provisdom.math.matrix — provisdom/math 2.65

assoc-column clj

(assoc-column m column numbers)

Sets a column in a matrix using the specified numbers.

assoc-diagonal clj

(assoc-diagonal m numbers)

Sets a diagonal in a matrix using the specified numbers.

assoc-row clj

(assoc-row m row numbers)

Sets a row in a matrix using the specified numbers.

column-matrix clj

(column-matrix numbers)

(column-matrix size row->number)

Returns a column matrix created from numbers or from size and row->number. size is the size of the returned matrix. Function row->number takes a row and returns a number.

column-matrix? clj

(column-matrix? x)

Returns true if a column-matrix (i.e., matrix with exactly one column).

columns clj

(columns m)

Returns the number of columns.

compute-matrix clj

(compute-matrix rows columns row+column->number)

Function row+column->number takes a row and column and returns a number.

concat-columns clj

(concat-columns)

(concat-columns m & ms)

Appends columns from all the 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 m & ms)

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

constant-matrix clj

(constant-matrix rows columns)

(constant-matrix rows columns number)

Constructs a new matrix of value's (or zeros (doubles)) with the given rows and columns.

deserialize-lower-triangular-matrix clj

(deserialize-lower-triangular-matrix numbers)

(deserialize-lower-triangular-matrix numbers
                                     {:provisdom.math.matrix/keys [by-row?]
                                      :or {by-row? true}})

(deserialize-lower-triangular-matrix diagonal-numbers
                                     off-diagonal-numbers
                                     {:provisdom.math.matrix/keys [by-row?]
                                      :or {by-row? true}})

Returns a (square) lower triangular matrix (a matrix with all elements above the diagonal being 0.0). numbers are the elements that will be used to create the lower triangular matrix. off-diagonal-numbers can be used to create the off-diagonal elements, and then any existing diagonal-numbers will fill the diagonal elements. The elements are placed by-row? (default is true).

deserialize-symmetric-matrix clj

(deserialize-symmetric-matrix numbers)

Returns a symmetric matrix (a matrix with elements at r,c equal to elements at c,r). numbers are the same as the elements used to create a triangular matrix.

deserialize-upper-triangular-matrix clj

(deserialize-upper-triangular-matrix numbers)

(deserialize-upper-triangular-matrix numbers
                                     {:provisdom.math.matrix/keys [by-row?]
                                      :or {by-row? true}})

(deserialize-upper-triangular-matrix diagonal-numbers
                                     off-diagonal-numbers
                                     {:provisdom.math.matrix/keys [by-row?]
                                      :or {by-row? true}})

Returns a (square) upper triangular matrix (a matrix with all elements below the diagonal being 0.0). numbers are the elements that will be used to create the upper triangular matrix. off-diagonal-numbers can be used to create the off-diagonal elements, and then any existing diagonal-numbers will fill the diagonal elements. The elements are placed by-row? (default is true).

diagonal clj

(diagonal m)

(diagonal m k)

Returns the specified diagonal of a 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-constant-matrix clj

See toeplitz-matrix

diagonal-matrix clj

(diagonal-matrix diagonal-numbers)

(diagonal-matrix size index->number)

(diagonal-matrix rows columns index->number)

Returns a diagonal matrix (a matrix with all elements not on the diagonal being 0.0). The values on the diagonal can be given by the vector diagonal-numbers. size is the size of the matrix given by a single number. f is a function that takes index and returns a number. Can also return a rectangular diagonal matrix using rows and columns.

diagonal-matrix? clj

(diagonal-matrix? x)

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

ecount-of-symmetric-or-triangular-matrix clj

(ecount-of-symmetric-or-triangular-matrix size)

Returns the element count (ecount) for a symmetric or triangular matrix. This is the number of elements on the diagonal plus the number of elements above or below the diagonal.

ecount-of-symmetric-or-triangular-matrix-without-diagonal clj

(ecount-of-symmetric-or-triangular-matrix-without-diagonal size)

Returns the element count (ecount) for a symmetric or triangular matrix without the diagonal. This is the number of elements above or below the diagonal.

empty-matrix? clj

(empty-matrix? x)

Returns true if the matrix is an empty matrix.

ereduce-kv clj

(ereduce-kv f init m)

(ereduce-kv f init m1 m2)

(ereduce-kv f init m1 m2 m3)

Function f takes a result, row, column, and number(s). Reduces over 1, 2, or 3 matrices. Number of columns in the first matrix must be the least.

filter-by-column clj

(filter-by-column column-v->bool m)

Returns a matrix. Function 'column-v->bool' takes a column-vector.

filter-by-row clj

(filter-by-row row-v->bool m)

Returns a matrix. Function 'row-v->bool' takes a row-vector.

filter-symmetric-matrix clj

(filter-symmetric-matrix v->bool symmetric-m)

Takes and returns a symmetric matrix. 'v->bool' takes a row-vector or column-vector.

get-column clj

(get-column m column)

Gets a column of a matrix, as a vector.

get-row clj

(get-row m row)

Gets a row of a matrix, as a vector.

get-slices-as-matrix clj

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

Performs a slice on the matrix given by the options. Options: ::row-indices returns all rows by default, can pass a row index or sequence of row indices ::column-indices returns all columns by default, can pass a column index or sequence of column indices ::exception-row-indices can pass a row index or sequence of row indices to exclude ::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.

identity-matrix clj

(identity-matrix size)

Constructs an identity matrix with the given size.

insert-column clj

(insert-column m column numbers)

Inserts a column of numbers in a matrix at the specified column.

insert-row clj

(insert-row m row numbers)

Inserts a row of numbers in a matrix at the specified row.

kronecker-product clj

(kronecker-product)

(kronecker-product m)

(kronecker-product m1 m2)

(kronecker-product m1 m2 & ms)

Generalization of the outer product.

lower-triangular-matrix? clj

(lower-triangular-matrix? x)

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

matrix->sparse clj

(matrix->sparse m)

(matrix->sparse m number->bool)

Returns a sparse-matrix (i.e., a vector of tuples of [row column number]). Function number->bool takes a number.

matrix-finite-non-? clj

(matrix-finite-non-? x)

Returns true if a matrix of finite non-negative numbers.

matrix-finite? clj

(matrix-finite? x)

Returns true if a matrix of finite numbers.

matrix-num? clj

(matrix-num? x)

Returns true if a matrix of num (numbers without NaN).

matrix-partition clj

(matrix-partition 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. Matrices can be merged back together using merge-matrices. 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.

matrix-prob? clj

(matrix-prob? x)

Returns true if a matrix of probabilities.

matrix? clj

(matrix? x)

Returns true if a matrix (i.e., dimensionality is 2, contains numbers only, rows have equal positive lengths unless the empty matrix.)

mdl clj

merge-matrices clj

(merge-matrices {:provisdom.math.matrix/keys [top-left bottom-left top-right
                                              bottom-right]})

Returns a Matrix created by binding four matrices together. Matrices can be partitioned into four matrices using matrix-partition. Takes a map containing keys: ::top-left ::bottom-left ::top-right ::bottom-right.

mx* clj

(mx* m)

(mx* m1 m2)

(mx* m1 m2 & ms)

Matrix multiplication. Number of columns of the first matrix must match the number of rows of the second matrix. Use [tensor/multiply] for more general multiplication.

outer-product clj

(outer-product v)

An outer product is the tensor product of two coordinate vectors, a special case of the Kronecker product of matrices. The outer product of two coordinate vectors is a matrix such that the coordinates satisfy w_ij = u_i × u_j.

remove-column clj

(remove-column m column)

Removes a column in a matrix

remove-row clj

(remove-row m row)

Removes a row in a matrix

replace-submatrix clj

(replace-submatrix m submatrix row-start column-start)

Returns a Matrix after substituting a submatrix at top-left location row-start and column-start. row-start and column-start can be negative. Unassigned elements will be 0.0.

rnd-matrix! clj

(rnd-matrix! rows columns)

Returns matrix with random elements.

rnd-reflection-matrix! clj

(rnd-reflection-matrix! size)

Returns a random Householder reflection matrix of size.

rnd-spectral-matrix! clj

(rnd-spectral-matrix! spectrum-vector)

Returns a random matrix with a particular spectrum-vector. The orthogonal matrices are generated by using 2 × size of spectrum-vector composed Householder reflections.

round-roughly-zero-columns clj

(round-roughly-zero-columns m accu)

Returns a matrix after rounding any roughly-zero columns.

round-roughly-zero-rows clj

(round-roughly-zero-rows m accu)

Returns a matrix after rounding any roughly-zero rows.

row-matrix clj

(row-matrix numbers)

(row-matrix size column->number)

Returns a row matrix created from numbers or from size and column->number. size is the size of the returned matrix. Function column->number takes a column and returns a number.

row-matrix? clj

(row-matrix? x)

Returns true if a row-matrix (i.e., matrix with exactly one row)

rows clj

(rows m)

Returns the number of rows.

serialize-symmetric-or-triangular-matrix clj

(serialize-symmetric-or-triangular-matrix m)

(serialize-symmetric-or-triangular-matrix m
                                          {:provisdom.math.matrix/keys [by-row?]
                                           :or {by-row? true}})

Returns a vector that contains the upper (default) or lower half of the matrix. m doesn't have to be symmetric. Options: ::by-row? (default: true). Set to false to get lower triangular values instead of upper.

size-of-symmetric-or-triangular-matrix clj

(size-of-symmetric-or-triangular-matrix ecount)

Returns the size of the matrix given ecount. ecount is the number of independent symmetric or triangular matrix elements (the number of elements on the diagonal plus the number either above or below the diagonal).

size-of-symmetric-or-triangular-matrix-without-diagonal clj

(size-of-symmetric-or-triangular-matrix-without-diagonal ecount)

Returns the size of the matrix given ecount. ecount is the number of elements above or below the diagonal.

some-kv clj

(some-kv pred m)

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

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

sparse->matrix clj

(sparse->matrix sparse m)

Builds a matrix using a sparse representation and an existing matrix (often a zero-matrix). sparse is a vector of triples of [row column value]. Later values will override prior overlapping values.

sparse->symmetric-matrix clj

(sparse->symmetric-matrix sparse symmetric-m)

Builds a symmetric matrix using a sparse representation and an existing symmetric matrix (often a zero-matrix). sparse is a vector of triples of [row column value]. Later values will override prior overlapping values. Each off-diagonal inner sparse form is applied twice, with the row and column switched.

square-matrix? clj

(square-matrix? x)

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

symmetric-matrix->sparse clj

(symmetric-matrix->sparse symmetric-m)

(symmetric-matrix->sparse symmetric-m number->bool)

Returns a sparse-matrix (i.e., a vector of tuples of [row column number]). number->bool takes a number and will be evaluated only for upper-right triangle of symmetric-m.

symmetric-matrix-by-averaging clj

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

Returns a symmetric 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-matrix? clj

(symmetric-matrix? x)

Returns true if a symmetric matrix.

to-matrix clj

(to-matrix tensor rows)

(to-matrix tensor
           rows
           {:provisdom.math.matrix/keys [by-row?] :or {by-row? true}})

Builds a matrix representing the flattened elements of tensor (onto a matrix of zeros (doubles) if necessary). rows is the number of rows of the returned matrix. The elements are placed by-row? (default is true). To set the number of columns instead, transpose returned matrix.

toeplitz-matrix clj

(toeplitz-matrix first-row first-column)

Returns a toeplitz matrix (a matrix whose elements on any diagonal are the same). A Toeplitz matrix is also called a diagonal-constant matrix. first-row is the first row in the matrix and first-column is the first column in the matrix.

trace clj

(trace square-m)

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

transpose clj

(transpose m)

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

update-column clj

(update-column m column row+number->number)

Updates a column of matrix m, using function row+number->number, which is a function the row and number and returns a number.

update-diagonal clj

(update-diagonal m row+number->number)

Updates the diagonal of matrix m, using function row+number->number, which is a function of the row and number and returns a number.

update-row clj

(update-row m row column+number->number)

Updates a row of matrix m, using function column+number->number, which is a function of the column and number and returns a number.

upper-triangular-matrix? clj

(upper-triangular-matrix? x)

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

zero-matrix? clj

(zero-matrix? x)

Returns true if all the elements of the matrix are zeros.