# ones

Create array of all ones with fixed-point properties

## Syntax

X = ones('like',p)
X = ones(n,'like',p)
X = ones(sz1,...,szN,'like',p)
X = ones(sz,'like',p)

## Description

example

X = ones('like',p) returns a scalar 1 with the same numerictype, complexity (real or complex), and fimath as p.

example

X = ones(n,'like',p) returns an n-by-n array of ones like p.

example

X = ones(sz1,...,szN,'like',p) returns an sz1-by-...-by-szN array of ones like p.

example

X = ones(sz,'like',p) returns an array of ones like p. The size vector, sz, defines size(X).

## Examples

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Create a 2-by-3 array of ones with specified numerictype and fimath properties.

Create a signed fi object with word length of 24 and fraction length of 12.

p = fi([],1,24,12);

Create a 2-by-3- array of ones that has the same numerictype properties as p.

X = ones(2,3,'like',p)
X =

1     1     1
1     1     1

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 24
FractionLength: 12

Define a 3-by-2 array A.

A = [1 4 ; 2 5 ; 3 6];

sz = size(A)
sz =

3     2

Create a signed fi object with word length of 24 and fraction length of 12.

p = fi([],1,24,12);

Create an array of ones that is the same size as A and has the same numerictype properties as p.

X = ones(sz,'like',p)
X =

1     1
1     1
1     1

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 24
FractionLength: 12

Create a 4-by-4 array of ones with specified numerictype and fimath properties.

Create a signed fi object with word length of 24 and fraction length of 12.

p = fi([],1,24,12);

Create a 4-by-4 array of ones that has the same numerictype properties as p.

X = ones(4, 'like', p)
X =

1     1     1     1
1     1     1     1
1     1     1     1
1     1     1     1

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 24
FractionLength: 12

Create a signed fi object with word length of 16, fraction length of 15 and OverflowAction set to Wrap.

format long
p = fi([],1,16,15,'OverflowAction','Wrap');

Create a 2-by-2 array of ones with the same numerictype properties as p.

X = ones(2,'like',p)
X =

0.999969482421875   0.999969482421875
0.999969482421875   0.999969482421875

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 15

RoundingMethod: Nearest
OverflowAction: Wrap
ProductMode: FullPrecision
SumMode: FullPrecision

1 cannot be represented by the data type of p, so the value saturates. The output fi object X has the same numerictype and fimath properties as p.

Create a scalar fixed-point 1 that is not real valued, but instead is complex like an existing array.

Define a complex fi object.

p = fi( [1+2i 3i],1,24,12);

Create a scalar 1 that is complex like p.

X = ones('like',p)
X =

1.0000 + 0.0000i

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 24
FractionLength: 12

Write a MATLAB® algorithm that you can run with different data types without changing the algorithm itself. To reuse the algorithm, define the data types separately from the algorithm.

This approach allows you to define a baseline by running the algorithm with floating-point data types. You can then test the algorithm with different fixed-point data types and compare the fixed-point behavior to the baseline without making any modifications to the original MATLAB code.

Write a MATLAB function, my_filter, that takes an input parameter, T, which is a structure that defines the data types of the coefficients and the input and output data.

function [y,z] = my_filter(b,a,x,z,T)
% Cast the coefficients to the coefficient type
b = cast(b,'like',T.coeffs);
a = cast(a,'like',T.coeffs);
% Create the output using zeros with the data type
y = zeros(size(x),'like',T.data);
for i = 1:length(x)
y(i) = b(1)*x(i) + z(1);
z(1) = b(2)*x(i) + z(2) - a(2) * y(i);
z(2) = b(3)*x(i)        - a(3) * y(i);
end
end

Write a MATLAB function, zeros_ones_cast_example, that calls my_filter with a floating-point step input and a fixed-point step input, and then compares the results.

function zeros_ones_cast_example

% Define coefficients for a filter with specification
% [b,a] = butter(2,0.25)
b = [0.097631072937818   0.195262145875635   0.097631072937818];
a = [1.000000000000000  -0.942809041582063   0.333333333333333];

% Define floating-point types
T_float.coeffs = double([]);
T_float.data   = double([]);

% Create a step input using ones with the
% floating-point data type
t = 0:20;
x_float = ones(size(t),'like',T_float.data);

% Initialize the states using zeros with the
% floating-point data type
z_float = zeros(1,2,'like',T_float.data);

% Run the floating-point algorithm
y_float = my_filter(b,a,x_float,z_float,T_float);

% Define fixed-point types
T_fixed.coeffs = fi([],true,8,6);
T_fixed.data   = fi([],true,8,6);

% Create a step input using ones with the
% fixed-point data type
x_fixed = ones(size(t),'like',T_fixed.data);

% Initialize the states using zeros with the
% fixed-point data type
z_fixed = zeros(1,2,'like',T_fixed.data);

% Run the fixed-point algorithm
y_fixed = my_filter(b,a,x_fixed,z_fixed,T_fixed);

% Compare the results
coder.extrinsic('clf','subplot','plot','legend')
clf
subplot(211)
plot(t,y_float,'co-',t,y_fixed,'kx-')
legend('Floating-point output','Fixed-point output')
title('Step response')
subplot(212)
plot(t,y_float - double(y_fixed),'rs-')
legend('Error')
figure(gcf)
end

## Input Arguments

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Size of square matrix, specified as an integer value, defines the output as a square, n-by-n matrix of ones.

• If n is zero, X is an empty matrix.

• If n is negative, it is treated as zero.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Size of each dimension, specified as two or more integer values, defines X as a sz1-by...-by-szN array.

• If the size of any dimension is zero, X is an empty array.

• If the size of any dimension is negative, it is treated as zero.

• If any trailing dimensions greater than two have a size of one, the output, X, does not include those dimensions.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output size, specified as a row vector of integer values. Each element of this vector indicates the size of the corresponding dimension.

• If the size of any dimension is zero, X is an empty array.

• If the size of any dimension is negative, it is treated as zero.

• If any trailing dimensions greater than two have a size of one, the output, X, does not include those dimensions.

Example: sz = [2,3,4] defines X as a 2-by-3-by-4 array.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Prototype, specified as a fi object or numeric variable. To use the prototype to specify a complex object, you must specify a value for the prototype. Otherwise, you do not need to specify a value.

If the value 1 overflows the numeric type of p, the output saturates regardless of the specified OverflowAction property of the attached fimath. All subsequent operations performed on the output obey the rules of the attached fimath.

Complex Number Support: Yes

## Tips

Using the b = cast(a,'like',p) syntax to specify data types separately from algorithm code allows you to:

• Reuse your algorithm code with different data types.

• Keep your algorithm uncluttered with data type specifications and switch statements for different data types.

• Improve readability of your algorithm code.

• Switch between fixed-point and floating-point data types to compare baselines.

• Switch between variations of fixed-point settings without changing the algorithm code.