org.soulspace.qclojure.domain.math.linear-algebra
lu-decompositionclj
(lu-decomposition matrix)Perform LU decomposition with partial pivoting for matrix inversion. Returns [L U P] where P is the permutation matrix.
This function uses Gaussian elimination with partial pivoting to decompose the matrix.
Parameters:
- matrix: A square matrix to decompose (n×n)
Returns: A vector [L U P] where:
- L is the lower triangular matrix
- U is the upper triangular matrix
- P is the permutation vector (indices of rows after pivoting)
Example: (lu-decomposition [[4 3 2] [2 1 1] [1 1 1]]) ;=> [[[1.0 0.0 0.0] [0.5 1.0 0.0] [0.25 0.5 1.0]] [[4.0 3.0 2.0] [0.0 -0.5 -0.5] [0.0 0.0 0.0]] [0 1 2]] ; Permutation
Perform LU decomposition with partial pivoting for matrix inversion.
Returns [L U P] where P is the permutation matrix.
This function uses Gaussian elimination with partial pivoting to decompose the matrix.
Parameters:
- matrix: A square matrix to decompose (n×n)
Returns:
A vector [L U P] where:
- L is the lower triangular matrix
- U is the upper triangular matrix
- P is the permutation vector (indices of rows after pivoting)
Example:
(lu-decomposition [[4 3 2] [2 1 1] [1 1 1]])
;=> [[[1.0 0.0 0.0] [0.5 1.0 0.0] [0.25 0.5 1.0]]
[[4.0 3.0 2.0] [0.0 -0.5 -0.5] [0.0 0.0 0.0]]
[0 1 2]] ; Permutationmatrix-inverseclj
(matrix-inverse M)Compute matrix inverse using Gauss-Jordan elimination.
This is a simple implementation suitable for small matrices (< 20x20). For larger matrices, consider using a dedicated linear algebra library.
Parameters:
- M: Square matrix as vector of row vectors
Returns: Inverse matrix, or nil if matrix is singular
Compute matrix inverse using Gauss-Jordan elimination. This is a simple implementation suitable for small matrices (< 20x20). For larger matrices, consider using a dedicated linear algebra library. Parameters: - M: Square matrix as vector of row vectors Returns: Inverse matrix, or nil if matrix is singular
matrix-multiplyclj
(matrix-multiply A B)Multiply two matrices represented as vectors of vectors.
Parameters:
- A: Matrix A as vector of row vectors
- B: Matrix B as vector of row vectors
Returns: Matrix product A*B
Multiply two matrices represented as vectors of vectors. Parameters: - A: Matrix A as vector of row vectors - B: Matrix B as vector of row vectors Returns: Matrix product A*B
matrix-transposeclj
(matrix-transpose M)Transpose a matrix.
Parameters:
- M: Matrix as vector of row vectors
Returns: Transposed matrix
Transpose a matrix. Parameters: - M: Matrix as vector of row vectors Returns: Transposed matrix
solve-linear-systemclj
(solve-linear-system matrix b)Solve Ax = b using LU decomposition with partial pivoting.
This function solves the linear system Ax = b where A is a square matrix and b is a vector. It uses LU decomposition with partial pivoting to efficiently solve the system.
Parameters:
- matrix: Square matrix A (n×n)
- b: Vector b (n×1)
Returns: Vector x (n×1) that satisfies Ax = b, or nil if no solution
Example: (solve-linear-system [[4 3 2] [2 1 1] [1 1 1]] [1 2 3]) ;=> [0.0 1.0 1.0] ; Solution to the system
Solve Ax = b using LU decomposition with partial pivoting.
This function solves the linear system Ax = b where A is a square matrix
and b is a vector. It uses LU decomposition with partial pivoting to
efficiently solve the system.
Parameters:
- matrix: Square matrix A (n×n)
- b: Vector b (n×1)
Returns:
Vector x (n×1) that satisfies Ax = b, or nil if no solution
Example:
(solve-linear-system [[4 3 2] [2 1 1] [1 1 1]]
[1 2 3])
;=> [0.0 1.0 1.0] ; Solution to the systemtensor-productclj
(tensor-product matrix-a matrix-b)Compute the tensor product of two matrices.
For matrices A (m×n) and B (p×q), returns the Kronecker product A⊗B (mp×nq).
Parameters:
- matrix-a: First matrix (m×n)
- matrix-b: Second matrix (p×q)
Returns: A new matrix representing the tensor product (mp×nq).
Compute the tensor product of two matrices. For matrices A (m×n) and B (p×q), returns the Kronecker product A⊗B (mp×nq). Parameters: - matrix-a: First matrix (m×n) - matrix-b: Second matrix (p×q) Returns: A new matrix representing the tensor product (mp×nq).
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