Skip to content

systemMatrices (Model)

First-order system matrices describing the unsolved model

Syntax

output = systemMatrices(model)

Input Arguments

model [ Model ]

Model object whose system matrices will be returned.

Output Arguments

output [ struct ]

Output struct with the matrices describing the unsolved system, see Description.

numF [ numeric ]

Number of non-predetermined (aka forward-looking) transition variables (multiplied by the first numF columns of matrices A and B).

Options

ForceDiff=false [ true | false ]

If false, automatically detect which equations need to be re-differentiated based on parameter changes from the last time the system matrices were calculated; if true, recalculate all derivatives.

MatrixFormat="NamedMatrix" [ "plain" | "NamedMatrix" ]

Format of the output matrix.

Normalize=true [ true | false ]

Normalize (divide) the derivatives within each equation by the largest of them.

Sparse=false [ true | false ]

Return the system matrices output.A, output.B, output.D, output.F, output.G, and output.J as sparse matrices; this option can be true only in models with one parameterization.

Description

The output struct contains the following fields:

  • .A, .B, .C, .D - matrices (plain arrays or or NamedMat objects, depending on the option MatrixFormat) describing the first-order expansion of transition equations around steady state;

  • .F, .G, .H, .J - matrices (plain arrays or or NamedMat objects, depending on the option MatrixFormat) describing the first-order expansion of measurement equations around steady state;

  • .NumForward - the number of non-predetermined (forward-looking) variables in the transition vector;

  • .NumBackward - the number of predetermined (backward-looking) variables in the transition vector;

The system before the model is solved has the following form:

A E[xf;xb] + B [xf(-1);xb(-1)] + C + D e = 0

F y + G xb + H + J e = 0

where

  • E is a conditional expectations operator;

  • xf is a vector of non-predetermined (forward-looking) transition variables;

  • xb is a vector of predetermined (backward-looking) transition variables;

  • y is a vector of measurement variables

  • e is a vector of transition and measurement shocks.

Example