symfunmatrix2symfun

Convert symbolic matrix function to symbolic function

Since R2022a

Syntax

f = symfunmatrix2symfun(fM)

Description

f = symfunmatrix2symfun(fM) converts a symbolic matrix function fM of type symfunmatrix to a symbolic function f of type symfun.

The output symbolic function has the same matrix dimensions as the input symbolic matrix function, and its components are filled with automatically generated elements. For example, syms fM(x) [1 2] matrix; f = symfunmatrix2symfun(fM) converts the symbolic matrix function fM(x) to the symbolic function f(x) = [fM1_1(x), fM1_2(x)]. The generated elements fM1_1 and fM1_2 do not appear in the MATLAB^® workspace.

Examples

Differentiate Function with Respect to Matrix Argument

Create 2-by-1 and 2-by-2 symbolic matrix variables to represent the matrices $\mathit{X}$ and $\mathit{A}$.

syms X [2 1] matrix
syms A [2 2] matrix

Create two symbolic matrix functions to represent the functions $\mathit{F}\left(\mathit{X},\mathit{A}\right)$ and $\partial \mathit{F}\left(\mathit{X},\mathit{A}\right)/\partial {\mathit{X}}^{\mathit{T}}$. When creating the symbolic matrix functions, keep existing definitions of the symbolic matrix variables $\mathit{X}$ and $\mathit{A}$ in the workspace. The symbolic matrix functions require matrices of the same sizes as $\mathit{X}$ and $\mathit{A}$ as their input arguments.

syms F(X,A) [1 1] matrix keepargs
syms dF(X,A) [2 1] matrix keepargs

Define the function $\mathit{F}\left(\mathit{X},\mathit{A}\right)={\mathit{X}}^{\mathit{T}}\mathit{A}\mathit{X}$ and find its derivative $\partial \mathit{F}\left(\mathit{X},\mathit{A}\right)/\partial {\mathit{X}}^{\mathit{T}}$. The resulting symbolic functions are in matrix notation in terms of $\mathit{X}$ and $\mathit{A}$.

F(X,A) = X.'*A*X

F(X, A) = $$X^{\mathrm{T}}\hspace{0.17em}A\hspace{0.17em}X$$

dF(X,A) = diff(F,X.')

dF(X, A) = $$A\hspace{0.17em}X+A^{\mathrm{T}}\hspace{0.17em}X$$

Convert the symbolic matrix functions from data type symfunmatrix to symfun. The resulting symbolic functions are in scalar notation in terms of the matrix elements of $\mathit{X}$ and $\mathit{A}$. These functions accept scalars as their input arguments.

Fsymfun = symfunmatrix2symfun(F)

Fsymfun(X1, X2, A1_1, A1_2, A2_1, A2_2) = $$X_1\hspace{0.17em}\left(A_{1,1}\hspace{0.17em}{X}_1+A_{1,2}\hspace{0.17em}{X}_2\right)+X_2\hspace{0.17em}\left(A_{2,1}\hspace{0.17em}{X}_1+A_{2,2}\hspace{0.17em}{X}_2\right)$$

dFsymfun = symfunmatrix2symfun(dF)

dFsymfun(X1, X2, A1_1, A1_2, A2_1, A2_2) = 
$$\left(\begin{array}{c}2\hspace{0.17em}{A}_{1,1}\hspace{0.17em}{X}_1+A_{1,2}\hspace{0.17em}{X}_2+A_{2,1}\hspace{0.17em}{X}_2\\ A_{1,2}\hspace{0.17em}{X}_1+A_{2,1}\hspace{0.17em}{X}_1+2\hspace{0.17em}{A}_{2,2}\hspace{0.17em}{X}_2\end{array}\right)$$

Input Arguments

fM — Input

symbolic matrix function

Input, specified as a symbolic matrix function.

Data Types: symfunmatrix

Tips

• To show all the functions in Symbolic Math Toolbox™ that accept symbolic matrix functions as input, use the command methods symfunmatrix.

• Instead of using symfunmatrix2symfun to convert a symbolic matrix function to a symbolic function, you can use the shortcut symfun. For an example, see Convert Symbolic Matrix Function to Symbolic Function. (since R2024b)

Version History

Introduced in R2022a