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### 18.1 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. For example,

```          isnan ([13, Inf, NA, NaN])
=> [ 0, 0, 0, 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 ]
```

Return a vector of indices of nonzero elements of a matrix. 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 ]
```

— 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.