/usr/include/simbody/SimTKcommon/internal/VectorMath.h is in libsimbody-dev 3.5.4+dfsg-1ubuntu2.
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#define SimTK_SimTKCOMMON_VECTOR_MATH_H_
/* -------------------------------------------------------------------------- *
* Simbody(tm): SimTKcommon *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2008-12 Stanford University and the Authors. *
* Authors: Peter Eastman *
* Contributors: Michael Sherman *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may *
* not use this file except in compliance with the License. You may obtain a *
* copy of the License at http://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. *
* -------------------------------------------------------------------------- */
#include "SimTKcommon/basics.h"
#include "SimTKcommon/Simmatrix.h"
#include <cmath> // for std:sin, sqrt, etc.
#include <algorithm> // for std:sort, nth_element, etc.
/** @file
* This file defines a large number of standard math functions that can be
* applied to vectors and matrices (both the large matrix and small matrix
* classes).
*/
namespace SimTK {
// We can use a single definition for a number of functions that simply call a
// function on each element, returning a value of the same type.
// Note that some of these intentionally copy their argument for use as a temp.
#define SimTK_ELEMENTWISE_FUNCTION(func) \
template <class ELEM> \
VectorBase<ELEM> func(const VectorBase<ELEM>& v) { \
const int size = v.size(); \
Vector_<ELEM> temp(size); \
for (int i = 0; i < size; ++i) \
temp[i] = std::func(v[i]); \
return temp; \
} \
template <class ELEM> \
RowVectorBase<ELEM> func(const RowVectorBase<ELEM>& v){\
const int size = v.size(); \
RowVector_<ELEM> temp(size); \
for (int i = 0; i < size; ++i) \
temp[i] = std::func(v[i]); \
return temp; \
} \
template <class ELEM> \
MatrixBase<ELEM> func(const MatrixBase<ELEM>& v) { \
const int rows = v.nrow(), cols = v.ncol(); \
Matrix_<ELEM> temp(rows, cols); \
for (int i = 0; i < rows; ++i) \
for (int j = 0; j < cols; ++j) \
temp(i, j) = std::func(v(i, j)); \
return temp; \
} \
template <int N, class ELEM> \
Vec<N, ELEM> func(Vec<N, ELEM> v) { \
for (int i = 0; i < N; ++i) \
v[i] = std::func(v[i]); \
return v; \
} \
template <int N, class ELEM> \
Row<N, ELEM> func(Row<N, ELEM> v) { \
for (int i = 0; i < N; ++i) \
v[i] = std::func(v[i]); \
return v; \
} \
template <int M, int N, class ELEM> \
Mat<M, N, ELEM> func(Mat<M, N, ELEM> v) { \
for (int i = 0; i < M; ++i) \
for (int j = 0; j < N; ++j) \
v(i, j) = std::func(v(i, j)); \
return v; \
} \
template <int N, class ELEM> \
SymMat<N, ELEM> func(SymMat<N, ELEM> v) { \
for (int i = 0; i < N; ++i) \
for (int j = 0; j <= i; ++j) \
v(i, j) = std::func(v(i, j)); \
return v; \
} \
SimTK_ELEMENTWISE_FUNCTION(exp)
SimTK_ELEMENTWISE_FUNCTION(log)
SimTK_ELEMENTWISE_FUNCTION(sqrt)
SimTK_ELEMENTWISE_FUNCTION(sin)
SimTK_ELEMENTWISE_FUNCTION(cos)
SimTK_ELEMENTWISE_FUNCTION(tan)
SimTK_ELEMENTWISE_FUNCTION(asin)
SimTK_ELEMENTWISE_FUNCTION(acos)
SimTK_ELEMENTWISE_FUNCTION(atan)
SimTK_ELEMENTWISE_FUNCTION(sinh)
SimTK_ELEMENTWISE_FUNCTION(cosh)
SimTK_ELEMENTWISE_FUNCTION(tanh)
#undef SimTK_ELEMENTWISE_FUNCTION
// The abs() function.
template <class ELEM>
VectorBase<typename CNT<ELEM>::TAbs> abs(const VectorBase<ELEM>& v) {
return v.abs();
}
template <class ELEM>
RowVectorBase<typename CNT<ELEM>::TAbs> abs(const RowVectorBase<ELEM>& v) {
return v.abs();
}
template <class ELEM>
MatrixBase<typename CNT<ELEM>::TAbs> abs(const MatrixBase<ELEM>& v) {
return v.abs();
}
template <int N, class ELEM>
Vec<N, typename CNT<ELEM>::TAbs> abs(const Vec<N, ELEM>& v) {
return v.abs();
}
template <int N, class ELEM>
Row<N, typename CNT<ELEM>::TAbs> abs(const Row<N, ELEM>& v) {
return v.abs();
}
template <int M, int N, class ELEM>
Mat<M, N, typename CNT<ELEM>::TAbs> abs(const Mat<M, N, ELEM>& v) {
return v.abs();
}
template <int N, class ELEM>
SymMat<N, typename CNT<ELEM>::TAbs> abs(const SymMat<N, ELEM>& v) {
return v.abs();
}
// The sum() function.
template <class ELEM>
ELEM sum(const VectorBase<ELEM>& v) {
return v.sum();
}
template <class ELEM>
ELEM sum(const RowVectorBase<ELEM>& v) {
return v.sum();
}
template <class ELEM>
RowVectorBase<ELEM> sum(const MatrixBase<ELEM>& v) {
return v.sum();
}
template <int N, class ELEM>
ELEM sum(const Vec<N, ELEM>& v) {
return v.sum();
}
template <int N, class ELEM>
ELEM sum(const Row<N, ELEM>& v) {
return v.sum();
}
template <int M, int N, class ELEM>
Row<N, ELEM> sum(const Mat<M, N, ELEM>& v) {
return v.sum();
}
template <int N, class ELEM>
Row<N, ELEM> sum(const SymMat<N, ELEM>& v) {
return v.sum();
}
// The min() function.
template <class ELEM>
ELEM min(const VectorBase<ELEM>& v) {
const int size = v.size();
ELEM min = NTraits<ELEM>::getMostPositive();
for (int i = 0; i < size; ++i) {
ELEM val = v[i];
if (val < min)
min = val;
}
return min;
}
template <class ELEM>
ELEM min(const RowVectorBase<ELEM>& v) {
const int size = v.size();
ELEM min = NTraits<ELEM>::getMostPositive();
for (int i = 0; i < size; ++i) {
ELEM val = v[i];
if (val < min)
min = val;
}
return min;
}
template <class ELEM>
RowVectorBase<ELEM> min(const MatrixBase<ELEM>& v) {
int cols = v.ncol();
RowVectorBase<ELEM> temp(cols);
for (int i = 0; i < cols; ++i)
temp[i] = min(v(i));
return temp;
}
template <int N, class ELEM>
ELEM min(const Vec<N, ELEM>& v) {
ELEM min = NTraits<ELEM>::getMostPositive();
for (int i = 0; i < N; ++i) {
ELEM val = v[i];
if (val < min)
min = val;
}
return min;
}
template <int N, class ELEM>
ELEM min(const Row<N, ELEM>& v) {
ELEM min = NTraits<ELEM>::getMostPositive();
for (int i = 0; i < N; ++i) {
ELEM val = v[i];
if (val < min)
min = val;
}
return min;
}
template <int M, int N, class ELEM>
Row<N, ELEM> min(const Mat<M, N, ELEM>& v) {
Row<N, ELEM> temp;
for (int i = 0; i < N; ++i)
temp[i] = min(v(i));
return temp;
}
template <int N, class ELEM>
Row<N, ELEM> min(const SymMat<N, ELEM>& v) {
Row<N, ELEM> temp(~v.getDiag());
for (int i = 1; i < N; ++i)
for (int j = 0; j < i; ++j) {
ELEM value = v.getEltLower(i, j);
if (value < temp[i])
temp[i] = value;
if (value < temp[j])
temp[j] = value;
}
return temp;
}
// The max() function.
template <class ELEM>
ELEM max(const VectorBase<ELEM>& v) {
const int size = v.size();
ELEM max = NTraits<ELEM>::getMostNegative();
for (int i = 0; i < size; ++i) {
ELEM val = v[i];
if (val > max)
max = val;
}
return max;
}
template <class ELEM>
ELEM max(const RowVectorBase<ELEM>& v) {
const int size = v.size();
ELEM max = NTraits<ELEM>::getMostNegative();
for (int i = 0; i < size; ++i) {
ELEM val = v[i];
if (val > max)
max = val;
}
return max;
}
template <class ELEM>
RowVectorBase<ELEM> max(const MatrixBase<ELEM>& v) {
int cols = v.ncol();
RowVectorBase<ELEM> temp(cols);
for (int i = 0; i < cols; ++i)
temp[i] = max(v(i));
return temp;
}
template <int N, class ELEM>
ELEM max(const Vec<N, ELEM>& v) {
ELEM max = NTraits<ELEM>::getMostNegative();
for (int i = 0; i < N; ++i) {
ELEM val = v[i];
if (val > max)
max = val;
}
return max;
}
template <int N, class ELEM>
ELEM max(const Row<N, ELEM>& v) {
ELEM max = NTraits<ELEM>::getMostNegative();
for (int i = 0; i < N; ++i) {
ELEM val = v[i];
if (val > max)
max = val;
}
return max;
}
template <int M, int N, class ELEM>
Row<N, ELEM> max(const Mat<M, N, ELEM>& v) {
Row<N, ELEM> temp;
for (int i = 0; i < N; ++i)
temp[i] = max(v(i));
return temp;
}
template <int N, class ELEM>
Row<N, ELEM> max(const SymMat<N, ELEM>& v) {
Row<N, ELEM> temp(~v.getDiag());
for (int i = 1; i < N; ++i)
for (int j = 0; j < i; ++j) {
ELEM value = v.getEltLower(i, j);
if (value > temp[i])
temp[i] = value;
if (value > temp[j])
temp[j] = value;
}
return temp;
}
// The mean() function.
template <class ELEM>
ELEM mean(const VectorBase<ELEM>& v) {
return sum(v)/v.size();
}
template <class ELEM>
ELEM mean(const RowVectorBase<ELEM>& v) {
return sum(v)/v.size();
}
template <class ELEM>
RowVectorBase<ELEM> mean(const MatrixBase<ELEM>& v) {
return sum(v)/v.nrow();
}
template <int N, class ELEM>
ELEM mean(const Vec<N, ELEM>& v) {
return sum(v)/N;
}
template <int N, class ELEM>
ELEM mean(const Row<N, ELEM>& v) {
return sum(v)/N;
}
template <int M, int N, class ELEM>
Row<N, ELEM> mean(const Mat<M, N, ELEM>& v) {
return sum(v)/M;
}
template <int N, class ELEM>
Row<N, ELEM> mean(const SymMat<N, ELEM>& v) {
return sum(v)/N;
}
// The sort() function.
template <class ELEM>
VectorBase<ELEM> sort(const VectorBase<ELEM>& v) {
VectorBase<ELEM> temp(v);
std::sort(temp.begin(), temp.end());
return temp;
}
template <class ELEM>
RowVectorBase<ELEM> sort(const RowVectorBase<ELEM>& v) {
RowVectorBase<ELEM> temp(v);
std::sort(temp.begin(), temp.end());
return temp;
}
template <class ELEM>
MatrixBase<ELEM> sort(const MatrixBase<ELEM>& v) {
const int cols = v.ncol();
MatrixBase<ELEM> temp(v);
for (int i = 0; i < cols; ++i)
temp.updCol(i) = sort(temp.col(i));
return temp;
}
template <int N, class ELEM>
Vec<N, ELEM> sort(Vec<N, ELEM> v) { // intentional copy of argument
ELEM* pointer = reinterpret_cast<ELEM*>(&v);
std::sort(pointer, pointer+N);
return v;
}
template <int N, class ELEM>
Row<N, ELEM> sort(Row<N, ELEM> v) { // intentional copy of argument
ELEM* pointer = reinterpret_cast<ELEM*>(&v);
std::sort(pointer, pointer+N);
return v;
}
template <int M, int N, class ELEM>
Mat<M, N, ELEM> sort(Mat<M, N, ELEM> v) { // intentional copy of argument
for (int i = 0; i < N; ++i)
v.col(i) = sort(v.col(i));
return v;
}
template <int N, class ELEM>
Mat<N, N, ELEM> sort(const SymMat<N, ELEM>& v) {
return sort(Mat<N, N, ELEM>(v));
}
// The median() function.
template <class ELEM, class RandomAccessIterator>
ELEM median(RandomAccessIterator start, RandomAccessIterator end) {
const ptrdiff_t size = (ptrdiff_t)(end-start);
RandomAccessIterator mid = start+(size-1)/2;
std::nth_element(start, mid, end);
if (size%2 == 0 && mid+1 < end) {
// An even number of element. The median is the mean of the two middle elements.
// nth_element has given us the first of them and partially sorted the list.
// We need to scan through the rest of the list and find the next element in
// sorted order.
RandomAccessIterator min = mid+1;
for (RandomAccessIterator iter = mid+1; iter < end; iter++) {
if (*iter < *min)
min = iter;
}
return (*mid+*min)/2;
}
return *mid;
}
template <class ELEM>
ELEM median(const VectorBase<ELEM>& v) {
VectorBase<ELEM> temp(v);
return median<ELEM>(temp.begin(), temp.end());
}
template <class ELEM>
ELEM median(const RowVectorBase<ELEM>& v) {
RowVectorBase<ELEM> temp(v);
return median<ELEM>(temp.begin(), temp.end());
}
template <class ELEM>
RowVectorBase<ELEM> median(const MatrixBase<ELEM>& v) {
int cols = v.ncol(), rows = v.nrow();
RowVectorBase<ELEM> temp(cols);
VectorBase<ELEM> column(rows);
for (int i = 0; i < cols; ++i) {
column = v.col(i);
temp[i] = median<ELEM>(column);
}
return temp;
}
template <int N, class ELEM>
ELEM median(Vec<N, ELEM> v) { // intentional copy of argument
ELEM* pointer = reinterpret_cast<ELEM*>(&v);
return median<ELEM>(pointer, pointer+N);
}
template <int N, class ELEM>
ELEM median(Row<N, ELEM> v) { // intentional copy of argument
ELEM* pointer = reinterpret_cast<ELEM*>(&v);
return median<ELEM>(pointer, pointer+N);
}
template <int M, int N, class ELEM>
Row<N, ELEM> median(const Mat<M, N, ELEM>& v) {
Row<N, ELEM> temp;
for (int i = 0; i < N; ++i)
temp[i] = median(v(i));
return temp;
}
template <int N, class ELEM>
Row<N, ELEM> median(const SymMat<N, ELEM>& v) {
return median(Mat<N, N, ELEM>(v));
}
} // namespace SimTK
#endif // SimTK_SimTKCOMMON_VECTOR_MATH_H_
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