Utility Functions

Utility functions support the implementation of Gaussian Processes on Graphs and Likelihood Evaluations Based on Fast Fourier Transforms, such as

  • rfft, inv_rfft, rfft2, and inv_rfft2 to evaluate real fast Fourier transforms in one and two dimensions.

  • gp_conditional_loc_scale to evaluate the conditional location and scale parameter of a univariate normal random variable given observations of correlated variables.

  • functions to compare values and assertions for debugging.

Function Reference

void assert_equal(int actual, int desired)

Assert that two integers are equal.

Parameters

  • actual – Actual value.

  • desired – Desired value.

int is_close(real actual, real desired, real rtol, real atol)

Check whether two values are close.

The actual value x and desired value y may differ by at most tol = rtol * y + atol, where rtol is the relative tolerance, and atol is the absolute tolerance. The tolerance tol is clipped below at \(10^{-15}\) to avoid rejection due to rounding errors.

Parameters

  • actual – Actual value x.

  • desired – Desired value y.

  • rtol – Relative tolerance r.

  • atol – Absolute tolerance a.

Returns

1 if the values are close, 0 otherwise.

void assert_close(real actual, real desired, real rtol, real atol)

Assert that two values are close. See is_close(real, real, real, real) for a description of the parameters.

void assert_close(real actual, real desired)

Assert that two values are close. See is_close(real, real, real, real) for a description of the parameters.

int is_finite(complex x)

Check whether a possibly complex value is finite.

Parameters

x – Value to check.

Returns

1 if the value is finite, 0 otherwise.

void assert_close(vector actual, vector desired, real rtol, real atol)

Assert that two vectors are close. See is_close(real, real, real, real) for a description of the parameters.

void assert_close(vector actual, vector desired)

Assert that two vectors are close. See is_close for description of parameters.

void assert_close(vector actual, real desired, real rtol, real atol)

Assert that two vectors are close. See is_close for description of parameters.

void assert_close(vector actual, real desired)

Assert that two vectors are close. See is_close for description of parameters.

int is_finite(vector x)

Check whether all elements of a vector are finite.

Parameters

x – Vector to check.

Returns

1 if all elements of the vector are finite, 0 otherwise.

void assert_finite(vector x)

Assert that all elements of a vector are finite.

Param

Vector to check.

int is_finite(matrix x)

Check whether all elements of a matrix are finite.

Param

Vector to check.

void print_matrix(complex_matrix x)

Pretty-print a matrix.

void assert_close(matrix actual, matrix desired, real rtol, real atol)

Assert that two matrices are close. See is_close for description of parameters.

void assert_close(matrix actual, matrix desired)

Assert that two matrices are close. See is_close for description of parameters.

void assert_close(matrix actual, real desired, real rtol, real atol)

Assert that two matrices are close. See is_close for description of parameters.

void assert_close(matrix actual, real desired)

Assert that two matrices are close. See is_close for description of parameters.

void assert_close(complex_vector actual, complex_vector desired, real rtol, real atol)

Assert that two vectors are close. See is_close for description of parameters.

void assert_close(complex_vector actual, complex_vector desired)

Assert that two vectors are close. See is_close for description of parameters.

void assert_close(complex_vector actual, complex desired, real rtol, real atol)

Assert that two vectors are close. See is_close for description of parameters.

void assert_close(complex_vector actual, complex desired)

Assert that two vectors are close. See is_close for description of parameters.

complex_vector rfft(vector y)

Compute the one-dimensional discrete Fourier transform for real input.

Parameters

y – Real signal with n elements to transform.

Returns

Truncated vector of Fourier coefficients with n %/% 2 + 1 elements.

complex_vector expand_rfft(complex_vector y, int n)

Expand truncated one-dimensional discrete Fourier transform coefficients for real input to full Fourier coefficients.

vector inv_rfft(complex_vector z, int n)

Compute the one-dimensional inverse discrete Fourier transform for real output.

Parameters

  • z – Truncated vector of Fourier coefficents with n %/% 2 + 1 elements.

  • n – Length of the signal (required because the length of the signal cannot be determined from z alone).

Returns

Real signal with n elements.

complex_matrix rfft2(matrix y)

Compute the two-dimensional discrete Fourier transform for real input.

Parameters

y – Real signal with n rows and m columns to transform.

Returns

Truncated vector of Fourier coefficients with n rows and m %/% 2 + 1 elements.

matrix inv_rfft2(complex_matrix z, int m)

Compute the two-dimensional inverse discrete Fourier transform for real output.

Parameters

  • z – Truncated vector of Fourier coefficients with n rows and m %/% 2 + 1 elements.

  • m – Number of columns of the signal (required because the number of columns cannot be determined from z alone).

Returns

Real signal with n rows and m columns.

vector gp_conditional_loc_scale(vector y, real cov11, vector cov21, matrix cov22)

Evaluate the conditional location and scale parameter of a univariate normal random variable given correlated observations from a multivariate normal distribution.

Parameters

  • y – Observation to condition on.

  • cov11 – Marginal variance of the target random variable.

  • cov21 – Covariance between y and the target random variable.

  • cov22 – Covariance amongst the elements of y.

Returns

Location and scale as a vector.