Finding Elements and Checking Conditions - GNU Octave
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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)
— Built-in Function: any (x, dim)

> For a vector argument, return true (logical 1) if any element of the vector is nonzero.

> For a matrix argument, return a row vector of logical 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 ]

> See also: all.

— Built-in Function: all (x)
— Built-in Function: all (x, dim)

> For a vector argument, return true (logical 1) if all elements of the vector are nonzero.

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

>               all ([2, 3; 1, 0]))
>                    ⇒ [ 1, 0 ]

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

> See also: any.

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: z = 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 one of x or y is true. Otherwise, for x and y both true or both false, `xor` returns false.

> The truth table for the xor operation is

> | x | y | z |
> | 0 | 0 | 0 |
> | 1 | 0 | 1 |
> | 0 | 1 | 1 |
> | 1 | 1 | 0 |

> See also: and, or, not.

— Built-in Function: diff (x)
— Built-in Function: diff (x, k)
— Built-in Function: 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 the 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`)` an empty matrix is returned.

— Mapping Function: isinf (x)

> Return a logical array which is true where the elements of x are are infinite and false where they are not. For example:

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

> See also: isfinite, isnan, isna.

— Mapping Function: isnan (x)

> Return a logical array which is true where the elements of x are NaN values and false where they are not. NA values are also considered NaN values. For example:

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

> See also: isna, isinf, isfinite.

— Mapping Function: isfinite (x)
— Mapping Function: finite (x)

> Return a logical array which is true where the elements of x are finite values and false where they are not. For example:

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

> See also: isinf, isnan, isna.

— 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, err 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.

— Loadable Function: idx = find (x)
— Loadable Function: idx = find (x, n)
— Loadable Function: idx = find (x, n, direction)
— Loadable Function: [i, j] = find (...)
— Loadable Function: [i, j, v] = find (...)

> Return a vector of indices of nonzero elements of a matrix, as a row if x is a row vector 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: nonzeros.

— Loadable Function: idx = lookup (table, y)
— Loadable Function: idx = lookup (table, y, opt)

> Lookup values in a sorted table. Usually used as a prelude to interpolation.

> If table is increasing and `idx = lookup (table, y)`, then `table(idx(i)) <= y(i) < table(idx(i+1))` for all `y(i)` within the table. If `y(i) < table(1)` then `idx(i)` is 0. If `y(i) >= table(end)` or `isnan (y(i))` then `idx(i)` is `n`.

> If the table is decreasing, then the tests are reversed. For non-strictly monotonic tables, empty intervals are always skipped. The result is undefined if table is not monotonic, or if table contains a NaN.

> The complexity of the lookup is O(M*log(N)) where N is the size of table and M is the size of y. In the special case when y is also sorted, the complexity is O(min(M*log(N),M+N)).

> table and y can also be cell arrays of strings (or y can be a single string). In this case, string lookup is performed using lexicographical comparison.

> If opts is specified, it must be a string with letters indicating additional options.

> `m`
>   `table(idx(i)) == val(i)` if `val(i)` occurs in table; otherwise, `idx(i)` is zero.
> `b`
>   `idx(i)` is a logical 1 or 0, indicating whether `val(i)` is contained in table or not.
> `l`
>   For numeric lookups the leftmost subinterval shall be extended to infinity (i.e., all indices at least 1)
> `r`
>   For numeric lookups the rightmost subinterval shall be extended to infinity (i.e., all indices at most n-1).