# Matrix 1-Norm

Compute 1-norm of matrix

• Library:
• DSP System Toolbox / Math Functions / Matrices and Linear Algebra / Matrix Operations

## Description

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

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

Equivalent MATLAB® code is given by:

`y = max(sum(abs(A))) `

## Ports

### Input

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Input signal, specified as a vector or matrix.

The block treats length-M unoriented vector input as an M-by-1 matrix.

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

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `uint8` | `uint16` | `uint32` | `fixed point`
Complex Number Support: Yes

### Output

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Matrix 1-norm or maximum column-sum of the input, returned as a scalar. The output y is always a scalar.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `uint8` | `uint16` | `uint32` | `fixed point`

## Parameters

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### Main

There are no parameters on the Main Tab.

### Data Types

Specify the rounding mode for fixed-point operations as one of the following:

• `Floor`

• `Ceiling`

• `Convergent`

• `Nearest`

• `Round`

• `Simplest`

• `Zero`

For more details, see Rounding Modes.

Note

The Rounding mode and Saturate on integer overflow parameters have no effect on numerical results when all these conditions are met:

• Accumulator data type is ```Inherit: Inherit via internal rule```.

• Output data type is ```Inherit: Same as accumulator```.

With these data-type settings, the block operates in a full-precision mode.

Select this parameter to saturate the result of the fixed-point operation. Clear this parameter to wrap the result of the fixed-point operation. For details on saturate and wrap, see Overflow Handling for fixed-point operations.

Note

The Rounding mode and Saturate on integer overflow parameters have no effect on numeric results when all these conditions are met:

• Product output data type is ```Inherit: Inherit via internal rule```.

• Accumulator data type is ```Inherit: Inherit via internal rule```.

With these data-type settings, the block operates in a full-precision mode.

Accumulator specifies the data type of the output of an accumulation operation in the Matrix 1-Norm block.

• `Inherit: Inherit via internal rule` — The block inherits the accumulator data type based on an internal rule. For more information on this rule, see Inherit via Internal Rule.

• `Inherit: Same as input` — The block specifies the accumulator data type to be the same as the input data type.

• `fixdt([],16,0)` — The block specifies an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Accumulator data type by using the Data Type Assistant. To use the assistant, click the button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

For illustrations on how to use the accumulator data type in this block, see Fixed-Point Conversion in Extended Capabilities.

Output specifies the data type of the output of the Matrix 1-Norm block.

• `Inherit: Same as input` — The block specifies the output data type to be the same as the input data type.

• `Inherit: Same as accumulator` — The block specifies the output data type to be the same as the accumulator data type.

• `fixdt([],16,0)` — The block specifies an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Output data type by using the Data Type Assistant. To use the assistant, click the button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

For more information on the output data type, see Fixed-Point Conversion in Extended Capabilities.

Specify the minimum value the block can output. Simulink® uses this minimum value to perform:

• Simulation range checking. See Specify Signal Ranges (Simulink).

• Automatic scaling of fixed-point data types.

Specify the maximum value the block can output. Simulink uses this maximum value to perform:

• Simulation range checking. See Specify Signal Ranges (Simulink).

• Automatic scaling of fixed-point data types.

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in the block dialog box.

Note

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

## Block Characteristics

 Data Types `double` | `fixed point` | `integer` | `single` Direct Feedthrough `no` Multidimensional Signals `no` Variable-Size Signals `no` Zero-Crossing Detection `no`

## References

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

## Version History

Introduced before R2006a