erfInv function

double erfInv(num x)

Returns the inverse error function.

Implementation

double erfInv(num x) {
  if (x <= -1.0) {
    return double.negativeInfinity;
  } else if (x >= 1.0) {
    return double.infinity;
  } else {
    const x0 = 0.7;
    const a = [0.886226899, -1.645349621, 0.914624893, -0.140543331];
    const b = [-2.118377725, 1.442710462, -0.329097515, 0.012229801];
    const c = [-1.970840454, -1.624906493, 3.429567803, 1.641345311];
    const d = [3.543889200, 1.637067800];
    var r = 0.0;
    if (x < -x0) {
      final z = sqrt(-log((1.0 + x) / 2.0));
      r = -(((c[3] * z + c[2]) * z + c[1]) * z + c[0]) /
          ((d[1] * z + d[0]) * z + 1.0);
    } else if (x < x0) {
      final z = x * x;
      r = x *
          (((a[3] * z + a[2]) * z + a[1]) * z + a[0]) /
          ((((b[3] * z + b[3]) * z + b[1]) * z + b[0]) * z + 1.0);
    } else {
      final z = sqrt(-log((1.0 - x) / 2.0));
      r = (((c[3] * z + c[2]) * z + c[1]) * z + c[0]) /
          ((d[1] * z + d[0]) * z + 1.0);
    }
    for (var i = 0; i < 2; i++) {
      r -= (erf(r) - x) / (2.0 / sqrt(pi) * exp(-r * r));
    }
    return r;
  }
}