provisdom.math.apache-matrix — provisdom/math 2.67

=== clj

(=== apache-m)

(=== apache-m1 apache-m2)

(=== apache-m1 apache-m2 & apache-ms)

Apache Commons matrix equality that works with NaN.

add clj

(add apache-m)

(add apache-m1 apache-m2)

(add apache-m1 apache-m2 & apache-ms)

Apache Commons matrix addition.

apache-matrix clj

(apache-matrix m)

Returns a matrix using the Apache Commons matrix implementation.

apache-matrix->matrix clj

(apache-matrix->matrix apache-m)

Converts an Apache Commons matrix into a matrix.

apache-matrix-finite? clj

(apache-matrix-finite? x)

Returns true if an Apache Commons matrix without infinite numbers.

apache-matrix? clj

(apache-matrix? x)

Returns true if an Apache Commons matrix.

apache-square-matrix? clj

assoc-diagonal! clj

(assoc-diagonal! apache-m numbers)

Sets a diagonal in an Apache Commons matrix using the specified numbers.

assoc-entry! clj

(assoc-entry! apache-m row column number)

Sets an entry in an Apache Commons matrix.

cholesky-decomposition clj

(cholesky-decomposition positive-definite-apache-m)

Computes the Cholesky decomposition of a positive definite Apache Commons matrix. Returns a map of two Apache Commons matrices ::cholesky-L and ::choleskyLT. This is the Cholesky square root of a matrix, 'L' and 'LT' such that positive-definite-apache-m = L × LT. Note that positive-definite-apache-m must be positive semidefinite for this to exist, but cholesky-decomposition requires strict positivity.

columns clj

(columns apache-m)

Returns the number of columns.

concat-columns clj

(concat-columns)

(concat-columns apache-m)

(concat-columns apache-m & apache-ms)

Appends columns from all the Apache Common matrices after the first to the first. Each matrix's row count must be the same or will return nil.

concat-rows clj

(concat-rows)

(concat-rows apache-m)

(concat-rows apache-m & apache-ms)

Appends rows from all the Apache Common matrices after the first to the first. Each matrix's column count must be the same or will return nil.

condition clj

(condition singular-values-apache-matrix)

The singular-values-apache-matrix is the diagonal matrix of ::singular-values from sv-decomposition. Returns the norm2 condition number, which is the maximum element value from the singular-values-apache-matrix divided by the minimum element value.

correlation-apache-matrix->covariance-apache-matrix clj

(correlation-apache-matrix->covariance-apache-matrix correlation-apache-matrix
                                                     variances)

Returns Covariance Apache Commons matrix from a Correlation Apache Commons matrix.

correlation-apache-matrix-by-squaring clj

(correlation-apache-matrix-by-squaring square-apache-m-finite)

Returns a finite Correlation Apache Commons matrix by first squaring square-apache-m-finite.

correlation-apache-matrix? clj

(correlation-apache-matrix? x accu)

Returns true if a finite positive definite Apache Commons matrix with a unit diagonal. Larger accu creates more false negatives and less false positives.

covariance-apache-matrix->correlation-apache-matrix clj

(covariance-apache-matrix->correlation-apache-matrix covariance-apache-matrix)

Returns Correlation Apache Commons matrix from a Covariance Apache Commons matrix.

diagonal clj

(diagonal apache-m)

(diagonal apache-m k)

Returns the specified diagonal of an Apache Commons matrix as a vector. If 'k'>0, returns a diagonal above the main diagonal. If 'k'<0, returns a diagonal below the main diagonal. Works on both square and rectangular matrices.

diagonal-apache-matrix? clj

(diagonal-apache-matrix? x)

Returns true if a diagonal matrix (the entries outside the main diagonal are all zero).

eigen-decomposition clj

(eigen-decomposition square-apache-m-finite)

Computes the Eigendecomposition of a diagonalisable matrix. Returns a map containing: ::eigenvectorsT -- square Apache Commons matrix with each column containing the eigenvectors ::eigenvalues-matrix -- Apache Commons matrix whose diagonal elements are the eigenvalues, if they exist ::eigenvalues -- vector of real parts of eigenvalues (nil if imaginary parts exist) ::eigenvectors -- square Apache Commons matrix with each row containing the eigenvectors square-apache-m-finite = eigenvectorsT × eigenvalues-matrix × (inverse eigenvectorsT).

empty-apache-matrix? clj

(empty-apache-matrix? x)

Returns true if an empty Apache Commons matrix.

get-column clj

(get-column apache-m column)

Gets a column of an Apache Commons matrix, as a vector.

get-entry clj

(get-entry apache-m row column)

Returns the specified Apache Commons matrix element.

get-row clj

(get-row apache-m row)

Gets a row of an Apache Commons matrix, as a vector.

get-slices-as-matrix clj

(get-slices-as-matrix apache-m
                      {:keys [:provisdom.math.matrix/row-indices
                              :provisdom.math.matrix/column-indices
                              :provisdom.math.matrix/exception-row-indices
                              :provisdom.math.matrix/exception-column-indices]})

Performs a slice on the Apache Commons matrix given by the options. Options: ::mx/row-indices returns all rows by default, can pass a row index or sequence of row indices ::mx/column-indices returns all columns by default, can pass a column index or sequence of column indices ::mx/exception-row-indices can pass a row index or sequence of row indices to exclude ::mx/exception-column-indices can pass a column index or sequence of column indices to exclude. Exceptions override inclusions. Can be used to permute matrix through index sequence ordering.

inverse clj

(inverse square-apache-m)

Returns the inverse of a square Apache Commons matrix. Uses QR Decomposition by default but will use other methods depending on matrix structure.

lower-triangular-apache-matrix? clj

(lower-triangular-apache-matrix? x)

Returns true if a lower triangular matrix (the entries above the main diagonal are all zero).

lu-decomposition-with-determinant clj

(lu-decomposition-with-determinant square-apache-m)

Returns a map containing: ::L -- the lower triangular factor Apache Commons matrix ::U -- the upper triangular factor Apache Commons matrix ::LU-permutation -- the permutation Apache Commons matrix ::determinant -- the determinant.

lu-decomposition-with-determinant-and-inverse clj

(lu-decomposition-with-determinant-and-inverse square-apache-m)

Returns a map containing ::L -- the lower triangular factor Apache Commons matrix ::U -- the upper triangular factor Apache Commons matrix ::LU-permutation -- the permutation Apache Commons matrix ::determinant -- the determinant ::inverse -- the inverse Apache Commons matrix.

matrix-partition clj

(matrix-partition apache-m first-bottom-row first-right-column)

Returns a map containing the four sub-matrices labeled ::top-left, ::bottom-left, ::top-right, and ::bottom-right. first-bottom-row is the bottom of where the slice will occur. first-right-column is the right edge of where the slice will occur.

mx* clj

(mx* apache-m)

(mx* apache-m1 apache-m2)

(mx* apache-m1 apache-m2 & apache-ms)

Apache Commons matrix multiplication. Number of columns of the first matrix must match the number of rows of the second matrix.

positive-definite-apache-matrix-finite-by-squaring clj

(positive-definite-apache-matrix-finite-by-squaring square-apache-m-finite)

Returns a finite positive definite Apache Commons matrix squaring it. Will tweak original matrix if necessary to ensure positive definite.

positive-definite-apache-matrix-finite? clj

(positive-definite-apache-matrix-finite? x accu)

Returns true if a finite positive definite Apache matrix. Larger accu creates more false negatives and less false positives.

positive-semidefinite-apache-matrix-finite-by-squaring clj

(positive-semidefinite-apache-matrix-finite-by-squaring square-apache-m-finite)

Returns a finite positive semidefinite Apache Commons matrix by first squaring square-apache-m-finite.

positive-semidefinite-apache-matrix-finite? clj

(positive-semidefinite-apache-matrix-finite? x accu)

Returns true if a finite positive-semidefinite Apache matrix. Larger accu creates more false positives and less false negatives.

qr-decomposition clj

(qr-decomposition apache-m)

Computes the QR decomposition of an Apache Commons matrix. Returns a map containing Apache Commons matrices Q and R: ::Q -- orthogonal factors ::R -- the upper triangular factors (not necessarily an upper triangular Apache Commons matrix).

qr-decomposition-with-linear-least-squares clj

(qr-decomposition-with-linear-least-squares apache-m1 apache-m2)

Returns a map containing: ::Q -- orthogonal factors of apache-m1 ::R -- the upper triangular factors of apache-m2 ::linear-least-squares -- Apache Commons matrix with linear least squares solution.

qr-decomposition-with-linear-least-squares-and-error-matrix clj

(qr-decomposition-with-linear-least-squares-and-error-matrix apache-m1
                                                             apache-m2)

Returns a map containing: ::Q -- orthogonal factors of apache-m1 ::R -- the upper triangular factors of apache-m2 (not necessarily square) ::LLS-solution -- Apache Commons matrix with linear least squares solution ::error -- Apache Commons matrix of errors.

rank-revealing-qr-decomposition clj

(rank-revealing-qr-decomposition apache-m accu)

Calculates the rank-revealing QR-decomposition of a matrix, with column pivoting. The rank-revealing QR-decomposition of apache-m consists of three matrices Q, R, and RRQR-permutation such that: apache-m × permutation = Q × R. Q is orthogonal (QT × Q = I), and R is upper triangular. If apache-m is m × n, Q is m × m, R is m × n, and RRQR-permutation is n × n. QR decomposition with column pivoting produces a rank-revealing QR decomposition. This class computes the decomposition using Householder reflectors. Returns a map containing: ::Q -- orthogonal factors ::R -- the upper triangular factors ::RRQR-permutation -- Permutation Matrix ::rank -- the rank.

rectangular-cholesky-decomposition clj

(rectangular-cholesky-decomposition positive-semidefinite-apache-m accu)

Calculates the rectangular Cholesky decomposition of a positive semidefinite Apache Commons matrix. The rectangular Cholesky decomposition of a real positive-semidefinite-apache-m consists of a rectangular-root matrix with the same number of rows such that positive-semidefinite-apache-m is almost equal to rectangular-root × (transpose rectangular-root), depending on a user-defined tolerance. In a sense, this is the square root of positive-semidefinite-apache-m. The difference with respect to the regular CholeskyDecomposition is that rows/columns may be permuted (hence the rectangular shape instead of the traditional triangular shape) and there is a threshold to ignore small diagonal elements. This is used for example to generate correlated random n-dimensions vectors in a p-dimension subspace (p < n). In other words, it allows generating random vectors from a covariance matrix that is only positive semidefinite, and not positive definite.

accu - Diagonal elements threshold under which columns are considered to be dependent on previous ones and are discarded.

Returns a map containing: ::rectangular-root -- rectangular root Apache Commons matrix ::rank -- rank is the number of independent rows of original matrix, and the number of columns of rectangular-root matrix.

rnd-correlation-apache-matrix! clj

(rnd-correlation-apache-matrix! size)

Returns a correlation Apache Commons matrix from a covariance matrix with a random spectrum. The orthogonal matrices are generated by using 2 * size composed Householder reflections. Alternative #1: Sample Covariance from the Inverse-Wishart Distribution. Alternative #2: Use correlation-apache-matrix-by-squaring with a random square matrix.

rnd-positive-definite-apache-matrix-finite! clj

(rnd-positive-definite-apache-matrix-finite! size)

Returns a finite positive definite Apache Commons matrix with a random spectrum. The orthogonal matrices are generated by using 2 × size composed Householder reflections. Alternative #1: Sample from the Inverse-Wishart Distribution. Alternative #2: Use positive-definite-apache-matrix-finite-by-squaring with a random square matrix.

rows clj

(rows apache-m)

Returns the number of rows.

rrqr-decomposition clj

scalar-add clj

(scalar-add apache-m number)

Apache Commons matrix addition to a scalar.

scalar-multiply clj

(scalar-multiply apache-m number)

Apache Commons matrix multiplication to a scalar.

some-kv clj

(some-kv pred apache-m)

(some-kv pred
         apache-m
         {:keys [:provisdom.math.matrix/by-row?] :or {by-row? true}})

Returns the first logical true value of (pred row column number) for any number in Apache Commons matrix, else nil. Options: ::mx/by-row? (default: true).

square-apache-matrix? clj

(square-apache-matrix? x)

Returns true if a square Apache Commons matrix (i.e., same number of rows and columns).

subtract clj

(subtract apache-m)

(subtract apache-m1 apache-m2)

(subtract apache-m1 apache-m2 & apache-ms)

Apache Commons matrix subtraction.

sv-decomposition clj

(sv-decomposition apache-m)

Calculates the compact Singular Value Decomposition of an Apache Commons matrix. The Singular Value Decomposition of apache-m is a set of three matrices: svd-left, singular-values, and svd-right such that: apache-m = svd-left × singular-values × svd-right. Let apache-m be a m × n matrix, then svd-left is a m × p orthogonal matrix of the left singular vectors, singular-values is a p × p diagonal matrix of singular values with positive or nil elements, and are ordered from largest to smallest. svd-right is a p × n orthogonal matrix of the right singular vectors where p = min(m,n). Note that: Identity Matrix = (transpose svd-left) × svd-left = svd-right × (transpose svd-right). Returns a map containing: ::svd-left -- Apache Commons matrix of left singular vectors ::singular-values -- diagonal Apache Commons matrix ::svd-right -- transpose of Apache Commons matrix of right singular vectors ::rank -- rank.

symmetric-apache-matrix-by-averaging! clj

(symmetric-apache-matrix-by-averaging! square-apache-m)

Updates symmetric Apache Commons matrix where each element above or below the diagonal is equal to the average of the corresponding numbers. This is useful to help with rounding errors.

symmetric-apache-matrix? clj

(symmetric-apache-matrix? x)

Returns true is a symmetric Apache Commons matrix.

trace clj

(trace square-apache-m)

Calculates the trace of a square Apache Commons matrix (sum of elements on main diagonal).

transpose clj

(transpose apache-m)

Transposes an Apache Commons matrix by swapping rows and columns, returning a new Apache Commons matrix.

upper-triangular-apache-matrix? clj

(upper-triangular-apache-matrix? x)

Returns true if an upper triangular matrix (the entries below the main diagonal are all zero).