18. Matrix and Integer Array functions

ICREATE(elements, mode)

Creates an integer array with the size elements. Returned is the array number to be used to address the array with ISET and IGET. You can have up to 64 integer arrays. Depending on the virtual storage they may contain 1 million elements and more. Accessing integer arrays is very fast as there is no overhead compared to STEM variables.

Parameters

elements – Number entries available
mode – The initialization type. If mode is not set the array remains uninitialized.

Mode	Description
Element-Number	index of element
NULL	elements are set to 0
DESCENT	index of the element in reverse order
SUNDARAM	prime numbers (Sundaram algorithm)
PRIME	prime numbers (sieve of Erasthones)

ISET(array-number, element-number, integer-value): Sets a certain element of an array with an integer value.

IGET(array-number, element-number): Gets (returns) a certain element of an array with an integer value.

MCREATE(rows, columns): Creates a (Float) matrix with size [rows x columns]. Returned is the Matrix number to be used in various matrix operations. You can have up to 128 matrixes, depending on the virtual storage available. Accessing a matrix is very fast as there is no overhead compared to STEM variables.

MSET(matrix-number, row, column, float-value): Sets a certain element of the matrix with a float value.

MGET(matrix-number, row, column): Gets (returns) a certain element of the matrix.

MMULTIPLY(matrix-number-1, matrix-number-2): Multiplies 2 matrices and creates a new matrix, which is returned. Input matrices remain untouched. The format of matrix-1 is [rows x columns], therefore the format of matrix-2 must be [columns x rows]. The format of the result matrix is rows x rows.

MINVERT(matrix-number): Inverts the given matrix and creates a new matrix, which is returned. The input matrix must be squared and remains untouched. The format of the result matrix remains the same as the input matrix.

MTRANSPOSE(matrix-number): Transposes the given matrix and creates a new matrix, which is returned. The input matrix remains untouched. If the format of the input matrix is [rows x columns] then the result matrix is columns x rows.

MCOPY(matrix-number): Copies the given matrix and creates a new matrix, which is returned. The input matrix remains untouched. Formats of both matrices are equal.

MNORMALISE(matrix-number, mode)

Normalises the given matrix and creates a new matrix, which is returned. The input matrix remains untouched. Formats of both matrices are equal.

Mode	Description
STANDARD	row is normalized to mean=0 variance=1
ROWS	row value is divided by number of rows
MEAN	row value is normalized to mean=0, variance remains unchanged

MDELROW(matrix-number, row-number[, row-number[, row-number...]]): Copies the given matrix without the specified rows-to-delete as a new matrix, which is returned. The input matrix remains untouched.

MDELCOL(matrix-number, col-number[, col-number[, col-number...]]): Copies the given matrix without the specified columns-to-delete as a new matrix, which is returned. The input matrix remains untouched.

MPROPERTY(matrix-number[, ”FULL”/”BASIC”])

Returns the properties of the given matrix in BREXX variables:

_rows	number of rows of matrix
_cols	number of columns of matrix

If FULL is specified additionally the the following stem variables are returned:

Stem	Description
_rowmean.column-i	mean of rows of column-i
_rowvariance.column-i	variance of rows of column-i
_rowlow.column-i	lowest row value of column-i
_rowhigh.column-i	highest row value of column-i
_rowsum.column-i	sum of row value of column-i
_rowsqr.column-i	sum of squared row value of column-i
_colsum.row-i	sum of column values of row-i

MSCALAR(matrix-number, number): Multiplies each element of a matrix with a number (float). The result is stored in a new matrix, which is returned. The input matrix remains untouched.

MADD(matrix-number-1, matrix-number-2): Adds each element of a matrix-1 with the same element of matrix-2. The result is stored in a new matrix, which is returned. The input matrix remains untouched. Matrix-1 and matrix-2 must have the same dimensions.

MSUBTRACT(matrix-number-1, matrix-number-2): Subtracts each element of a matrix-2 from the same element of matrix-1. The result is stored in a new matrix, which is returned. The input matrix remains untouched. Matrix-1 and matrix-2 must have the same dimensions.

MPROD(matrix-number-1, matrix-number-2): Multiplies each element of a matrix-1 with the same element of matrix-2. The result is stored in a new matrix, which is returned. The input matrix remains untouched. Matrix-1 and matrix-2 must have the same dimensions.

MSQR(matrix-number): Squares each element of the matrix. The result is stored in a new matrix, which is returned. The input matrix remains untouched.

MINSCOL(matrix-number): Inserts a new column as the first column. The initial first column becomes the second column, etc. The result is stored in a new matrix, which is returned. The input matrix remains untouched.

MFREE([matrix-number/integer-array-number, “MATRIX”/”INTEGER-ARRAY”]): Frees the storage of allocated matrices and/or integer arrays. If no parameter is specified all allocations are freed. To release a specific matrix or integer-array the matrix-number or integer-array-number must be used as the first parameter, followed by the type to release.