sicmutils.matrix — sicmutils 0.14.0

*careful-conversion* clj/s

Set this dynamic variable to false to allow s->m to operate on structures for which (* ls ms rs) does NOT yield a numerical value.

->structure clj/s

(->structure m)

(->structure m outer-orientation inner-orientation t?)

Returns a structure generated by converting m into a nested structure with the supplied outer-orientation and inner-orientation.

If t? is true, the columns of m will form the inner tuples. If t? is false, the rows of m will form the inner tuples.

By default, if you supply a single argument (the matrix m), a matrix turns into a single outer ::s/down of inner columns represented as ::up structures.

by-cols clj/s

(by-cols & cols)

Returns a matrix whose columns consist of the supplied sequence of cols. These all must be the same length.

Variadic equivalent to by-cols*.

by-cols* clj/s

(by-cols* cols)

Returns a matrix whose columns consist of the supplied sequence of cols. These all must be the same length.

for a variadic equivalent, see by-cols.

by-rows clj/s

(by-rows & rows)

Returns a matrix whose rows consist of the supplied sequence of rows. These all must be the same length.

Variadic equivalent to by-rows*.

by-rows* clj/s

(by-rows* rows)

Returns a matrix whose rows consist of the supplied sequence of rows. These all must be the same length.

for a variadic equivalent, see by-rows.

characteristic-polynomial clj/s

(characteristic-polynomial m x)

Compute the characteristic polynomial of the square matrix m, evaluated at x. Typically x will be a dummy variable, but if you wanted to get the value of the characteristic polynomial at some particular point, you could supply a different expression.

cofactors clj/s

(cofactors m)

Returns the matrix of cofactors of the supplied square matrix m.

column clj/s

(column & xs)

Returns a column matrix populated by the supplied xs. Variadic equivalent to column*.

column* clj/s

(column* xs)

Returns a column matrix populated by the supplied xs. For a variadic equivalent, see column.

column-matrix->up clj/s

(column-matrix->up m)

Returns the single column from the supplied column matrix as an up. Errors if some other type is supplied.

column-matrix->vector clj/s

(column-matrix->vector m)

Returns the single column from the supplied column matrix as a vector. Errors if some other type is supplied.

column? clj/s

(column? m)

Returns true if m is a matrix with a single column (a 'column matrix'), false otherwise.

determinant clj/s

(determinant m)

Returns the determinant of the supplied square matrix m. Generic operations are used, so this works on symbolic square matrices.

diagonal clj/s

(diagonal m)

Returns the diagonal of the supplied matrix m as an up structure. Errors if a type other than a diagonal matrix is supplied.

dimension clj/s

(dimension m)

Returns the 'dimension', ie, the number of rows & columns, of the supplied square matrix. Errors if some other type is supplied.

down->row-matrix clj/s

(down->row-matrix v)

Returns a row matrix with the contents of the supplied down structure. Errors if any other type is provided.

fmap clj/s

(fmap f m)

Maps f over the elements of the matrix m returning a new matrix of the same dimensions as m.

fmap-indexed clj/s

(fmap-indexed f m)

Maps f over three arguments:

• each element of the matrix m
• its row i
• its column j

and returns a new matrix of the same dimensions as m.

generate clj/s

(generate r c f)

Returns a matrix with r rows and c columns, whose entries are generated by the supplied function f.

The entry in the ith row and j-th column is (f i j).

get-in clj/s

(get-in m is)

Like [[clojure.core/get-in]] for matrices, but obeying the scmutils convention: only one index is required to get an unboxed element from a column vector.

NOTE that this is perhaps an unprincipled exception...

I clj/s

(I n)

Return the identity matrix of order n.

identity-like clj/s

(identity-like M)

Return an identity matrix whose ones and zeros match the types of the supplied square matrix. Errors if a non-square matrix is supplied.

identity? clj/s

(identity? m)

Returns true if the supplied matrix is an identity matrix, false otherwise.

invert clj/s

(invert m)

Returns the inverse of the supplied square matrix m.

literal-matrix clj/s

(literal-matrix sym nrows ncols)

Generates a nrows x ncols matrix of symbolic entries, each prefixed by the supplied symbol sym.

NOTE: The symbols in the returned matrix record their Einstein-notation path into the structure that this matrix represents; a down of up columns. This means that the returned indices embedded in the symbols look flipped, ji vs ij.

For example:

(= (literal-matrix 'x 2 2) (by-rows ['x_0↑0 'x_1↑0] ['x_0↑1 'x_1↑1]))

m->s clj/s

(m->s ls m rs)

Convert the matrix m into a structure S, guided by the requirement that (* ls S rs) should be a scalar

make-diagonal clj/s

(make-diagonal v)

Returns the diagonal matrix of order (count v) with the elements of v along the diagonal.

make-zero clj/s

(make-zero n)

(make-zero m n)

Return a zero-valued matrix of m rows and n columns (nXn if only n is supplied).

Matrix cljs

matrix->vector clj/s

(matrix->vector m)

If m is already a vector, acts as identity. Else, returns the matrix as a vector of rows (or throws if neither of these types is passed).

matrix? clj/s

(matrix? m)

Returns true if the supplied m is an instance of Matrix, false otherwise.

nth-col clj/s

(nth-col m n)

Returns the n-th column of the supplied matrix m as an up structure.

nth-row clj/s

(nth-row m n)

Returns the n-th row of the supplied matrix m as a down structure.

num-cols clj/s

(num-cols m)

Returns the number of columns of the supplied matrix m. Throws if a non-matrix is supplied.

num-rows clj/s

(num-rows m)

Returns the number of rows of the supplied matrix m. Throws if a non-matrix is supplied.

row clj/s

(row & xs)

Returns a row matrix populated by the supplied xs. Variadic equivalent to row*.

row* clj/s

(row* xs)

Returns a row matrix populated by the supplied xs. For a variadic equivalent, see row.

row-matrix->down clj/s

(row-matrix->down m)

Returns the single row from the supplied row matrix as a down. Errors if some other type is supplied.

row-matrix->vector clj/s

(row-matrix->vector m)

Returns the single row from the supplied row matrix as a vector. Errors if some other type is supplied.

row? clj/s

(row? m)

Returns true if m is a matrix with a single row (a 'row matrix'), false otherwise.

s->m clj/s

(s->m ls ms rs)

Convert the structure ms, which would be a scalar if the (compatible) multiplication (* ls ms rs) were performed, to a matrix.

s:inverse clj/s

(s:inverse ls ms rs)

s:transpose clj/s

(s:transpose ls ms rs)

seq-> clj/s

(seq-> xs)

Convert a sequence (typically, of function arguments) to an up-structure.

GJS: Any matrix in the argument list wants to be converted to a row of columns

some clj/s

(some f m)

Returns true if f is true for some element of the matrix m, false otherwise. (Also works on arbitrary nested sequences.)

square-structure-> clj/s

(square-structure-> s continue)

Converts the square structure s into a matrix, and calls the supplied continuation continue with

• the generated matrix.
• a function which will restore a matrix to a structure with the same inner and outer orientations as s.

Returns the result of the continuation.

square-structure-operation clj/s

(square-structure-operation s f)

Applies matrix operation f to square structure s and returns a structure of the same type as the supplied structure.

square? clj/s

(square? m)

Returns true if m is a square matrix, false otherwise.

submatrix clj/s

(submatrix m lowrow hirow lowcol hicol)

Returns the submatrix of m generated by taking

• rows from lowrow -> hirow,
• columns from lowcol -> hicol

trace clj/s

(trace m)

Returns the trace (the sum of diagonal elements) of the square matrix m. Generic operations are used, so this works on symbolic square matrices.

transpose clj/s

(transpose m)

Returns the transpose of the matrix m. The transpose is the original matrix, with rows and columns swapped.

up->column-matrix clj/s

(up->column-matrix v)

Returns a column matrix with the contents of the supplied up structure. Errors if any other type is provided.

with-substituted-row clj/s

(with-substituted-row m i v)

Returns a new matrix of identical shape to m, with the vector v substituted for the ith row.

without clj/s

(without m i j)

Returns the matrix formed by deleting the i-th row and j-th column of the given matrix m.