Finding Elements and Checking Conditions - Untitled
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### 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 Comparison Ops) 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 nonnegative 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 ]

— 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 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" indicating that it should start counting found elements from the first or last element.

— 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.