MatrixArray : Object
Extension
ExtensionDescription
A two-dimensional array structure to facilitate matrix operations. This is a partial refactoring of the Matrix class from the MathLib quark. The modifications enable much faster calculation of some matrix operations, namely the determinant (-det), which subsequently speeds up the inverse and others. Performance is further enhanced by storing the transpose , and doing in-place operations when possible.
pseudoInverse, for efficiency, many of the underlying operations are done through Array's methods. As a consequence most methods will return a new Array rather than the MatrixArray object. So if you expect to call further methods on a result, the preferred pattern is to "cast" it into a new MatrixArray using *with.Class Methods
MatrixArray.fill(rows, cols, func)
Fill the matrix by evaluating function.
Arguments:
| rows |
The number of rows. |
| cols |
The number of columns. |
| func |
The function used to fill the matrix. The function is passed row and col as arguments. |
Returns:
A MatrixArray.
MatrixArray.with(array)
Create a MatrixArray with values from a 2-D Array.
Arguments:
| array |
A 2-D Array — an array of rows. |
Returns:
A MatrixArray.
MatrixArray.newClear(rows: 1, cols: 1)
Create a MatrixArray of a specified size, filled with nils.
Arguments:
| rows |
The number of rows. |
| cols |
The number of columns. |
Returns:
A MatrixArray.
Inherited class methods
Instance Methods
Access
.rowAt(row)
.colAt(col)
.at(row, col)
Get the value at [row, col].
Arguments:
| row |
The row index. |
| col |
The column index. |
Returns:
The value stored at [row, col].
.matrix
Get the MatrixArray as a 2-D array. Synonymous with -asArray.
Returns:
.asArray
Get the MatrixArray as a 2-D array. Synonymous with -matrix.
Returns:
.transpose
Get the flopped matrix (transpose). This transpose is computed on first request and stored thereafter for internal use and quick access.
Returns:
.flopped
Get the flopped matrix (transpose). This transpose is computed on first request and stored thereafter for internal use and quick access.
Returns:
.rows
Get the number of rows in the matrix.
.cols
Get the number of columns in the matrix.
Filtering
The following filter methods will return new objects (Arrays).
.getSub(rowStart: 0, colStart: 0, rowLength, colHeight)
Get a sub-matrix from within matrix.
Arguments:
| rowStart |
Row index to begin copying. |
| colStart |
Column index to begin copying. |
| rowLength |
The number of elements to copy from each row. |
| colHeight |
The number of elements to copy from each column. |
Returns:
.withoutRow(row)
Get a new matrix that is this one without a specified row.
Arguments:
| row |
The index of the row to omit. |
Returns:
.withoutCol(col)
Get a new matrix that is this one without a specified column.
Arguments:
| col |
The index of the column to omit. |
Returns:
.withoutRowCol(row, col)
A convenience method, for optimized use by -cofactor, which, unlike -withoutRow and -withoutCol, returns a MatrixArray that is this one without a specified row and column.
Arguments:
| row |
The index of the row to be removed. |
| col |
The index of the column to be removed. |
Returns:
A new MatrixArray.
Manipulation
.put(row, col, val)
Set the value in the matrix at a location.
Arguments:
| row |
A row index. |
| col |
A column index. |
| val |
The value to set. |
.removeRow(row)
Remove a row from the matrix.
Arguments:
| row |
The index of the row to remove. |
Returns:
This MatrixArray, which is now without row row.
.removeCol(col)
Remove a column from the matrix.
Arguments:
| col |
The index of the column to remove. |
Returns:
This MatrixArray, which is now without column col.
.zeroWithin(within)
.thresh2(thresh)
Bilateral thresholding in place.
Arguments:
| thresh |
When the input.abs < thresh, the output is forced to 0. Should be a positive value. Default is |
Returns:
This MatrixArray.
Characteristic Values of the Matrix
.cofactor(row, col)
Get the cofactor to element [row, col]. This is the determinant of the sub-matrix up to [row, col] mutiplied with (-1)**(row+col).
Arguments:
| row |
The row index. |
| col |
The column index. |
Returns:
A Number, the cofactor.
.adjoint
.det
.gram
Compute the gram matrix (the transpose of this matrix multiplied with itself).
T^t * T
Returns:
A 2-D Array.
.inverse
.pseudoInverse
.isSquare
Matrix Operations
*(that)
Matrix multiplication by another matrix or a number. If multiplying by another matrix, this * that. this.cols must equal that.rows. See also -mulMatrix.
Arguments:
| that |
Can be a Number, a MatrixArray, or a (2D) Array. |
Returns:
A 2-D Array.
.mulMatrix(mArray)
Matrix multiplication: this * that. this.cols must equal that.rows.
A(m,n) * B(n,r) = AB(m,r)
Arguments:
| mArray |
Can be a MatrixArray, or a (2D) Array. |
Returns:
A 2-D Array.
.mulNumber(aNumber)
.mixCoeffs(coeffs)
A convenience method for "mixing" one-dimensional coefficients with this matrix, i.e. a matrix multiplication. For example, mixing ambisonic signal coefficients with a transform matrix.
Arguments:
| coeffs |
Returns:
An Array with size this.rows.
Inherited instance methods
Examples
Attribution
This is a partial refactoring of the Matrix class from the MathLib quark originally authored by sc.solar, Till Bovermann, Christofer Fraunberger, and Dan Stowell.
This refactoring also includes a much faster determinant caclulation based on LU Decomposition.
The algorithm is published in:
Intel Application Notes AP-931, Streaming SIMD Extensions - LU Decomposition
link::Classes/MatrixArray::