16.1 Finding Elements and Checking Conditions

The functions any and all are useful for determining whether any or all of the elements of a matrix satisfy some condition. The find function is also useful in determining which elements of a matrix meet a specified condition.

Built-in Function: any (x, dim)

For a vector argument, return 1 if any element of the vector is nonzero.

For a matrix argument, return a row vector of ones and zeros with each element indicating whether any of the elements of the corresponding column of the matrix are nonzero. For example,

any (eye (2, 4)) ⇒ [ 1, 1, 0, 0 ]

If the optional argument dim is supplied, work along dimension dim. For example,

any (eye (2, 4), 2) ⇒ [ 1; 1 ]

Built-in Function: all (x, dim)

The function all behaves like the function any, except that it returns true only if all the elements of a vector, or all the elements along dimension dim of a matrix, are nonzero.

Since the comparison operators (see section Comparison Operators) return matrices of ones and zeros, it is easy to test a matrix for many things, not just whether the elements are nonzero. For example,

all (all (rand (5) < 0.9))
     ⇒ 0

tests a random 5 by 5 matrix to see if all of its elements are less than 0.9.

Note that in conditional contexts (like the test clause of if and while statements) Octave treats the test as if you had typed all (all (condition)).

Mapping Function: xor (x, y)

Return the `exclusive or' of the entries of x and y. For boolean expressions x and y, xor (x, y) is true if and only if x or y is true, but not if both x and y are true.

Function File: is_duplicate_entry (x)

Return non-zero if any entries in x are duplicates of one another.

Function File: diff (x, k, dim)

If x is a vector of length n, diff (x) is the vector of first differences x(2) - x(1), …, x(n) - x(n-1).

If x is a matrix, diff (x) is the matrix of column differences along the first non-singleton dimension.

The second argument is optional. If supplied, diff (x, k), where k is a non-negative integer, returns the k-th differences. It is possible that k is larger than then first non-singleton dimension of the matrix. In this case, diff continues to take the differences along the next non-singleton dimension.

The dimension along which to take the difference can be explicitly stated with the optional variable dim. In this case the k-th order differences are calculated along this dimension. In the case where k exceeds size (x, dim) then an empty matrix is returned.

Mapping Function: isinf (x)

Return 1 for elements of x that are infinite and zero otherwise. For example,

isinf ([13, Inf, NA, NaN]) ⇒ [ 0, 1, 0, 0 ]

Mapping Function: isnan (x)

Return 1 for elements of x that are NaN values and zero otherwise. NA values are also considered NaN values. For example,

isnan ([13, Inf, NA, NaN]) ⇒ [ 0, 0, 1, 1 ]

See also: isna.

Mapping Function: finite (x)

Return 1 for elements of x that are finite values and zero otherwise. For example,

finite ([13, Inf, NA, NaN]) ⇒ [ 1, 0, 0, 0 ]

Loadable Function: find (x)

Loadable Function: find (x, n)

Loadable Function: find (x, n, direction)

Return a vector of indices of nonzero elements of a matrix, as a row if x is a row or as a column otherwise. To obtain a single index for each matrix element, Octave pretends that the columns of a matrix form one long vector (like Fortran arrays are stored). For example,

find (eye (2)) ⇒ [ 1; 4 ]

If two outputs are requested, find returns the row and column indices of nonzero elements of a matrix. For example,

[i, j] = find (2 * eye (2)) ⇒ i = [ 1; 2 ] ⇒ j = [ 1; 2 ]

If three outputs are requested, find also returns a vector containing the nonzero values. For example,

[i, j, v] = find (3 * eye (2)) ⇒ i = [ 1; 2 ] ⇒ j = [ 1; 2 ] ⇒ v = [ 3; 3 ]

If two inputs are given, n indicates the maximum number of elements to find from the beginning of the matrix or vector.

If three inputs are given, direction should be one of "first" or "last", requesting only the first or last n indices, respectively. However, the indices are always returned in ascending order.

Note that this function is particularly useful for sparse matrices, as it extracts the non-zero elements as vectors, which can then be used to create the original matrix. For example,

sz = size(a); [i, j, v] = find (a); b = sparse(i, j, v, sz(1), sz(2));

See also: sparse.

Function File: [err, y1, …] = common_size (x1, …)

Determine if all input arguments are either scalar or of common size. If so, err is zero, and yi is a matrix of the common size with all entries equal to xi if this is a scalar or xi otherwise. If the inputs cannot be brought to a common size, errorcode is 1, and yi is xi. For example,

[errorcode, a, b] = common_size ([1 2; 3 4], 5) ⇒ errorcode = 0 ⇒ a = [ 1, 2; 3, 4 ] ⇒ b = [ 5, 5; 5, 5 ]

This is useful for implementing functions where arguments can either be scalars or of common size.