QuadraticCheck

QuadraticCheck Functions

yroots.QuadraticCheck.quadratic_check_2D(test_coeff, tol)

2D specialization of quadratic_check().

Finds the min of the absolute value of the quadratic part and compares it to the sum of the remaining terms. There can’t be a root if min(extreme_values) > other_sum or if max(extreme_values) < -other_sum. Short-circuits as soon as one value below other_sum and one value above -other_sum are found.

Parameters:

  • test_coeff (numpy array) – The coefficient matrix of the polynomial to check.

  • tol (float) – The bound of the sup norm error of the Chebyshev approximation.

Returns:

True if the polynomial is guaranteed to have no zero on the unit box, False otherwise.

Return type:

bool

yroots.QuadraticCheck.quadratic_check_3D(test_coeff, tol)

3D specialization of quadratic_check().

Finds the min of the absolute value of the quadratic part and compares it to the sum of the remaining terms. There can’t be a root if min(extreme_values) > other_sum or if max(extreme_values) < -other_sum. Short-circuits as soon as one value below other_sum and one value above -other_sum are found.

Parameters:

  • test_coeff (numpy array) – The coefficient matrix of the polynomial to check.

  • tol (float) – The bound of the sup norm error of the Chebyshev approximation.

Returns:

True if the polynomial is guaranteed to have no zero on the unit box, False otherwise.

Return type:

bool

yroots.QuadraticCheck.quadratic_check_nd(test_coeff, tol)

N-dimensional specialization of quadratic_check().

Finds the min of the absolute value of the quadratic part and compares it to the sum of the remaining terms. There can’t be a root if min(extreme_values) > other_sum or if max(extreme_values) < -other_sum. Short-circuits as soon as one value below other_sum and one value above -other_sum are found.

Parameters:

  • test_coeff (numpy array) – The coefficient matrix of the polynomial to check.

  • tol (float) – The bound of the sup norm error of the Chebyshev approximation.

Returns:

True if the polynomial is guaranteed to have no zero on the unit box, False otherwise.

Return type:

bool