Create array of all ones with fixed-point properties

`X = ones('like',`

returns
a scalar `p`

)`1`

with the same `numerictype`

,
complexity (real or complex), and `fimath`

as `p`

.

`X = ones(`

returns
an `sz1,...,szN`

,'like',`p`

)`sz1`

-by-...-by-`szN`

array of
ones like `p`

.

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

`n`

— Size of square matrixinteger valueSize 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`

`sz1,...,szN`

— Size of each dimensiontwo or more integer valuesSize 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`

`sz`

— Output sizerow vector of integer valuesOutput 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`

`p`

— Prototype`fi`

object | numeric variablePrototype, 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

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.

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