There are a number of functions available for checking to see if the elements of a matrix meet some condition, and for rearranging the elements of a matrix. For example, Octave can easily tell you if all the elements of a matrix are finite, or are less than some specified value. Octave can also rotate the elements, extract the upper- or lower-triangular parts, or sort the columns of a matrix.

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.

Given a vector, the function `any`

returns 1 if any element of the
vector is nonzero.

For a matrix argument, `any`

returns 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,

octave:13> any (eye (2, 4)) ans = 1 1 0 0

To see if any of the elements of a matrix are nonzero, you can use a statement like

any (any (a))

For a matrix argument, `any`

returns 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.

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 in a column 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,

octave:13> all (all (rand (5) < 0.9)) ans = 0

tests a random 5 by 5 matrix to see if all of it's 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))`

.

The functions `isinf`

, `finite`

, and `isnan`

return 1 if
their arguments are infinite, finite, or not a number, respectively, and
return 0 otherwise. For matrix values, they all work on an element by
element basis. For example, evaluating the expression

isinf ([1, 2; Inf, 4])

produces the matrix

ans = 0 0 1 0

The function `find`

returns 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,

octave:13> find (eye (2)) ans = 1 4

If two outputs are requested, `find`

returns the row and column
indices of nonzero elements of a matrix. For example,

octave:13> [i, j] = find (eye (2)) i = 1 2 j = 1 2

If three outputs are requested, `find`

also returns the nonzero
values in a vector.

The function `fliplr`

reverses the order of the columns in a
matrix, and `flipud`

reverses the order of the rows. For example,

octave:13> fliplr ([1, 2; 3, 4]) ans = 2 1 4 3 octave:13> flipud ([1, 2; 3, 4]) ans = 3 4 1 2

The function `rot90 (`

rotates a matrix
counterclockwise in 90-degree increments. The second argument is
optional, and specifies how many 90-degree rotations are to be applied
(the default value is 1). Negative values of `a`, `n`)`n` rotate the matrix
in a clockwise direction. For example,

rot90 ([1, 2; 3, 4], -1) ans = 3 1 4 2

rotates the given matrix clockwise by 90 degrees. The following are all equivalent statements:

rot90 ([1, 2; 3, 4], -1) rot90 ([1, 2; 3, 4], 3) rot90 ([1, 2; 3, 4], 7)

The function `reshape (`

returns a matrix
with `a`, `m`, `n`)`m` rows and `n` columns whose elements are taken from the
matrix `a`. To decide how to order the elements, Octave pretends
that the elements of a matrix are stored in column-major order (like
Fortran arrays are stored).

For example,

octave:13> reshape ([1, 2, 3, 4], 2, 2) ans = 1 3 2 4

If the variable `do_fortran_indexing`

is `"true"`

, the
`reshape`

function is equivalent to

retval = zeros (m, n); retval (:) = a;

but it is somewhat less cryptic to use `reshape`

instead of the
colon operator. Note that the total number of elements in the original
matrix must match the total number of elements in the new matrix.

The function ``sort'` can be used to arrange the elements of a vector
in increasing order. For matrices, `sort`

orders the elements in
each column.

For example,

octave:13> sort (rand (4)) ans = 0.065359 0.039391 0.376076 0.384298 0.111486 0.140872 0.418035 0.824459 0.269991 0.274446 0.421374 0.938918 0.580030 0.975784 0.562145 0.954964

The `sort`

function may also be used to produce a matrix
containing the original row indices of the elements in the sorted
matrix. For example,

s = 0.051724 0.485904 0.253614 0.348008 0.391608 0.526686 0.536952 0.600317 0.733534 0.545522 0.691719 0.636974 0.986353 0.976130 0.868598 0.713884 i = 2 4 2 3 4 1 3 4 1 2 4 1 3 3 1 2

These values may be used to recover the original matrix from the sorted version. For example,

The `sort`

function does not allow sort keys to be specified, so it
can't be used to order the rows of a matrix according to the values of
the elements in various columns(5)
in a single call. Using the second output, however, it is possible to
sort all rows based on the values in a given column. Here's an example
that sorts the rows of a matrix based on the values in the third column.

octave:13> a = rand (4) a = 0.080606 0.453558 0.835597 0.437013 0.277233 0.625541 0.447317 0.952203 0.569785 0.528797 0.319433 0.747698 0.385467 0.124427 0.883673 0.226632 octave:14> [s, i] = sort (a (:, 3)); octave:15> a (i, :) ans = 0.569785 0.528797 0.319433 0.747698 0.277233 0.625541 0.447317 0.952203 0.080606 0.453558 0.835597 0.437013 0.385467 0.124427 0.883673 0.226632

The functions `triu (`

and `a`, `k`)`tril (`

extract the upper or lower triangular part of the matrix
`a`,
`k`)`a`, and set all other elements to zero. The second argument is
optional, and specifies how many diagonals above or below the main
diagonal should also be set to zero.

The default value of `k` is zero, so that `triu`

and
`tril`

normally include the main diagonal as part of the result
matrix.

If the value of `k` is negative, additional elements above (for
`tril`

) or below (for `triu`

) the main diagonal are also
selected.

The absolute value of `k` must not be greater than the number of
sub- or super-diagonals.

For example,

octave:13> tril (rand (4), 1) ans = 0.00000 0.00000 0.00000 0.00000 0.09012 0.00000 0.00000 0.00000 0.01215 0.34768 0.00000 0.00000 0.00302 0.69518 0.91940 0.00000

forms a lower triangular matrix from a random 4 by 4 matrix, omitting the main diagonal, and

octave:13> tril (rand (4), -1) ans = 0.06170 0.51396 0.00000 0.00000 0.96199 0.11986 0.35714 0.00000 0.16185 0.61442 0.79343 0.52029 0.68016 0.48835 0.63609 0.72113

forms a lower triangular matrix from a random 4 by 4 matrix, including the main diagonal and the first super-diagonal.

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