Power Series Utilities
StructuralIdentifiability._matrix_inv_newton_iteration
StructuralIdentifiability.ps_diff
StructuralIdentifiability.ps_integrate
StructuralIdentifiability.ps_matrix_homlinear_de
StructuralIdentifiability.ps_matrix_inv
StructuralIdentifiability.ps_matrix_linear_de
StructuralIdentifiability.ps_matrix_log
StructuralIdentifiability.ps_ode_solution
StructuralIdentifiability._matrix_inv_newton_iteration
— Method_matrix_inv_newton_iteration(M, Minv)
Performs a single step of Newton iteration for inverting M
with Minv
being a partial result
StructuralIdentifiability.ps_diff
— Methodps_diff(ps)
Input:
ps
- (absolute capped) univariate power series
Output:
- the derivative of
ps
StructuralIdentifiability.ps_integrate
— Methodps_integrate(ps)
Input:
ps
- (absolute capped) univariate power series
Output:
- the integral of
ps
without constant term
StructuralIdentifiability.ps_matrix_homlinear_de
— Methodps_matrix_homlinear_de(A, Y0, prec)
Input:
A
- a square matrix with entries in a univariate power series ringY0
- a square invertible matrix over the base field
Output:
- matrix
Y
such thatY' = AY
up to precision ofA - 1
andY(0) = Y0
StructuralIdentifiability.ps_matrix_inv
— Functionps_matrix_inv(M, prec)
Input:
M
- a square matrix with entries in a univariate power series ring it is assumed thatM(0)
is invertible and all entries having the same precisionprec
- an integer, precision, if-1
then defaults to precision ofM
Output:
- the inverse of
M
computed up toprec
StructuralIdentifiability.ps_matrix_linear_de
— Methodps_matrix_linear_de(A, B, Y0, prec)
Input:
A
,B
- square matrices with entries in a univariate power series ringY0
- a matrix over the base field with the rows number the same asA
Output:
- matrix
Y
such thatY' = AY + B
up to precision ofA - 1
andY(0) = Y0
StructuralIdentifiability.ps_matrix_log
— Methodps_matrix_log(M)
Input:
M
- a square matrix with entries in a univariate power series ring it is assumed thatM(0)
is the identity
Output:
- the natural log of
M
StructuralIdentifiability.ps_ode_solution
— Methodps_ode_solution(equations, ic, inputs, prec)
Input:
equations
- a system of the form $A(x, u, mu)x' - B(x, u, mu) = 0$, where $A$ is a generically nonsingular square matrix. Assumption: $A$ is nonzero at zeroic
- initial conditions for $x$'s (dictionary)inputs
- power series for inputs represented as arrays (dictionary)prec
- precision of the solution
Output:
- power series solution of the system