# Documentation

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# Matrix 1-Norm

Compute 1-norm of matrix

## Library

Math Functions / Matrices and Linear Algebra / Matrix Operations

`dspmtrx3`

## Description

The Matrix 1-Norm block computes the 1-norm, or maximum column-sum, of an M-by-N input matrix, A.

`$y={‖A‖}_{1}=\underset{1\le j\le N}{\mathrm{max}}\sum _{i=1}^{M}|{a}_{ij}|$`

This is equivalent to

```y = max(sum(abs(A))) % Equivalent MATLAB code ```

The block treats length-M unoriented vector input as an M-by-1 matrix. The output, y, is always a scalar.

The Matrix 1-Norm block supports real and complex floating-point inputs, and real fixed-point inputs.

### Fixed-Point Data Types

The following diagram shows the data types used within the Matrix 1-Norm block for fixed-point signals.

The block calculations are all done in the accumulator data type until the `max` is performed. The result is then cast to the output data type. You can set the accumulator and output data types in the block dialog as discussed in Parameters below.

## Parameters

There are no parameters on the Main Tab.

Data Types Tab

### Note

Floating-point inheritance takes precedence over the data type settings defined on this pane. When inputs are floating point, the block ignores these settings, and all internal data types are floating point.

Rounding mode

Select the rounding mode for fixed-point operations.

Saturate on integer overflow

Select the overflow mode for fixed-point operations.

Accumulator data type

Specify the accumulator data type. See Fixed-Point Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

• A rule that inherits a data type, for example, ```Inherit: Inherit via internal rule```. For more information on this rule, see Inherit via Internal Rule.

• An expression that evaluates to a valid data type, for example, `fixdt([],16,0)`

Click the button to display the Data Type Assistant, which helps you set the Accumulator data type parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Output data type

Specify the output data type. See Fixed-Point Data Types for illustrations depicting the use of the output data type in this block. You can set it to:

• A rule that inherits a data type, for example, ```Inherit: Same as accumulator```

• An expression that evaluates to a valid data type, for example, `fixdt([],16,0)`

Click the button to display the Data Type Assistant, which helps you set the Output data type parameter.

Minimum

Specify the minimum value that the block should output. The default value is `[]` (unspecified). Simulink® software uses this value to perform:

• Simulation range checking (see Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Maximum

Specify the maximum value that the block should output. The default value is `[]` (unspecified). Simulink software uses this value to perform:

• Simulation range checking (see Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Lock data type settings against changes by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask.

## References

Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

## Supported Data Types

PortSupported Data Types

Input

• Double-precision floating point

• Single-precision floating point

• Fixed point (signed and unsigned)

• 8-, 16-, and 32-bit signed integers

• 8-, 16-, and 32-bit unsigned integers

Output

• Double-precision floating point

• Single-precision floating point

• Fixed point (signed and unsigned)

• 8-, 16-, and 32-bit signed integers

• 8-, 16-, and 32-bit unsigned integers

 Normalization DSP System Toolbox Reciprocal Condition DSP System Toolbox `norm` MATLAB