Test whether all equations and inequalities represented as elements of symbolic array are valid
Create vector V that contains the symbolic
equation and inequalities as its elements:
syms x V = [x ~= x + 1, abs(x) >= 0, x == x];
Use all to test whether all of them are valid for all values of
x:
all(V)
ans = logical 1
Create this matrix of symbolic equations and inequalities:
syms x M = [x == x, x == abs(x); abs(x) >= 0, x ~= 2*x]
M = [ x == x, x == abs(x)] [ 0 <= abs(x), x ~= 2*x]
Use all to test equations and inequalities of this matrix. By
default, all tests whether all elements of each column are valid for all
possible values of variables. If all equations and inequalities in the column are valid
(return logical 1), then all returns logical
1 for that column. Otherwise, it returns logical 0
for the column. Thus, it returns 1 for the first column and
0 for the second column:
all(M)
ans = 1×2 logical array 1 0
Create this matrix of symbolic equations and inequalities:
syms x M = [x == x, x == abs(x); abs(x) >= 0, x ~= 2*x]
M = [ x == x, x == abs(x)] [ 0 <= abs(x), x ~= 2*x]
For matrices and multidimensional arrays, all can test all elements
along the specified dimension. To specify the dimension, use the second argument of
all. For example, to test all elements of each column of a matrix, use
the value 1 as the second argument:
all(M, 1)
ans = 1×2 logical array 1 0
To test all elements of each row, use the value 2 as the second argument:
all(M, 2)
ans = 2×1 logical array 0 1
Test whether all elements of this vector return logical
1s. Note that all also converts all numeric values
outside equations and inequalities to logical 1s and
0s. The numeric value 0 becomes logical 0:
syms x all([0, x == x])
ans = logical 0
All nonzero numeric values, including negative and complex values, become logical
1s:
all([1, 2, -3, 4 + i, x == x])
ans = logical 1
If A is an empty symbolic array, all(A)
returns logical 1.
If some elements of A are just numeric values (not equations or
inequalities), all converts these values as follows. All numeric values
except 0 become logical 1. The value 0 becomes logical
0.
If A is a vector and all its elements return logical
1, all(A) returns logical 1. If
one or more elements are zero, all(A) returns logical
0.
If A is a multidimensional array, all(A)
treats the values along the first dimension that is not equal to 1 (nonsingleton
dimension) as vectors, returning logical 1 or 0 for
each vector.