1) C++信号处理库 SP++
2)线性算术的C++模板库 Eigen
3)C 科学计算库 GSL
https://my.oschina.net/zmjerry/blog/13049,sp++ 用啥调啥,模板设计如kalman filter
https://my.oschina.net/zmjerry/blog/8517
Kalman滤波算法的C++实现
/*
* Copyright (c) 2008-2011 Zhang Ming (M. Zhang), zmjerry@163.com
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation, either version 2 or any later version.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* This program is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
* more details. A copy of the GNU General Public License is available at:
* http://www.fsf.org/licensing/licenses
*/
/*****************************************************************************
* kalman.h
*
* Kalman Filter.
*
* The Kalman filter is an efficient recursive filter that estimates the
* internal state of a linear dynamic system from a series of noisy
* measurements. In most applications, the internal state is much larger
* (more degrees of freedom) than the few "observable" parameters which are
* measured. However, by combining a series of measurements, the Kalman
* filter can estimate the entire internal state.
*
* A wide variety of Kalman filters have now been developed, from Kalman's
* original formulation, now called the simple Kalman filter, the Kalman-Bucy
* filter, Schmidt's extended filter, the information filter, and a variety
* of square-root filters that were developed by Bierman, Thornton and so on.
*
* Zhang Ming, 2010-10, Xi'an Jiaotong University.
*****************************************************************************/
#ifndef KALMAN_H
#define KALMAN_H
#include <vector.h>
#include <matrix.h>
#include <inverse.h>
namespace splab
{
template<typename Type>
Vector<Type> kalman( const Matrix<Type>&, const Matrix<Type>&,
const Matrix<Type>&, const Matrix<Type>&,
const Vector<Type>&, const Vector<Type>&,
const Vector<Type>& );
#include <kalman-impl.h>
}
// namespace splab
#endif
// KALMAN_H
实现文件:
/*
* Copyright (c) 2008-2011 Zhang Ming (M. Zhang), zmjerry@163.com
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation, either version 2 or any later version.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* This program is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
* more details. A copy of the GNU General Public License is available at:
* http://www.fsf.org/licensing/licenses
*/
/*****************************************************************************
* kalman-impl.h
*
* Implementation for Kalman Filter.
*
* Zhang Ming, 2010-10, Xi'an Jiaotong University.
*****************************************************************************/
/**
* The simple Kalman filter for one step.
* A ---> system matrix defining linear dynamic system
* C ---> measurement matrix defining relationship between system's state
* and measurements
* Q ---> covariance matrix of process noise in system state dynamics
* R ---> covariance matrix of measurements uncertainty
* y ---> measurements at time t
* xPrev ---> previous estimated state vector of the linear dynamic system
* initDiagV ---> diagonal vector for initializing the covariance matrix of
* state estimation uncertainty
*/
template <typename Type>
Vector<Type> kalman( const Matrix<Type> &A, const Matrix<Type> &C,
const Matrix<Type> &Q, const Matrix<Type> &R,
const Vector<Type> &xPrev, const Vector<Type> &y,
const Vector<Type> &initDiagV )
{
int N = xPrev.size();
// covariance matrix of state estimation uncertainty
static Matrix<Type> V = diag(initDiagV);
// previoused state vector
Vector<Type> xPred = A * xPrev;
// inovation
Vector<Type> alpha = y - C * xPred;
Matrix<Type> CTran = trT( C );
Matrix<Type> VPred = A*V*trT(A) + Q;
// Kalman gain matrix
Matrix<Type> KGain = VPred*CTran * inv(C*VPred*CTran+R);
V = ( eye(N,Type(1.0)) - KGain*C ) * VPred;
// return the estimation of the state vector
return xPred + KGain * alpha;
}
测试代码:
/*****************************************************************************
* kalman.h
*
* Kalman filter testing.
*
* Zhang Ming, 2010-10, Xi'an Jiaotong University.
*****************************************************************************/
#define BOUNDS_CHECK
#include <iostream>
#include <kalman.h>
using namespace std;
using namespace splab;
typedef double Type;
const int N = 2;
const int M = 2;
const int T = 20;
int main()
{
Matrix<Type> A(N,N), C(M,N), Q(N,N), R(M,M);
A = eye( N, Type(1.0) ); C = eye( N, Type(1.0) );
Q = eye( N, Type(1.0) ); R = eye( N, Type(2.0) );
Vector<Type> x(N,Type(1.0)), y(M), ytInit(M);
ytInit[0] = Type(0.5); ytInit[1] = Type(2.0);
Matrix<Type> yt(M,T);
for( int t=0; t<T; ++t )
yt.setColumn( ytInit, t );
Vector<Type> intV( N, Type(10.0) );
for( int t=0; t<T; ++t )
{
y = yt.getColumn(t);
x = kalman( A, C, Q, R, x, y, intV );
cout << "Estimation of xt at the " << t << "th iteratin: " << x << endl;
}
cout << "The theoretical xt should converge to: " << ytInit << endl;
return 0;
}
运行结果:
2) Eigen
https://www.cnblogs.com/python27/p/EigenQuickRef.html
C++矩阵库 Eigen 快速入门
最近需要用 C++ 做一些数值计算,之前一直采用Matlab 混合编程的方式处理矩阵运算,非常麻烦,直到发现了 Eigen 库,简直相见恨晚,好用哭了。 Eigen 是一个基于C++模板的线性代数库,直接将库下载后放在项目目录下,然后包含头文件就能使用,非常方便。此外,Eigen的接口清晰,稳定高效。唯一的问题是之前一直用 Matlab,对 Eigen 的 API 接口不太熟悉,如果能有 Eigen 和 Matlab 对应的说明想必是极好的,终于功夫不负有心人,让我找到了,原文在这里,不过排版有些混乱,我将其重新整理了一下,方便日后查询。
Eigen 矩阵定义
#include <Eigen/Dense>
Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d.
Matrix<double, 3, Dynamic> B; // Fixed rows, dynamic cols.
Matrix<double, Dynamic, Dynamic> C; // Full dynamic. Same as MatrixXd.
Matrix<double, 3, 3, RowMajor> E; // Row major; default is column-major.
Matrix3f P, Q, R; // 3x3 float matrix.
Vector3f x, y, z; // 3x1 float matrix.
RowVector3f a, b, c; // 1x3 float matrix.
VectorXd v; // Dynamic column vector of doubles
// Eigen // Matlab // comments
x.size() // length(x) // vector size
C.rows() // size(C,1) // number of rows
C.cols() // size(C,2) // number of columns
x(i) // x(i+1) // Matlab is 1-based
C(i,j) // C(i+1,j+1) //
Eigen 基础使用
// Basic usage
// Eigen // Matlab // comments
x.size() // length(x) // vector size
C.rows() // size(C,1) // number of rows
C.cols() // size(C,2) // number of columns
x(i) // x(i+1) // Matlab is 1-based
C(i, j) // C(i+1,j+1) //
A.resize(4, 4); // Runtime error if assertions are on.
B.resize(4, 9); // Runtime error if assertions are on.
A.resize(3, 3); // Ok; size didn't change.
B.resize(3, 9); // Ok; only dynamic cols changed.
A << 1, 2, 3, // Initialize A. The elements can also be
4, 5, 6, // matrices, which are stacked along cols
7, 8, 9; // and then the rows are stacked.
B << A, A, A; // B is three horizontally stacked A's.
A.fill(10); // Fill A with all 10's.
Eigen 特殊矩阵生成
// Eigen // Matlab
MatrixXd::Identity(rows,cols) // eye(rows,cols)
C.setIdentity(rows,cols) // C = eye(rows,cols)
MatrixXd::Zero(rows,cols) // zeros(rows,cols)
C.setZero(rows,cols) // C = ones(rows,cols)
MatrixXd::Ones(rows,cols) // ones(rows,cols)
C.setOnes(rows,cols) // C = ones(rows,cols)
MatrixXd::Random(rows,cols) // rand(rows,cols)*2-1 // MatrixXd::Random returns uniform random numbers in (-1, 1).
C.setRandom(rows,cols) // C = rand(rows,cols)*2-1
VectorXd::LinSpaced(size,low,high) // linspace(low,high,size)'
v.setLinSpaced(size,low,high) // v = linspace(low,high,size)'
Eigen 矩阵分块
// Matrix slicing and blocks. All expressions listed here are read/write.
// Templated size versions are faster. Note that Matlab is 1-based (a size N
// vector is x(1)...x(N)).
// Eigen // Matlab
x.head(n) // x(1:n)
x.head<n>() // x(1:n)
x.tail(n) // x(end - n + 1: end)
x.tail<n>() // x(end - n + 1: end)
x.segment(i, n) // x(i+1 : i+n)
x.segment<n>(i) // x(i+1 : i+n)
P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols)
P.block<rows, cols>(i, j) // P(i+1 : i+rows, j+1 : j+cols)
P.row(i) // P(i+1, :)
P.col(j) // P(:, j+1)
P.leftCols<cols>() // P(:, 1:cols)
P.leftCols(cols) // P(:, 1:cols)
P.middleCols<cols>(j) // P(:, j+1:j+cols)
P.middleCols(j, cols) // P(:, j+1:j+cols)
P.rightCols<cols>() // P(:, end-cols+1:end)
P.rightCols(cols) // P(:, end-cols+1:end)
P.topRows<rows>() // P(1:rows, :)
P.topRows(rows) // P(1:rows, :)
P.middleRows<rows>(i) // P(i+1:i+rows, :)
P.middleRows(i, rows) // P(i+1:i+rows, :)
P.bottomRows<rows>() // P(end-rows+1:end, :)
P.bottomRows(rows) // P(end-rows+1:end, :)
P.topLeftCorner(rows, cols) // P(1:rows, 1:cols)
P.topRightCorner(rows, cols) // P(1:rows, end-cols+1:end)
P.bottomLeftCorner(rows, cols) // P(end-rows+1:end, 1:cols)
P.bottomRightCorner(rows, cols) // P(end-rows+1:end, end-cols+1:end)
P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols)
P.topRightCorner<rows,cols>() // P(1:rows, end-cols+1:end)
P.bottomLeftCorner<rows,cols>() // P(end-rows+1:end, 1:cols)
P.bottomRightCorner<rows,cols>() // P(end-rows+1:end, end-cols+1:end)
Eigen 矩阵元素交换
// Of particular note is Eigen's swap function which is highly optimized.
// Eigen // Matlab
R.row(i) = P.col(j); // R(i, :) = P(:, i)
R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1])
Eigen 矩阵转置
// Views, transpose, etc; all read-write except for .adjoint().
// Eigen // Matlab
R.adjoint() // R'
R.transpose() // R.' or conj(R')
R.diagonal() // diag(R)
x.asDiagonal() // diag(x)
R.transpose().colwise().reverse(); // rot90(R)
R.conjugate() // conj(R)
Eigen 矩阵乘积
// All the same as Matlab, but matlab doesn't have *= style operators.
// Matrix-vector. Matrix-matrix. Matrix-scalar.
y = M*x; R = P*Q; R = P*s;
a = b*M; R = P - Q; R = s*P;
a *= M; R = P + Q; R = P/s;
R *= Q; R = s*P;
R += Q; R *= s;
R -= Q; R /= s;
Eigen 矩阵单个元素操作
// Vectorized operations on each element independently
// Eigen // Matlab
R = P.cwiseProduct(Q); // R = P .* Q
R = P.array() * s.array();// R = P .* s
R = P.cwiseQuotient(Q); // R = P ./ Q
R = P.array() / Q.array();// R = P ./ Q
R = P.array() + s.array();// R = P + s
R = P.array() - s.array();// R = P - s
R.array() += s; // R = R + s
R.array() -= s; // R = R - s
R.array() < Q.array(); // R < Q
R.array() <= Q.array(); // R <= Q
R.cwiseInverse(); // 1 ./ P
R.array().inverse(); // 1 ./ P
R.array().sin() // sin(P)
R.array().cos() // cos(P)
R.array().pow(s) // P .^ s
R.array().square() // P .^ 2
R.array().cube() // P .^ 3
R.cwiseSqrt() // sqrt(P)
R.array().sqrt() // sqrt(P)
R.array().exp() // exp(P)
R.array().log() // log(P)
R.cwiseMax(P) // max(R, P)
R.array().max(P.array()) // max(R, P)
R.cwiseMin(P) // min(R, P)
R.array().min(P.array()) // min(R, P)
R.cwiseAbs() // abs(P)
R.array().abs() // abs(P)
R.cwiseAbs2() // abs(P.^2)
R.array().abs2() // abs(P.^2)
(R.array() < s).select(P,Q); // (R < s ? P : Q)
Eigen 矩阵化简
// Reductions.
int r, c;
// Eigen // Matlab
R.minCoeff() // min(R(:))
R.maxCoeff() // max(R(:))
s = R.minCoeff(&r, &c) // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);
s = R.maxCoeff(&r, &c) // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);
R.sum() // sum(R(:))
R.colwise().sum() // sum(R)
R.rowwise().sum() // sum(R, 2) or sum(R')'
R.prod() // prod(R(:))
R.colwise().prod() // prod(R)
R.rowwise().prod() // prod(R, 2) or prod(R')'
R.trace() // trace(R)
R.all() // all(R(:))
R.colwise().all() // all(R)
R.rowwise().all() // all(R, 2)
R.any() // any(R(:))
R.colwise().any() // any(R)
R.rowwise().any() // any(R, 2)
Eigen 矩阵点乘
// Dot products, norms, etc.
// Eigen // Matlab
x.norm() // norm(x). Note that norm(R) doesn't work in Eigen.
x.squaredNorm() // dot(x, x) Note the equivalence is not true for complex
x.dot(y) // dot(x, y)
x.cross(y) // cross(x, y) Requires #include <Eigen/Geometry>
Eigen 矩阵类型转换
//// Type conversion
// Eigen // Matlab
A.cast<double>(); // double(A)
A.cast<float>(); // single(A)
A.cast<int>(); // int32(A)
A.real(); // real(A)
A.imag(); // imag(A)
// if the original type equals destination type, no work is done
Eigen 求解线性方程组 Ax = b
// Solve Ax = b. Result stored in x. Matlab: x = A \ b.
x = A.ldlt().solve(b)); // A sym. p.s.d. #include <Eigen/Cholesky>
x = A.llt() .solve(b)); // A sym. p.d. #include <Eigen/Cholesky>
x = A.lu() .solve(b)); // Stable and fast. #include <Eigen/LU>
x = A.qr() .solve(b)); // No pivoting. #include <Eigen/QR>
x = A.svd() .solve(b)); // Stable, slowest. #include <Eigen/SVD>
// .ldlt() -> .matrixL() and .matrixD()
// .llt() -> .matrixL()
// .lu() -> .matrixL() and .matrixU()
// .qr() -> .matrixQ() and .matrixR()
// .svd() -> .matrixU(), .singularValues(), and .matrixV()
Eigen 矩阵特征值
// Eigenvalue problems
// Eigen // Matlab
A.eigenvalues(); // eig(A);
EigenSolver<Matrix3d> eig(A); // [vec val] = eig(A)
eig.eigenvalues(); // diag(val)
eig.eigenvectors(); // vec
// For self-adjoint matrices use SelfAdjointEigenSolver<>
参考文献
【1】http://eigen.tuxfamily.org/dox/AsciiQuickReference.txt
【2】http://blog.youkuaiyun.com/augusdi/article/details/12907341
https://blog.youkuaiyun.com/liu_tian_wei/article/details/83615441
Linux系统
1. 在gnu的ftp站点http://ftp.gnu.org/gnu/gsl/ 上, 下载最新的gsl-2.x.tar.gz
2. 解压下载好的gsl-2.x.tar.gz 压缩包,$tar -zxvf gsl-2.x.tar.gz. 直接解压在了Downloads文件夹中。
3. $ cd gsl-2.x, 进入到gsl文件夹中, 运行$./configure --prefix=/usr , 该命令指定之后安装的include, lib, bin等文件夹都安装在usr目录下。
4. 相继运行,$make,$make check(可不使用), $make install, gsl库便安装在了/usr 目录下。
test.cpp
#include<iostream>
#include<gsl/gsl_fit.h>
using namespace std;
int main(){
double c0 = 0, c1 = 0, cov00 = 0, cov01 = 0, cov11 = 0, sumsq = 0;
double x[]={1,2,3,4,5};
double y[]={3,4,5,6,7};
gsl_fit_linear(x, 1, y, 1, 5, &c0, &c1, &cov00, &cov01, &cov11, &sumsq);
cout<<c0<<" "<<c1<<endl;
}
g++:
g++ -o Test test.cpp -std=c++11 -lgsl -lgslcblas
执行
./Test
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原文链接:https://blog.youkuaiyun.com/liu_tian_wei/article/details/83615441