Octave supports several basic set operations. Octave can compute the union, intersection, and difference of two sets. Octave also supports the Exclusive Or set operation.
The functions for set operations all work in the same way by accepting two
input sets and returning a third set. As an example, assume that a and
b contains two sets, then
union (a, b)
computes the union of the two sets.
Finally, determining whether elements belong to a set can be done with the
ismember function. Because sets are ordered this operation is very
efficient and is of order O(log2(n)) which is preferable to the find
function which is of order O(n).
c = intersect (a, b) ¶c = intersect (a, b, "rows") ¶c = intersect (…, "sorted") ¶c = intersect (…, "stable") ¶c = intersect (…, "legacy") ¶[c, ia, ib] = intersect (…) ¶Return the unique elements common to both a and b.
If a and b are both row vectors then return a row vector; Otherwise, return a column vector. The inputs may also be cell arrays of strings.
If the optional input "rows" is given then return the common rows of
a and b. The inputs must be 2-D numeric matrices to use this
option.
The optional argument "sorted"/"stable" controls the order
in which unique values appear in the output. The default is
"sorted" and values in the output are placed in ascending order.
The alternative "stable" preserves the order found in the input.
If requested, return column index vectors ia and ib such that
c = a(ia) and c = b(ib).
Programming Note: The input flag "legacy" changes the algorithm
to be compatible with MATLAB releases prior to R2012b.
c = union (a, b) ¶c = union (a, b, "rows") ¶c = union (…, "sorted") ¶c = union (…, "stable") ¶c = union (…, "legacy") ¶[c, ia, ib] = union (…) ¶Return the unique elements that are in either a or b.
If a and b are both row vectors then return a row vector; Otherwise, return a column vector. The inputs may also be cell arrays of strings.
If the optional input "rows" is given then return rows that are in
either a or b. The inputs must be 2-D numeric matrices to use
this option.
The optional argument "sorted"/"stable" controls the order
in which unique values appear in the output. The default is
"sorted" and values in the output are placed in ascending order.
The alternative "stable" preserves the order found in the input.
The optional outputs ia and ib are column index vectors such
that a(ia) and b(ib) are disjoint sets
whose union is c.
Programming Note: The input flag "legacy" changes the algorithm
to be compatible with MATLAB releases prior to R2012b.
c = setdiff (a, b) ¶c = setdiff (a, b, "rows") ¶c = setdiff (…, "sorted") ¶c = setdiff (…, "stable") ¶c = setdiff (…, "legacy") ¶[c, ia] = setdiff (…) ¶Return the unique elements in a that are not in b.
If a is a row vector return a row vector; Otherwise, return a column vector. The inputs may also be cell arrays of strings.
If the optional input "rows" is given then return the rows in
a that are not in b. The inputs must be 2-D numeric matrices to
use this option.
The optional argument "sorted"/"stable" controls the order
in which unique values appear in the output. The default is
"sorted" and values in the output are placed in ascending order.
The alternative "stable" preserves the order found in the input.
If requested, return the index vector ia such that
c = a(ia).
Programming Note: The input flag "legacy" changes the algorithm
to be compatible with MATLAB releases prior to R2012b.
c = setxor (a, b) ¶c = setxor (a, b, "rows") ¶c = setxor (…, "sorted") ¶c = setxor (…, "stable") ¶c = setxor (…, "legacy") ¶[c, ia, ib] = setxor (…) ¶Return the unique elements exclusive to sets a or b.
If a and b are both row vectors then return a row vector; Otherwise, return a column vector. The inputs may also be cell arrays of strings.
If the optional input "rows" is given then return the rows exclusive
to sets a and b. The inputs must be 2-D numeric matrices to use
this option.
The optional argument "sorted"/"stable" controls the order
in which unique values appear in the output. The default is
"sorted" and values in the output are placed in ascending order.
The alternative "stable" preserves the order found in the input.
The optional outputs ia and ib are column index vectors such
that a(ia) and b(ib) are disjoint sets
whose union is c.
Programming Note: The input flag "legacy" changes the algorithm
to be compatible with MATLAB releases prior to R2012b.
tf = ismember (a, s) ¶tf = ismember (a, s, "rows") ¶[tf, s_idx] = ismember (…) ¶Return a logical matrix tf with the same shape as a which is true (1) if the element in a is found in s and false (0) if it is not.
If a second output argument is requested then the index into s of each matching element is also returned.
a = [3, 10, 1];
s = [0:9];
[tf, s_idx] = ismember (a, s)
⇒ tf = [1, 0, 1]
⇒ s_idx = [4, 0, 2]
The inputs a and s may also be cell arrays.
a = {"abc"};
s = {"abc", "def"};
[tf, s_idx] = ismember (a, s)
⇒ tf = 1
⇒ s_idx = 1
If the optional third argument "rows" is given then compare rows
in a with rows in s. The inputs must be 2-D matrices with the
same number of columns to use this option.
a = [1:3; 5:7; 4:6];
s = [0:2; 1:3; 2:4; 3:5; 4:6];
[tf, s_idx] = ismember (a, s, "rows")
⇒ tf = logical ([1; 0; 1])
⇒ s_idx = [2; 0; 5];
See also: lookup, unique, union, intersect, setdiff, setxor, ismembertol.
tf = ismembertol (a, s) ¶tf = ismembertol (a, s, tol) ¶tf = ismembertol (a, s, name, value) ¶[tf, s_idx] = ismembertol (…) ¶Check if values are members of a set within a tolerance.
This functions returns a logical matrix tf with the same shape as
a which is true (1) where the element in a is close to s
within a tolerance tol and false (0) if it is not. If tol is
not specified, a default tolerance of 1e-6 is used.
If a second output argument is requested then the index into s of each matching element is also returned.
The inputs a and s must be numeric values.
a = [3, 10, 1];
s = [0:9];
[tf, s_idx] = ismembertol (a, s)
⇒ tf = [1, 0, 1]
⇒ s_idx = [4, 0, 2]
Optional property/value pairs may be given to change the function’s behavior. The property may be one of following strings:
"ByRows"If set to false (default), all elements in a and s are
treated separately. If set to true, tf will be true
for each row in a that matches a row in s within the given
tolerance. Two rows, u and v, are within tolerance if they
fulfill the condition all (abs (u-v) <= tol*max (abs ([a;s]))).
"OutputAllIndices"If set to false (default), s_idx contains indices for one
of the matches. If set to true, s_idx is a cell array
containing the indices for all elements in s that are within tolerance
of the corresponding value in a.
"DataScale"The provided value DS is used to change the scale factor in the
tolerance test to abs (u-v) <= tol*DS. By default, the maximum
absolute value in a and s is used as the scale factor.
Example:
s = [1:6].' * pi; a = 10.^log10 (x); [tf, s_idx] = ismembertol (a, s);
See also: ismember, lookup, unique, union, intersect, setdiff, setxor.
p = powerset (a) ¶p = powerset (a, "rows") ¶Compute the powerset (all subsets) of the set a.
The set a must be a numerical matrix or a cell array of strings. The output will always be a cell array of either vectors or strings.
With the optional argument "rows", each row of the set a is
considered one element of the set. The input must be a 2-D numeric matrix
to use this argument.
See also: unique, union, intersect, setdiff, setxor, ismember.