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Symbolic substitution
Replace a with 4 in this expression.
syms a b subs(a + b, a, 4)
ans = b + 4
Replace a*b with 5 in this expression.
subs(a*b^2, a*b, 5)
ans = 5*b
Substitute the default value in this expression with a. If you do not specify which variable or expression that you want to replace, subs uses symvar to find the default variable. For x + y, the default variable is x.
syms x y a symvar(x + y, 1)
ans = x
Therefore, subs replaces x with a.
subs(x + y, a)
ans = a + y
Solve this ordinary differential equation.
syms a y(t) y = dsolve(diff(y) == -a*y)
y = C2*exp(-a*t)
Now, specify the values of the symbolic parameters a and C2.
a = 980; C2 = 3;
Although the values a and C2 are now in the MATLAB workspace, y is not evaluated with the account of these values.
y
y = C2*exp(-a*t)
To evaluate y taking into account the new values of a and C2, use subs.
subs(y)
ans = 3*exp(-980*t)
Make multiple substitutions by specifying the old and new values as vectors.
syms a b subs(cos(a) + sin(b), [a, b], [sym('alpha'), 2])
ans = sin(2) + cos(alpha)
You also can use cell arrays for that purpose.
subs(cos(a) + sin(b), {a, b}, {sym('alpha'), 2})
ans = sin(2) + cos(alpha)
Replace variable a in this expression with the 3-by-3 magic square matrix. Note that the constant 1 expands to the 3-by-3 matrix with all its elements equal to 1.
syms a t subs(exp(a*t) + 1, a, -magic(3))
ans = [ exp(-8*t) + 1, exp(-t) + 1, exp(-6*t) + 1] [ exp(-3*t) + 1, exp(-5*t) + 1, exp(-7*t) + 1] [ exp(-4*t) + 1, exp(-9*t) + 1, exp(-2*t) + 1]
You can also replace an element of a vector, matrix, or array with a nonscalar value. For example, create these 2-by-2 matrices.
A = sym('A', [2,2]) B = sym('B', [2,2])
A = [ A1_1, A1_2] [ A2_1, A2_2] B = [ B1_1, B1_2] [ B2_1, B2_2]
Replace the first element of the matrix A with the matrix B. While making this substitution, subs expands the 2-by-2 matrix A into this 4-by-4 matrix.
A44 = subs(A, A(1,1), B)
A44 = [ B1_1, B1_2, A1_2, A1_2] [ B2_1, B2_2, A1_2, A1_2] [ A2_1, A2_1, A2_2, A2_2] [ A2_1, A2_1, A2_2, A2_2]
subs does not let you replace a nonscalar with a scalar.
Replace variables x and y with these 2-by-2 matrices. When you make multiple substitutions involving vectors or matrices, use cell arrays to specify the old and new values.
syms x y subs(x*y, {x, y}, {[0 1; -1 0], [1 -1; -2 1]})
ans = [ 0, -1] [ 2, 0]
Note that these substitutions are elementwise.
[0 1; -1 0].*[1 -1; -2 1]
ans = 0 -1 2 0
Replace sin(x + 1) with a in this equation.
syms x a subs(sin(x + 1) + 1 == x, sin(x + 1), a)
ans = a + 1 == x
Replace x with a in this symbolic function.
syms x y a syms f(x, y) f(x, y) = x + y; f = subs(f, x, a)
f(x, y) = a + y
subs replaces the values in the symbolic function formula, but does not replace input arguments of the function.
formula(f) argnames(f)
ans = a + y ans = [ x, y]
You can replace the arguments of a symbolic function explicitly.
syms x y f(x, y) = x + y; f(a, y) = subs(f, x, a); f
f(a, y) = a + y
Assign the expression x + y to s.
syms x y s = x + y;
Replace y in this expression with the value 1. Here, s itself does not change.
subs(s, y, 1); s
s = x + y
To replace the value of s with the new expression, assign the result returned by subs to s.
s = subs(s, y, 1); s
s = x + 1
Suppose you want to verify the solutions of this system of equations.
syms x y eqs = [x^2 + y^2 == 1, x == y]; S = solve(eqs, x, y); S.x S.y
ans = -2^(1/2)/2 2^(1/2)/2 ans = -2^(1/2)/2 2^(1/2)/2
To verify the correctness of the returned solutions, substitute the solutions into the original system.
logical(subs(eqs, S))
ans = 1 1 1 1