matrixVander function

Array2d matrixVander(Array x, { int? N, bool increasing = false, })

Generate a Vandermonde matrix. The columns of the output matrix are powers of the input vector. The order of the powers is determined by the increasing boolean argument. Specifically, when increasing is False, the i-th output column is the input vector raised element-wise to the power of N - i - 1. Such a matrix with a geometric progression in each row is named for Alexandre- Theophile Vandermonde.

Parameters

• x : input array
• N : int, optional Number of columns in the output. If N is not specified, a square array is returned (N = x.length).
• increasing : bool, optional Order of the powers of the columns. If true, the powers increase from left to right, if false (the default) they are reversed.

Returns

out : Array2d Vandermonde matrix. If increasing is False, the first column is x^(N-1)``, the second ``x^(N-2)`` and so forth. If increasing` is True, the columns are x^0, x^1, ..., x^(N-1).

Examples

var x = Array([2.0, 4.0, 8.0]);

print(vander(x));
print(vander(x, increasing: true));

/* output:
Array2d([
  Array([4.0, 2.0, 1.0]),
  Array([16.0, 4.0, 1.0]),
  Array([64.0, 8.0, 1.0])
])

Array2d([
  Array([1.0, 2.0, 4.0]),
  Array([1.0, 4.0, 16.0]),
  Array([1.0, 8.0, 64.0])
])
*/

Implementation

Array2d matrixVander(Array x, {int? N, bool increasing = false}) {
  N ??= x.length;
  if (N <= 0) {
    throw FormatException('N must be greater than 0 (N > 0)');
  }

  var v = Array2d.fixed(x.length, N);

  // create other vander terms: column 0 - N
  for (var row = 0; row < x.length; row++) {
    // create a matrix increasing order
    if (increasing) {
      for (var column = 0; column < N; column++) {
        v[row][column] = pow(x[row], column).toDouble();
      }
    }
    // create a matrix decreasing order
    else {
      for (var column = 0; column < N; column++) {
        v[row][column] = pow(x[row], N - 1 - column).toDouble();
      }
    }
  }

  return v;
}