacobiSVD.cpp

436 lines
13 KiB
C++

/*******************************************************************************
* 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 11.01.2018
//
#include <jacobiSVD.h>
#include <hhColPivQR.h>
#include <NDArrayFactory.h>
namespace nd4j {
namespace ops {
namespace helpers {
//////////////////////////////////////////////////////////////////////////
template <typename T>
JacobiSVD<T>::JacobiSVD(const NDArray& matrix, const bool calcU, const bool calcV, const bool fullUV) {
if(matrix.rankOf() != 2 || matrix.isScalar())
throw std::runtime_error("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::nd4j_min<int>(_rows, _cols);
_calcU = calcU;
_calcV = calcV;
_fullUV = fullUV;
_s = NDArrayFactory::create(matrix.ordering(), {_diagSize, 1}, matrix.dataType(), matrix.getContext());
if(_calcU) {
if(_fullUV)
_u = NDArrayFactory::create(matrix.ordering(), {_rows, _rows}, matrix.dataType(), matrix.getContext());
else
_u = NDArrayFactory::create(matrix.ordering(), {_rows, _diagSize}, matrix.dataType(), matrix.getContext());
}
else
_u = NDArrayFactory::create(matrix.ordering(), {_rows, 1}, matrix.dataType(), matrix.getContext());
if(_calcV) {
if(_fullUV)
_v = NDArrayFactory::create(matrix.ordering(), {_cols, _cols}, matrix.dataType(), matrix.getContext());
else
_v = NDArrayFactory::create(matrix.ordering(), {_cols, _diagSize}, matrix.dataType(), matrix.getContext());
}
else
_v = NDArrayFactory::create(matrix.ordering(), {_cols, 1}, matrix.dataType(), matrix.getContext());
_m = NDArrayFactory::create(matrix.ordering(), {_diagSize, _diagSize}, matrix.dataType(), matrix.getContext());
evalData(matrix);
}
//////////////////////////////////////////////////////////////////////////
template <typename T>
void JacobiSVD<T>::mulRotationOnLeft(const int i, const int j, NDArray& block, const NDArray& rotation) {
if(i < j) {
if(j+1 > block.sizeAt(0))
throw std::runtime_error("ops::helpers::JacobiSVD mulRotationOnLeft: second arguments is out of array row range !");
auto pTemp = block({i,j+1,j-i, 0,0,0}, true, true);
auto temp = pTemp;
pTemp.assign(mmul(rotation, temp));
}
else {
if(j+1 > block.sizeAt(0) || i+1 > block.sizeAt(0))
throw std::runtime_error("ops::helpers::JacobiSVD mulRotationOnLeft: some or both integer arguments are out of array row range !");
auto temp = NDArrayFactory::create(block.ordering(), {2, block.sizeAt(1)}, block.dataType(), block.getContext());
auto row1 = block({i,i+1, 0,0}, true);
auto row2 = block({j,j+1, 0,0}, true);
auto rowTemp1 = temp({0,1, 0,0}, true);
auto rowTemp2 = temp({1,2, 0,0}, true);
rowTemp1.assign(row1);
rowTemp2.assign(row2);
temp.assign(mmul(rotation, temp));
row1.assign(rowTemp1);
row2.assign(rowTemp2);
}
}
//////////////////////////////////////////////////////////////////////////
template <typename T>
void JacobiSVD<T>::mulRotationOnRight(const int i, const int j, NDArray& block, const NDArray& rotation) {
if(i < j) {
if(j+1 > block.sizeAt(1))
throw std::runtime_error("ops::helpers::JacobiSVD mulRotationOnRight: second argument is out of array column range !");
auto pTemp = block({0,0,0, i,j+1,j-i}, true, true);
auto temp = pTemp;
pTemp.assign(mmul(temp, rotation));
}
else {
if(j+1 > block.sizeAt(1) || i+1 > block.sizeAt(1))
throw std::runtime_error("ops::helpers::JacobiSVD mulRotationOnRight: some or both integer arguments are out of array column range !");
auto temp = NDArrayFactory::create(block.ordering(), {block.sizeAt(0), 2}, block.dataType(), block.getContext());
auto col1 = block({0,0, i,i+1}, true);
auto col2 = block({0,0, j,j+1}, true);
auto colTemp1 = temp({0,0, 0,1}, true);
auto colTemp2 = temp({0,0, 1,2}, true);
colTemp1.assign(col1);
colTemp2.assign(col2);
temp.assign(mmul(temp, rotation));
col1.assign(colTemp1);
col2.assign(colTemp2);
}
}
//////////////////////////////////////////////////////////////////////////
template <typename T>
bool JacobiSVD<T>::isBlock2x2NotDiag(NDArray& block, int p, int q, T& maxElem) {
auto rotation = NDArrayFactory::create(_m.ordering(), {2, 2}, _m.dataType(), _m.getContext());
T n = math::nd4j_sqrt<T,T>(block.e<T>(p,p) * block.e<T>(p,p) + block.e<T>(q,p) * block.e<T>(q,p));
const T almostZero = DataTypeUtils::min<T>();
const T precision = DataTypeUtils::eps<T>();
if(n == (T)0.f) {
block.p(p, p, 0.f);
block.p(q, p, 0.f);
} else {
T v = block.e<T>(p, p) / n;
rotation.p(0, 0, v);
rotation.p(1,1, v);
v = block.e<T>(q,p) / n;
rotation.p(0, 1, v);
rotation.p(1,0, -rotation.template e<T>(0, 1));
mulRotationOnLeft(p, q, block, rotation);
if(_calcU) {
auto temp2 = rotation.transpose();
mulRotationOnRight(p, q, _u, *temp2);
delete temp2;
}
}
maxElem = math::nd4j_max<T>(maxElem, math::nd4j_max<T>(math::nd4j_abs<T>(block.e<T>(p,p)), math::nd4j_abs<T>(block.e<T>(q,q))));
T threshold = math::nd4j_max<T>(almostZero, precision * maxElem);
const bool condition1 = math::nd4j_abs<T>(block.e<T>(p,q)) > threshold;
const bool condition2 = math::nd4j_abs<T>(block.e<T>(q,p)) > threshold;
return condition1 || condition2;
}
//////////////////////////////////////////////////////////////////////////
template <typename T>
bool JacobiSVD<T>::createJacobiRotation(const T& x, const T& y, const T& z, NDArray& rotation) {
T denom = 2.* math::nd4j_abs<T>(y);
if(denom < DataTypeUtils::min<T>()) {
rotation.p(0,0, 1.f);
rotation.p(1,1, 1.f);
rotation.p(0,1, 0.f);
rotation.p(1,0, 0.f);
return false;
}
else {
T tau = (x-z)/denom;
T w = math::nd4j_sqrt<T,T>(tau*tau + 1.);
T t;
if(tau > (T)0.)
t = 1. / (tau + w);
else
t = 1. / (tau - w);
T sign = t > (T)0. ? 1. : -1.;
T n = 1. / math::nd4j_sqrt<T,T>(t*t + 1.f);
rotation.p(0,0, n);
rotation.p(1,1, n);
rotation.p(0,1, -sign * (y / math::nd4j_abs<T>(y)) * math::nd4j_abs<T>(t) * n);
rotation.p(1,0, -rotation.e<T>(0,1));
return true;
}
}
//////////////////////////////////////////////////////////////////////////
template <typename T>
void JacobiSVD<T>::svd2x2(const NDArray& block, int p, int q, NDArray& left, NDArray& right) {
auto m = NDArrayFactory::create(block.ordering(), {2, 2}, block.dataType(), block.getContext());
m.p<T>(0,0, block.e<T>(p,p));
m.p<T>(0,1, block.e<T>(p,q));
m.p<T>(1,0, block.e<T>(q,p));
m.p<T>(1,1, block.e<T>(q,q));
auto rotation = NDArrayFactory::create(block.ordering(), {2, 2}, block.dataType(), block.getContext());
T t = m.e<T>(0,0) + m.e<T>(1,1);
T d = m.e<T>(1,0) - m.e<T>(0,1);
if(math::nd4j_abs<T>(d) < DataTypeUtils::min<T>()) {
rotation.p(0,0, 1.f);
rotation.p(1,1, 1.f);
rotation.p(0,1, 0.f);
rotation.p(1,0, 0.f);
}
else {
T u = t / d;
T tmp = math::nd4j_sqrt<T,T>(1. + u*u);
rotation.p(0,0, u / tmp);
rotation.p(1,1, u / tmp);
rotation.p(0,1, 1.f / tmp);
rotation.p(1,0, -rotation.e<T>(0,1));
}
m.assign(mmul(rotation, m));
auto _x = m.e<T>(0,0);
auto _y = m.e<T>(0,1);
auto _z = m.e<T>(1,1);
createJacobiRotation(_x, _y, _z, right);
m.p<T>(0, 0, _x);
m.p<T>(0, 1, _y);
m.p<T>(1, 1, _z);
auto temp = right.transpose();
left.assign(mmul(rotation, *temp));
delete temp;
}
//////////////////////////////////////////////////////////////////////////
template <typename T>
void JacobiSVD<T>::evalData(const NDArray& matrix) {
const T precision = (T)2.f * DataTypeUtils::eps<T>();
const T almostZero = DataTypeUtils::min<T>();
T scale = matrix.reduceNumber(reduce::AMax).e<T>(0);
if(scale== (T)0.f)
scale = (T)1.f;
if(_rows > _cols) {
HHcolPivQR qr(matrix / scale);
_m.assign(qr._qr({0,_cols, 0,_cols}));
_m.fillAsTriangular<T>(0., 0, 0, 'l');
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) {
auto matrixT = matrix.transpose();
HHcolPivQR qr(*matrixT / scale);
_m.assign(qr._qr({0,_rows, 0,_rows}));
_m.fillAsTriangular<T>(0., 0, 0, 'l');
_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 {
_m.assign(matrix({0,_diagSize, 0,_diagSize}) / scale);
if(_calcU)
_u.setIdentity();
if(_calcV)
_v.setIdentity();
}
T maxDiagElem = 0.;
for(int i = 0; i < _diagSize; ++i) {
T current = math::nd4j_abs<T>(_m.e<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::nd4j_max<T>(almostZero, precision * maxDiagElem);
if(math::nd4j_abs<T>(_m.e<T>(p,q)) > threshold || math::nd4j_abs<T>(_m.e<T>(q,p)) > threshold){
stop = false;
// if(isBlock2x2NotDiag(_m, p, q, maxDiagElem))
{
auto rotLeft = NDArrayFactory::create(_m.ordering(), {2, 2}, _m.dataType(), _m.getContext());
auto rotRight = NDArrayFactory::create(_m.ordering(), {2, 2}, _m.dataType(), _m.getContext());
svd2x2(_m, p, q, rotLeft, rotRight);
mulRotationOnLeft(p, q, _m, rotLeft);
if(_calcU) {
auto temp = rotLeft.transpose();
mulRotationOnRight(p, q, _u, *temp);
delete temp;
}
mulRotationOnRight(p, q, _m, rotRight);
if(_calcV)
mulRotationOnRight(p, q, _v, rotRight);
maxDiagElem = math::nd4j_max<T>(maxDiagElem, math::nd4j_max<T>(math::nd4j_abs<T>(_m.e<T>(p,p)), math::nd4j_abs<T>(_m.e<T>(q,q))));
}
}
}
}
}
for(int i = 0; i < _diagSize; ++i) {
_s.p(i, math::nd4j_abs<T>(_m.e<T>(i,i)));
if(_calcU && _m.e<T>(i,i) < (T)0.) {
auto temp = _u({0,0, i,i+1}, true);
temp.applyTransform(transform::Neg, &temp, nullptr);
}
}
_s *= scale;
for(int i = 0; i < _diagSize; i++) {
int pos = (_s({i,-1, 0,0}).indexReduceNumber(indexreduce::IndexMax, nullptr)).template e<int>(0);
T maxSingVal = _s({i,-1, 0,0}).reduceNumber(reduce::Max).template e<T>(0);
if(maxSingVal == (T)0.)
break;
if(pos) {
pos += i;
T _e0 = _s.e<T>(i);
T _e1 = _s.e<T>(pos);
_s.p(pos, _e0);
_s.p(i, _e1);
//math::nd4j_swap<T>(_s(i), _s(pos));
if(_calcU) {
auto temp1 = _u({0,0, pos,pos+1}, true);
auto temp2 = _u({0,0, i,i+1}, true);
auto temp3 = temp1;
temp1.assign(temp2);
temp2.assign(temp3);
}
if(_calcV) {
auto temp1 = _v({0,0, pos, pos+1}, true);
auto temp2 = _v({0,0, i, i+1}, true);
auto temp3 = temp1;
temp1.assign(temp2);
temp2.assign(temp3);
}
}
}
}
template class ND4J_EXPORT JacobiSVD<float>;
template class ND4J_EXPORT JacobiSVD<float16>;
template class ND4J_EXPORT JacobiSVD<bfloat16>;
template class ND4J_EXPORT JacobiSVD<double>;
}
}
}