pharmpy.math module

pharmpy.math.conditional_joint_normal(mu, sigma, a)

Give parameters of the conditional joint normal distribution

The condition is the last len(a) values

See https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Conditional_distributions

pharmpy.math.corr2cov(corr, sd)

Convert correlation matrix to covariance matrix

Parameters

• corr – Correlation matrix (ones on diagonal)

• sd – One dimensional array of standard deviations

pharmpy.math.cov2corr(cov)

Convert covariance matrix to correlation matrix

pharmpy.math.flattened_to_symmetric(x)

Convert a vector containing the elements of a lower triangular matrix into a full symmetric matrix

pharmpy.math.is_near_target(x, target, zero_limit, significant_digits)

pharmpy.math.is_posdef(A)

Checks whether a matrix is positive definite

pharmpy.math.nearest_posdef(A)

Return the nearest positive definite matrix in the Frobenius norm to a matrix

A Python/Numpy port of John D’Errico’s nearestSPD MATLAB code [1], which credits [2]. [1] https://www.mathworks.com/matlabcentral/fileexchange/42885-nearestspd [2] N.J. Higham, “Computing a nearest symmetric positive semidefinite matrix” (1988): https://doi.org/10.1016/0024-3795(88)90223-6 [3] https://gist.github.com/fasiha/fdb5cec2054e6f1c6ae35476045a0bbd

pharmpy.math.round_and_keep_sum(x, s)

Round values in Series x and their sum must be s

Algorithm: Floor all elements in series. If sum not correct add one to element with

highest fractional part until sum is reached.

pharmpy.math.round_to_n_sigdig(x, n)

pharmpy.math.sample_truncated_joint_normal(mu, sigma, a, b, n, seed=None)

Give an array of samples from the truncated joint normal distributon using sample rejection - mu, sigma - parameters for the normal distribution - a, b - vectors of lower and upper limits for each random variable - n - number of samples

pharmpy.math.se_delta_method(expr, values, cov)

Use the delta method to estimate the standard error of a function of parameters with covariance matrix available.

Parameters

• expr – A sympy expression for the function of parameters

• cov – Dataframe with symbol names as indices must include at least all parameters needed for expr

• values – dict/series parameter estimates. Must include at least all parameters needed for expr

Returns

Approximation of the standard error

pharmpy.math.triangular_root(x)

Calculate the triangular root of x. I.e. if x is a triangular number T_n what is n?

pharmpy.estimation module pharmpy.model module