sicmutils.matrix — io.samritchie/sicmutils 0.13.0-SNAPSHOT

*careful-conversion* clj/s

->structure clj/s

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

Convert m to a structure with given outer and inner orientations. Rows of M will become the inner tuples, unless t? is true, in which columns of m will form the inner tuples.

by-rows clj/s

(by-rows & rs)

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)

Computes the matrix of cofactors of the given structure with the same shape, if s is square.

column clj/s

(column & es)

determinant clj/s

(determinant m)

Computes the determinant of m, which must be square. Generic operations are used, so this works on symbolic square matrix.

dimension clj/s

(dimension m)

fmap clj/s

(fmap f m)

Maps f over the elements of m, returning an object of the same type.

generate clj/s

(generate r c f)

Create the r by c matrix whose entries are (f i j)

get-in clj/s

(get-in m is)

Like get-in for matrices, but obeying the scmutils convention: only one index is required to get an unboxed element from a column vector. This is perhaps an unprincipled exception...

I clj/s

(I n)

Return the identity matrix of order n.

invert clj/s

(invert m)

Computes the inverse of a square matrix.

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

matrix-some clj/s

(matrix-some f m)

True if f is true for some element of m.

matrix? clj/s

(matrix? m)

nth-col clj/s

(nth-col m j)

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-> s)

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

square-structure-> clj/s

(square-structure-> s k)

Converts the square structure s into a matrix, and calls the continuation with that matrix and a function which will restore a matrix to a structure with the same inner and outer orientations as s.

square-structure-operation clj/s

(square-structure-operation s f)

Applies matrix operation f to square structure s, returning a structure of the same type as that given.

transpose clj/s

(transpose m)

Transpose the matrix m.

without clj/s

(without m i j)

The matrix formed by deleting the i'th row and j'th column of the given matrix.