# Extract vector of positions from a parmetric piecewise

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Teodoro Lima el 28 de Sept. de 2022
Respondida: Pratheek el 23 de Mayo de 2023
i have a problem with piecewise. i need to extract values for each time instant. then substitute a vector of times (for example, t = 1:10) for the symbolic variable.
the end goal is to get a vector that has within it the values calculated at the instants of time.
below I have attached the qd function.
I know I have to use the children function and the subs function. but I don't know how to use them
syms t
qd=piecewise(t<tk(k),qd,tk(k)<=t<tk(k+1),a0(k)+a1(k)*(t-tk(k))+a2(k)*(t-tk(k))^2+a3(k)*(t-tk(k))^3)
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### Respuestas (1)

Pratheek el 23 de Mayo de 2023
Hi Teodoro,
I understand that you want to extract the values for each time instant and substitute a vector of times for the symbolic variable. You can follow these steps to do that:
1. Use the `children` function to get the conditions and expressions within the `piecewise` function:
[pw_conditions, pw_expressions] = children(qd);
This will give you two arrays: `pw_conditions` with the conditions and `pw_expressions` with the expressions.
2. Use the `subs` function to substitute the vector of times `t = 1:10` for the symbolic variable `t` in each expression:
pw_expressions_at_t = subs(pw_expressions, t, 1:10);
This will give you the values of the expressions at each instant of time.
3. Now combine the values of the expressions at each instant of time into a vector:
values = [pw_expressions_at_t{:}];
This will concatenate the array of values from each expression into a single vector.
Putting it all together:
syms t
qd = piecewise(t<tk(k),qd,tk(k)<=t<tk(k+1),a0(k)+a1(k)*(t-tk(k))+a2(k)*(t-tk(k))^2+a3(k)*(t-tk(k))^3)
[pw_conditions, pw_expressions] = children(qd);
pw_expressions_at_t = subs(pw_expressions, t, 1:10);
values = [pw_expressions_at_t{:}];
This should give you the vector of values calculated at the instants of time.
You can refer to this documentation link for more info: Conditionally defined expression or function - MATLAB piecewise (mathworks.com)
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