/**
 * Array of numbers.
 */
export type Vector = number[];
/**
 * Array of vectors.
 */
export type Matrix = Vector[];
/**
 * Solves system of equations using Gauss-Jordan elimination.
 *
 * Brings the matrix to reduced row echelon form, while simultaneously reducing and thus solving the augmented results
 * matrix.
 *
 * See also http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
 *
 *
 *  Note that the 'matrix' is given as a 'array of arrays' of rank size. That is values can be assigned
 *  as   matrix[row][column]   where 'row' is typically the equation, and 'column' is the term of the equation.
 *  That is the matrix is in the form of a 'row first array'.
 *
 *  However, 'vectors' is a 'array of arrays' which can have any number of columns, with each column array the same
 *  'rank' size as 'matrix'.
 *
 *  This allows for simpler handling of the results, especially is only one column 'vector' is all that is required
 *  to produce the desired solution.
 *
 *  For example, the 'vectors' can consist of simple array of numbers.  when only one set of simultaneous equations is
 *  to be solved from the given set of coefficient weighted terms.
 *
 *  However, by specifying more 'columns' (as an 'array of vector columns', you can use this function to solve a set of
 *  'separable' equations.
 *
 *  For example a distortion function where
 *  ```
 *  u = U(x,y)  v = V(x,y)
 *  ```
 *  And the functions U() and V() have separate coefficients, but are being generated from a common x,y->u,v  data set.
 *
 *  You can also use the 'vectors' to generate an inverse of the given 'matrix' though as a 'column first array' rather
 *  than a 'row first array'. For details see http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
 *
 *
 * @see https://imagemagick.org/api/MagickCore/matrix_8c_source.html#l00480 GaussJordanElimination() at
 * ImageMagick source.
 *
 * @param coefficients Linear equations system coefficients.
 * @param results Augment results matrix.
 */
export declare function gaussJordanElimination(coefficients: Matrix, results: Matrix): Matrix;