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.

- :
`tf`=**any**`(`

¶`x`) - :
`tf`=**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.

- :
`tf`=**all**`(`

¶`x`) - :
`tf`=**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 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))`

.

- :
`z`=**xor**`(`

¶`x`,`y`) - :
`z`=**xor**`(`

¶`x1`,`x2`, …) Return the

*exclusive or*of`x`and`y`.For boolean expressions

`x`and`y`,`xor (`

is true if and only if one of`x`,`y`)`x`or`y`is true. Otherwise, if`x`and`y`are 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 If more than two arguments are given the xor operation is applied cumulatively from left to right:

(...((x1 XOR x2) XOR x3) XOR ...)

- :
`y`=**diff**`(`

¶`x`) - :
`y`=**diff**`(`

¶`x`,`k`) - :
`y`=**diff**`(`

¶`x`,`k`,`dim`) If

`x`is a vector of length*n*,`diff (`

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

`x`is a matrix,`diff (`

is the matrix of column differences along the first non-singleton dimension.`x`)The second argument is optional. If supplied,

`diff (`

, where`x`,`k`)`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 (`

an empty matrix is returned.`x`,`dim`)

- :
`tf`=**isinf**`(`

¶`x`) Return a logical array which is true where the elements of

`x`are infinite and false where they are not.For example:

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

- :
`tf`=**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 ]

- :
`tf`=**isfinite**`(`

¶`x`) Return a logical array which is true where the elements of

`x`are finite values and false where they are not.For example:

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

- :
`[`

`err`,`yi`, …] =**common_size**`(`

¶`xi`, …) Determine if all input arguments are either scalar or of common size.

If true,

`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:[err, a, b] = common_size ([1 2; 3 4], 5) ⇒ err = 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.

**See also:**size, size_equal, numel, ndims.

- :
`idx`=**find**`(`

¶`x`) - :
`idx`=**find**`(`

¶`x`,`n`) - :
`idx`=**find**`(`

¶`x`,`n`,`direction`) - :
`[i, j] =`

**find**`(…)`

¶ - :
`[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 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.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

`x`is a multi-dimensional array of size m x n x p x …,`j`contains the column locations as if`x`was flattened into a two-dimensional matrix of size m x (n + p + …).Note that this function is particularly useful for sparse matrices, as it extracts the nonzero 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.

- :
`idx`=**lookup**`(`

¶`table`,`y`) - :
`idx`=**lookup**`(`

¶`table`,`y`,`opt`) Lookup values in a

**sorted**table.This function is usually used as a prelude to interpolation.

If table is increasing, of length N 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 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`

Match.

`table(idx(i)) == y(i)`

if`y(i)`

occurs in table; otherwise,`idx(i)`

is zero.`b`

Boolean.

`idx(i)`

is a logical 1 or 0, indicating whether`y(i)`

is contained in table or not.`l`

Left. For numeric lookups the leftmost subinterval shall be extended to minus infinity (i.e., all indices at least 1).

`r`

Right. For numeric lookups the rightmost subinterval shall be extended to infinity (i.e., all indices at most N-1).

**Note**: If`table`is not sorted the results from`lookup`

will be unpredictable.

If you wish to check if a variable exists at all, instead of properties its elements may have, consult Status of Variables.