Matrix | SuperCollider 3.13.0 Help

Description

Matrices are a 2-dimensional Array whose slots may only contain (at the moment 'real' ) numbers. Their shape is fully described by the number of rows and columns(cols). Each element can be adressed by 2 indices (row,col), where row (col) ranges between 0 and rows-1 (cols-1). For a lesson on matrices, read your math books from school. Or this reference if you like it the hard way: http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/intro.html#Intro

Array2DMatrix uses an array-of-rows–notation. This is the same concept as found in Array2D. As a subclass of Array, Matrix responds to far more methods than given in this helpfile. Be aware of strange results when using them. This is meant to support only the basic matrix manipulations. Most of this is not designed for realtime action. Too slow, not optimized.

Part of MathLib, a diverse library of mathematical functions.

Class Methods

.newClear

Create a new Matrix of shape (rows, cols) filled with zeros. Matrix.newClear(3,3).postln;

Arguments:

	rows
	cols

.with

Create a new Matrix whose rows are filled with the given subarrays.

Matrix.with([[1,2,3],[4,5,6],[7,8,9]]).postln;

Arguments:

array

.withFlatArray

Create a new Matrix from a 1-dimensional array of shape (rows , cols). Matrix.withFlatArray(3,3,[1,2,3,4,5,6,7,8,9]).postln;

Arguments:

	rows
	cols
	array

.newIdentity

Create a new identity matrix of shape (n,n). Matrix.newIdentity(3).postln;

Arguments:

.newDiagonal

Create a new square diagonal matrix.Matrix.newDiagonal(Array.series(8)); // Integer Matrix.newDiagonal(Array.series(8.0)); // Float

Arguments:

diagonal

An array of values with which to fill the diagonal.

.newDFT

Create a new discrete Fourier transform matrix of shape (n,n). Matrix.newDFT(3).postln;n = 51; // DFT size // Make a sinusoidal test signal (3 partials: 1st, 3rd and 10th) x = Matrix.withFlatArray(n, 1, n collect: { |i| sin(2pi*i/(n - 1)) + sin(6pi*i/(n - 1)) + sin(20pi*i/(n - 1)) }) // Calculate Fourier transform y = Matrix.newDFT(n)*x // Plot spectrum y.flat.abs.plot(discrete: true) // Recover original signal from Fourier transform z = Matrix.newIDFT(n)*y z.flat.real.plot; x.flat.plot;

Arguments:

.newIDFT

Create a new inverse discrete Foutier transform matrix of shape (n,n). Matrix.newIDFT(3).postln;// Show discrete Fourier transform is unitary n = 3; (Matrix.newDFT(n)*Matrix.newIDFT(n)).real.postln;

Arguments:

.fill

fill the matrix by evaluating function. function is passed two arguments: row, col

Arguments:

	rows
	cols
	function

.mul

Arguments:

	ArrayA
	ArrayB

Instance Methods

.rows

Returns:

the number of rows

.cols

Returns:

the number of columns

.shape

Returns:

the number of rows and columns as array [rows, cols]

.postmln

post the matrix as 2D representation.Matrix.withFlatArray(3,3,[1,2,3,4,5,6,7,8,9]).postln; Matrix.withFlatArray(3,3,[1,2,3,4,5,6,7,8,9]).postmln;

.doRow

evaluate function for each element of row; function is passed two arguments: item, col

Arguments:

	row
	function

.doCol

evaluate function for each element of col; function is passed two arguments: item, row

Arguments:

	col
	function

.doMatrix

evaluate function for each element ; function is passed three arguments: item, row,col;

Arguments:

function

.colsDo

Iterate over the columns. Each column will be passed to func in turn.a = Matrix.newIdentity(4); a.colsDo({ |item, i| format("Col %: ", i).post; (item * i).postln;});

.rowsDo

Iterate over the rows. Each row will be passed to func in turn.a = Matrix.newIdentity(4); a.rowsDo({ |item, i| format("Row %: ", i).post; (item * i).postln;});

Changing Matrices

.put

put a single element at (row, col)

Arguments:

	row
	col
	value

.putRow

put a row of elements at (row)

Matrix.newClear(3,3).putRow(0,[2,4,6]).postln

Arguments:

	row
	values

.putCol

put a column of elements at (col)

Matrix.newClear(3,3).putCol(1,[2,4,6]).postln

Arguments:

	col
	values

.fillRow

fill a row by evaluating function for each element; function is passed two arguments: row, col.

Arguments:

	row
	function

.fillCol

fill a column by evaluating function for each element; function is passed two arguments: row, col.

Arguments:

	col
	function

.exchangeRow

exchange two rows

Arguments:

	rowA
	rowB

.exchangeCol

exchange two cols

Arguments:

	colA
	colB

Return Arrays

.at

Arguments:

	row
	col

.get

Arguments:

	row
	col

.asArray

Returns:

an array of rows

.flat

Returns:

a one slot array of all elements

Return Matrices

.fromRow

Arguments:

row

Returns:

a new matrix from row

.fromCol

Arguments:

	row
	values

the adjoint or adjugate of a square matrix

.inverse

Returns:

the inverse of a square matrix

.gram

Returns:

the gram matrix (the transpose of matrix multiplied with matrix) T^t * T

.pseudoInverse

Returns:

the pseudoInverse of a matrix

*

Returns:

the result of matrix multiplication: matrix * matrix2 matrix.cols must equal matrix2.rows

multiplication with aNumber for each element

+

Returns:

(matrix + matrix2) matrix must have the same shape as matrix2

summation with aNumber for each element

-

Returns:

(matrix - matrix2) matrix must have the same shape as matrix2

subtraction with aNumber for each element

.center

Arguments:

mean

Returns:

a matrix centred around the mean vector (which will be calculated for you if not supplied)

.thresh2

Bilateral thresholding.

Arguments:

thresh	When the `input.abs < thresh`, the output is forced to `0`. Should be a positive value.
adverb	Optional, for processing Collections. See Adverbs for Binary Operators.