Hamiltonian Monte Carlo

linearalgebra.hpp
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1 
18 #ifndef HMC_VSP_LINEARALGEBRA_HPP
19 #define HMC_VSP_LINEARALGEBRA_HPP
20 
27 std::vector<double> MatrixVectorProduct(std::vector<std::vector<double>> M, std::vector<double> A);
28 
35 std::vector<std::vector<double>> MatrixMatrixProduct(std::vector<std::vector<double>> M, std::vector<std::vector<double>> N);
36 
43 std::vector<std::vector<double>> MatrixMatrixSum(std::vector<std::vector<double>> M, std::vector<std::vector<double>> N);
44 
51 std::vector<double> GetMatrixRow(std::vector<std::vector<double>> M, int row);
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59 std::vector<double> GetMatrixColumn(std::vector<std::vector<double>> M, int column);
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66 std::vector<std::vector<double>> TransposeMatrix(std::vector<std::vector<double>> M);
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73 std::vector<double> MatrixTrace(std::vector<std::vector<double>> M);
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80 std::vector<std::vector<double>> InvertMatrixElements(std::vector<std::vector<double>> M);
81 
87 std::vector<std::vector<double>> VectorToDiagonal(std::vector<double> A);
88 
95 double VectorVectorProduct(std::vector<double> A, std::vector<double> B);
96 
103 std::vector<double> VectorDifference(std::vector<double> A, std::vector<double> B);
104 
111 std::vector<double> VectorSum(std::vector<double> A, std::vector<double> B);
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119 std::vector<double> VectorScalarProduct(std::vector<double> A, double b);
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126 std::vector<double> NormalizeVector(std::vector<double> A);
127 
136 std::vector<double> SolveLowerTriangular(std::vector<std::vector<double>> L, std::vector<double> x);
137 
144 std::vector<std::vector<double>> InvertLowerTriangular(std::vector<std::vector<double>> L);
145 
152 std::vector<std::vector<double>> CholeskyDecompose(std::vector<std::vector<double>> A);
153 
154 /* ---------------------------------------------------------------------------------------------------------------------- *
155  * Operators which wrap to the above functions. The trick in getting these to use less memory is std::move.
156  * ---------------------------------------------------------------------------------------------------------------------- */
160 std::vector<std::vector<double>> operator*(std::vector<std::vector<double>> M, std::vector<std::vector<double>> N);
164 double operator*(std::vector<double> A, std::vector<double> B);
168 std::vector<double> operator*(std::vector<std::vector<double>> M, std::vector<double> A);
172 std::vector<double> operator*(double b, std::vector<double> A);
176 std::vector<double> operator*(std::vector<double> A, double b);
180 std::vector<double> operator/(std::vector<double> A, double b);
184 std::vector<double> operator+(std::vector<double> A, std::vector<double> B);
188 std::vector<double> operator-(std::vector<double> A, std::vector<double> B);
192 std::vector<std::vector<double>> operator+(std::vector<std::vector<double>> M, std::vector<std::vector<double>> N);
193 
194 #endif //HMC_VSP_LINEARALGEBRA_HPP
NormalizeVector
std::vector< double > NormalizeVector(std::vector< double > A)
Normalizes a vector to unit length.
Definition: linearalgebra.cpp:345
operator-
std::vector< double > operator-(std::vector< double > A, std::vector< double > B)
Operator form of VectorDifference(), using std library forwarding.
Definition: linearalgebra.cpp:263
VectorScalarProduct
std::vector< double > VectorScalarProduct(std::vector< double > A, double b)
Vector scalar prodcut of vector and scalar.
Definition: linearalgebra.cpp:29
MatrixMatrixSum
std::vector< std::vector< double > > MatrixMatrixSum(std::vector< std::vector< double >> M, std::vector< std::vector< double >> N)
A function to calculate the sum of the entries of two matrices.
Definition: linearalgebra.cpp:213
InvertLowerTriangular
std::vector< std::vector< double > > InvertLowerTriangular(std::vector< std::vector< double >> L)
Invert a lower triangular matrix by use of solving the system per column of using SolveLowerTriang...
Definition: linearalgebra.cpp:325
GetMatrixColumn
std::vector< double > GetMatrixColumn(std::vector< std::vector< double >> M, int column)
Function to get a column from a matrix.
Definition: linearalgebra.cpp:93
operator+
std::vector< double > operator+(std::vector< double > A, std::vector< double > B)
Operator form of VectorSum(), using std library forwarding.
Definition: linearalgebra.cpp:259
operator*
std::vector< std::vector< double > > operator*(std::vector< std::vector< double >> M, std::vector< std::vector< double >> N)
Operator form of MatrixMatrixProduct(), using std library forwarding.
Definition: linearalgebra.cpp:245
InvertMatrixElements
std::vector< std::vector< double > > InvertMatrixElements(std::vector< std::vector< double >> M)
Function to take the inverse of the individual matrix elements.
Definition: linearalgebra.cpp:158
VectorVectorProduct
double VectorVectorProduct(std::vector< double > A, std::vector< double > B)
Dot product of vectors.
Definition: linearalgebra.cpp:78
VectorToDiagonal
std::vector< std::vector< double > > VectorToDiagonal(std::vector< double > A)
Function which takes a std::vector of double to make a diagonal matrix of it, such that ...
Definition: linearalgebra.cpp:169
GetMatrixRow
std::vector< double > GetMatrixRow(std::vector< std::vector< double >> M, int row)
Function to get a row from a matrix.
Definition: linearalgebra.cpp:110
MatrixMatrixProduct
std::vector< std::vector< double > > MatrixMatrixProduct(std::vector< std::vector< double >> M, std::vector< std::vector< double >> N)
Function incorporating the standard matrix-matrix product, producing a new matrix. Matrix M should have as many columns as N has rows, otherwise an exception is thrown.
Definition: linearalgebra.cpp:184
MatrixTrace
std::vector< double > MatrixTrace(std::vector< std::vector< double >> M)
Function to the trace of a square matrix .
Definition: linearalgebra.cpp:144
TransposeMatrix
std::vector< std::vector< double > > TransposeMatrix(std::vector< std::vector< double >> M)
Function to transpose a matrix M of size i x j into a matrix N of size j x i, where ...
VectorSum
std::vector< double > VectorSum(std::vector< double > A, std::vector< double > B)
Vector sum between two vectors.
Definition: linearalgebra.cpp:36
operator/
std::vector< double > operator/(std::vector< double > A, double b)
Operator form of vector by scalar division. Uses VectorScalarProduct() with std library forwarding...
Definition: linearalgebra.cpp:341
VectorDifference
std::vector< double > VectorDifference(std::vector< double > A, std::vector< double > B)
Vector difference between two vectors.
Definition: linearalgebra.cpp:11
MatrixVectorProduct
std::vector< double > MatrixVectorProduct(std::vector< std::vector< double >> M, std::vector< double > A)
Function incorporating the standard matrix-vector product. The result is a column vector...
CholeskyDecompose
std::vector< std::vector< double > > CholeskyDecompose(std::vector< std::vector< double >> A)
Cholesky-decomposition of a positive definite Hermitian matrix .
Definition: linearalgebra.cpp:275
SolveLowerTriangular
std::vector< double > SolveLowerTriangular(std::vector< std::vector< double >> L, std::vector< double > x)
Solve linear equation where is a lower triangular matrix and and are dimensional vectors...
Definition: linearalgebra.cpp:303
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