# SparseModalTruncationOptions

## Description

This object contains model order reduction options of sparse linear time-invariant
models, and is contained in the `Options`

property of a
`SparseModalTruncation`

object `R`

created using `reducespec`

. To
configure these options, use dot notation, for example, ```
R.Options.ModeOnly =
true
```

.

For the full workflow, see Task-Based Model Order Reduction Workflow.

## Properties

`Focus`

— Frequency range of interest

`[0 inf]`

(default) | vector

Frequency range of interest, specified as a vector of form
`[fmin,fmax]`

. When you specify a value for this property, the
algorithm computes only modes in this frequency range.

By default, the focus is unspecified (`[0 inf]`

) and the algorithm
computes the `MaxOrder`

modes with smallest magnitude.

`MaxOrder`

— Maximum order of modal approximation

`1000`

(default) | positive integer

Maximum order of the modal approximation, specified as a positive integer. This value limits the number of eigenvalues computed by the Krylov-Schur iterations and the order of the modal approximation of the original sparse model.

`ModeOnly`

— Flag to only compute modes

`false`

or `0`

(default) | `true`

or `1`

Flag to only compute modes for the original system `sys`

, specified
as a logical `0`

(`false`

) or `1`

(`true`

).

When

`R.Options.ModeOnly`

is`true`

, the software computes only the pole locations, damping, and natural frequency of the poles, which correspond to the`Mode`

,`Damping`

, and`Frequency`

properties of`R`

, respectively.When

`R.Options.ModeOnly`

is`false`

, the software computes a full modal decomposition and populates all properties of`R`

.

`DCFrequency`

— Frequency for evaluating DC contributions

`0`

(default) | nonnegative scalar

Frequency for evaluating and matching DC contributions, specified as a nonnegative scalar.

For models with integrators, you cannot evaluate modal contributions at DC since the DC gain is infinite. To evaluate modal contributions and match gains at a different frequency, set the property to a positive value. The default value of this property corresponds to the DC contributions.

`InputScaling`

— Input scaling factors

`[]`

(default) | vector

Input scaling factors, specified as a vector of length *Nu*, where
*Nu* is the number of inputs in the original model
`sys`

.

Use this option to emphasize specific input channels in `sys`

. The
software evaluates the modal contributions for the scaled system.

This affects only the normalized DC contribution (`R.DCGain`

). For
the input scaling factor *D _{u}* and output scaling
factor

*D*, the normalized DC contribution of

_{y}*G*(

_{k}*s*) in continuous time is obtained as

$$\frac{\Vert {D}_{y}{G}_{k}(0){D}_{u}\Vert}{\Vert {D}_{y}G(0){D}_{u}\Vert}$$

In discrete time, the software uses the first time samples
*G _{k}*(1) and

*G*(1).

`OutputScaling`

— Output scaling factors

`[]`

(default) | vector

Output scaling factors, specified as a vector of length *Ny*, where
*Ny* is the number of outputs in the original model
`sys`

.

Use this option to emphasize specific output channels in `sys`

. The
software evaluates the modal contributions for the scaled system.

This affects only the normalized DC contribution (`R.DCGain`

). For
the input scaling factor *D _{u}* and output scaling
factor

*D*, the normalized DC contribution of

_{y}*G*(

_{k}*s*) in continuous time is obtained as

$$\frac{\Vert {D}_{y}{G}_{k}(0){D}_{u}\Vert}{\Vert {D}_{y}G(0){D}_{u}\Vert}$$

In discrete time, the software uses the first time samples
*G _{k}*(1) and

*G*(1).

`ModeTol`

— Accuracy of computed modes

`1e-12`

(default) | positive scalar

Tolerance for identifying converged eigenvalues in Krylov-Schur iterations, specified as a positive scalar.

`SepTol`

— Relative accuracy of modal contribution

`1e-12`

(default) | scalar between 0 and 1

Relative accuracy of modal contribution, specified as a scalar between 0 and 1.

This option limits the condition number of the block diagonalizing transformation to
roughly `SepTol`

/`eps`

. Increasing
`SepTol`

helps yield smaller modal components at the expense of
accuracy.

## Version History

**Introduced in R2023b**

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