1. All mathematical functions are written to ressemble paper algebra :
2. AxB --> $A->times($B);
3. A-B --> $A->minus($B);
4. A^(-1) --> $A->inv();
5. A' --> $A->prime();
6. det(A) --> $A->det($A);
7. etc.
8. This restricts nested calls, but augment readability.

Class Variable Summary

• $numbers = array()
  
• $numColumns = 0
  
• $numRows = 0
  
  
  

Method Summary

• matrix matrix($numbers [, $numRows, $numColumns])
  
  
  Matrix constructor.

• matrix eye($n, $m)
  
  
  Creates an $n by $m "identity" matrix.

• matrix ones($n, $m)
  
  
  Creates an $n by $m matrix of ones.

• matrix zeros($n, $m)
  
  
  Creates an $n by $m matrix of zeros.

• matrix diag($vector)
  
  
  Creates a diagonal matrix with $vector on the diagonal.

• matrix random($n, $m)
  
  
  Creates an $n by $m matrix of uniformly distributed numbers.

• unknown get_num_rows()
  
  
  Obtain the number of rows in the matrix.

• unknown get_num_columns()
  
  
  Obtain the number of columns in the matrix.

• array get_data()
  
  
  Obtain the two dimensionnal array of numbers.

• unknown get_value($i, $j)
  
  
  Obtain value at the entry $i,$j of the matrix.

• matrix get_columns($start, $stop)
  
  
  Obtain the matrix formed by the columns $start to (and including) $stop.

• matrix get_rows($start, $stop)
  
  
  Obtain the matrix formed by the rows $start to (and including) $stop.

• void set_data($numbers)
  
  
  Set the data of the matrix.

• void set_value($i, $j, $value)
  
  
  Set the value of the entry $i,$j of the matrix.

• void smoothe($tolerance)
  
  
  All values of $this within $tolerance of zero are set to zero.

• void set_columns($start, $stop, $block_matrix)
  
  
  Set the columns from $start to (and including) $stop to $block_matrix.

• void set_rows($start, $stop, $block_matrix)
  
  
  Set the rows from $start to (and including) $stop to $block_matrix .

• void delete_columns($start, $stop)
  
  
  Delete the columns from $start to (and including) $stop if $this.

• void delete_rows($start, $stop)
  
  
  Delete the rows from $start to (and including) $stop of $this.

• matrix utrig()
  
  
  Obtain the upper triangular matrix (without the diagonal) of $this.

• matrix ltrig()
  
  
  Obtain the lower triangular matrix (without the diagonal) of $this.

• matrix diag()
  
  
  Obtain the diagonal vector of $this.

• bool size_eq($someMatrix)
  
  
  Test if this matrix has the same dimensions as $someMatrix.

• bool is_square()
  
  
  Test if this matrix is square.

• matrix plus($someMatrix)
  
  
  Add this matrix to $someMatrix. $C = $A->plus($B);

• matrix minus($someMatrix)
  
  
  Substract $someMatrix from this matrix. $C = $A->minus($B);

• matrix times($someMatrix)
  
  
  Multiply this matrix by $someMatrix. $C = $A->times($B);

• matrix s_times($someScalar)
  
  
  Multiply this matrix by $someScalar. $C = $A->s_times($s);

• matrix det($someMatrix)
  
  
  Computes the determinant of $someMatrix. $det = $A->det($A);

• matrix minor_matrix($someMatrix, $column, $row)
  
  
  Returns $someMatrix matrix without the $columnth column and $rowth row. $C = $A->minor_matrix($A, $i, $j);

• matrix prime()
  
  
  Returns the transpose of the matrix. $A_p = $A->prime();

• matrix lu()
  
  
  Returns a 2n x n matrix containing the PLU decomposition of this matrix. $PLU = $A->LU();

• matrix inv()
  
  
  Returns the inverse of the matrix. $A_I = $A->inv();

• matrix p_times($someMatrix)
  
  
  Performs element by element multiplication of this matrix with $someMatrix. $C = $A->p_times($B);

• matrix p_div($someMatrix)
  
  
  Performs element by element division of this matrix by $someMatrix. $C = $A->p_div($B);

• matrix mat_max()
  
  
  Finds the maximum of each column of the matrix.$max = $A->mat_max();

• matrix mat_min()
  
  
  Finds the minimum of each column of the matrix.$max = $A->mat_min();

• matrix sum()
  
  
  Finds the sum of each column of the matrix.$sum = $A->sum();

• matrix mean()
  
  
  Finds the mean of each column of the matrix.$mean = $A->mean();

• matrix gt($someMatrix)
  
  
  Compares element by element if this matrix greater than $someMatrix.$max = $A->gt($B);

• matrix gteq($someMatrix)
  
  
  Compares element by element if this matrix greater or equal than $someMatrix.$max = $A->gteq($B);

• matrix lt($someMatrix)
  
  
  Compares element by element if this matrix less than $someMatrix.$max = $A->lt($B);

• matrix lteq($someMatrix)
  
  
  Compares element by element if this matrix less or equal than $someMatrix.$max = $A->lteq($B);

Method Detail

matrix::matrix

matrix(
array
$numbers );

Parameters

$numbers

[, $numRows

, $numColumns]

Remarks

$numbers[$i][$j] is a two-dimensionnal array of numbers where $i is the depth and $j is the width. If $numRows and $numColumns are specified, any column/row that is not defined by $numbers will be filled with zeros.

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matrix::eye

eye(
int $n, int $m );

Parameters

$n

$m

Remarks

Builds an $n by $m matrix with an identity matrix of size min($n, $m) in the north-east corner and puts zeros elsewhere




matrix::ones

ones(
int $n, int $m );

Parameters

$n

$m

Remarks

Builds an $n by $m matrix of ones.




matrix::zeros

zeros(
int $n, int $m );

Parameters

$n

$m

Remarks

Builds an $n by $m matrix of zeros.




matrix::random

random(
int $n, int $m );

Parameters

$n

$m

Remarks

Builds an $n by $m matrix of uniformly distributed random numbers (0,1).




matrix::diag

diag(
matrix $vector);

Parameters

$vector

Remarks

Builds a diagonal matrix with $vector on the diagonal. $vector must have one of its dimensions equal to one.




matrix::get_num_rows

get_num_rows();

Remarks

Returns the number of rows of this matrix.




matrix::get_num_columns

get_num_columns();

Remarks

Returns the number of columns of this matrix.




matrix::get_data

get_data();

Remarks

Returns the array of numbers of the data.




matrix::get_value

get_value(int $i, int $j);

Remarks

Returns the value at position $i, $j.




matrix::get_rows

get_rows(int $start, int $stop);

Remarks

Returns the rows starting at position $start and finishing at position $stop. $start and $stop must be within the number of rows of the matrix.




matrix::get_columns

get_columns(int $start, int $stop);

Remarks

Returns the columns starting at position $start and finishing at position $stop. $start and $stop must be within the number of rows of the matrix.




matrix::set_data

set_data(array $numbers);

Parameters

$numbers

Remarks

Sets the numbers of the matrix. $numbers[$i][$j] is a two-dimensionnal array of numbers where $i is the depth and $j is the width.




matrix::set_value

set_value(int $i, int $jfloat $value);

Parameters

$i

$j

$value

Remarks

Sets the value of the entry $i, $j of the matrix.




matrix::smoothe

smoothe(floar $tolerance);

Parameters

$tolerance

Remarks

Sets the all values of $this within $tolerance to zero to zero.




matrix::set_columns

set_columns(int $start, int $stopmatrix $block_matrix);

Parameters

$start

$stop

$bloc_matrix

Remarks

Sets the columns starting at position $start and finishing at position $stop in the matrix. $start and $stop must be within the number of columns of the matrix.




matrix::set_rows

set_rows(int $start, int $stopmatrix $block_matrix);

Parameters

$start

$stop

$block_matrix

Remarks

Sets the rows starting at position $start and finishing at position $stop in the matrix. $start and $stop must be within the number of rows of the matrix.




matrix::delete_columns

delete_columns(int $start, int $stop);

Parameters

$start

$stop

Remarks

Deletes the columns starting at position $start and finishing at position $stop in the matrix. $start and $stop must be within the number of columns of the matrix.




matrix::delete_rows

delete_rows(int $start, int $stop);

Parameters

$start

$stop

Remarks

Deletes the rows starting at position $start and finishing at position $stop in the matrix. $start and $stop must be within the number of rows of the matrix.




matrix::utrig

utrig();

Parameters

Remarks

Returns the upper triangular matrix of $this (without the diagonal).




matrix::ltrig

ltrig();

Parameters

Remarks

Returns the lower triangular matrix of $this (without the diagonal).




matrix::diag

diag();

Parameters

Remarks

Returns the diagonal vector of $this.




matrix::is_square

is_square();

Remarks

Checks if depth == width.




matrix::size_equal

size_equal(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Checks if this matrix has the same size as $someMatrix




matrix::plus

plus(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Adds this matrix with $someMatrix. Both matrices must have the same size.




matrix::minus

minus(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Substracts $someMatrix from this matrix. Both matrices must have the same size.




matrix::times

times(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Right-multiply this matrix by $someMatrix. The length of this matrix must equal the depth of $someMatrix.




matrix::s_times

s_times(float $someScalar);

Parameters

$someScalar

Remarks

Scalar multiplication of this matrix.




matrix::det

det(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Computes the determinant of $someMatrix (which must be square).




matrix::minor_matrix

minor_matrix(matrix $someMatrix, int $row, int $column);

Parameters

$someMatrix

$row

$column

Remarks

Finds the matrix used for computing the minor of a factor (e.g. : the original matrix where $column and $row are deleted).




matrix::prime

prime();

Remarks

Transposes this matrix.




matrix::lu

lu();

Remarks

Returns a 2n x n matrix containing the PLU decomposition of this matrix. The matrix must be square. The first n x n matrix contains the permutation matrix and the second n x n matrix contains the "stacked" L and U matrices. Since elements on the diagonal of the L matrix, these are deleted by convention (and thus, the diagonal of the second n x n matrix is the diagonal of the U matrix). See the file example.php for an example.




matrix::inv

inv();

Remarks

Finds the inverse of the matrix by PLU decomposition. The matrix must be square.




matrix::p_times

p_times(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Performs element by element multiplication. Both matrices must have the same size.




matrix::p_div

p_div(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Performs element by element division. Both matrices must have the same size and no element of $someMatrix can be zero.




matrix::mat_max

mat_max();

Remarks

Finds the column maximum.




matrix::mat_min

mat_min();

Remarks

Finds the column minimum.




matrix::sum

sum();

Remarks

Computes the column total.




matrix::mean

sum();

Remarks

Computes the column average.




matrix::gt

gt(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Compare if this matrix is greater than $someMatrix element by element . Both matrices must have the same size.




matrix::gteq

gteq(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Compare if this matrix is greater than or equal to $someMatrix element by element . Both matrices must have the same size.




matrix::lt

lt(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Compare if this matrix is lesser than $someMatrix element by element . Both matrices must have the same size.




matrix::lteq

lteq(matrix $someMatrix);

Parameters

$someMatrix

Remarks

Compare if this matrix is lesser than or equal to $someMatrix element by element . Both matrices must have the same size.