# Algebraic Constraint

Constrain input signal

• Library:

## Description

The Algebraic Constraint block constrains the input signal f(z) to z or 0 and outputs an algebraic state z. The block outputs a value that produces 0 or z at the input. The output must affect the input through a direct feedback path. In other words, the feedback path only contains blocks with direct feedthrough. For example, you can specify algebraic equations for index 1 differential-algebraic systems (DAEs).

## Ports

### Input

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Signal is subjected to the constraint f(z) = 0 or f(z) = z to solve the algebraic loop.

Data Types: `double`

### Output

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Solution to the algebraic loop when the input signal f(z) is subjected to the constraint f(z) = 0 or f(z) = z.

Data Types: `double`

## Parameters

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Type of constraint for which to solve. You can solve for ```f(z) = 0``` or `f(z) = z`.

Choice between the Trust Region [1], [2] or Line Search [3] algorithms to solve the algebraic loop. By default this value is set to `auto`, which selects the solver based on the model configuration.

This option is visible when you explicitly specify a solver to be used (Trust region or Line Search) in the Solver dropdown menu. Specify a smaller value for higher accuracy or a larger value for faster execution. By default it is set to `auto`.

Initial guess for the algebraic state z that is close to the expected solution value to improve the efficiency of the algebraic loop solver. By default, this value is set to 0.

## Block Characteristics

 Data Types `double` Multidimensional Signals `No` Variable-Size Signals `No`

## References

[1] Garbow, B. S., K. E. Hillstrom, and J. J. Moré. User Guide for MINPACK-1. Argonne, IL: Argonne National Laboratory, 1980.

[2] Rabinowitz, P. H. Numerical Methods for Nonlinear Algebraic Equations. New York: Gordon and Breach, 1970.

[3] Kelley, C. T. Iterative Methods for Linear and Nonlinear Equations. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1995.