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# max

Largest elements

## Syntax

``C = max(A)``
``C = max(A,[],dim)``
``````[C,I] = max(___)``````
``C = max(A,B)``

## Description

example

````C = max(A)` returns the largest element of `A` if `A` is a vector. If `A` is a matrix, this syntax treats the columns of `A` as vectors, returning a row vector containing the largest element from each column.```

example

````C = max(A,[],dim)` returns the largest elements of matrix `A` along the dimension `dim`. Thus, `max(A,[],1)` returns a row vector containing the largest elements of each column of `A`, and `max(A,[],2)` returns a column vector containing the largest elements of each row of `A`.Here, the required argument `[]` serves as a divider. If you omit it, `max(A,dim)` compares elements of `A` with the value `dim`.```

example

``````[C,I] = max(___)``` finds the indices of the largest elements, and returns them in output vector `I`. If there are several identical largest values, this syntax returns the index of the first largest element that it finds.```

example

````C = max(A,B)` compares each element of `A` with the corresponding element of `B` and returns `C` containing the largest elements of each pair.```

## Examples

### Maximum of Vector of Numbers

Find the largest of these numbers. Because these numbers are not symbolic objects, you get a floating-point result.

`max([-pi, pi/2, 1, 1/3])`
```ans = 1.5708```

Find the largest of the same numbers converted to symbolic objects.

`max(sym([-pi, pi/2, 1, 1/3]))`
```ans = pi/2```

### Maximum of Each Column in Symbolic Matrix

Create matrix `A` containing symbolic numbers, and call `max` for this matrix. By default, `max` returns the row vector containing the largest elements of each column.

```A = sym([0, 1, 2; 3, 4, 5; 1, 2, 3]) max(A)```
```A = [ 0, 1, 2] [ 3, 4, 5] [ 1, 2, 3] ans = [ 3, 4, 5]```

### Maximum of Each Row in Symbolic Matrix

Create matrix `A` containing symbolic numbers, and find the largest elements of each row of the matrix. In this case, `max` returns the result as a column vector.

```A = sym([0, 1, 2; 3, 4, 5; 1, 2, 3]) max(A,[],2)```
```A = [ 0, 1, 2] [ 3, 4, 5] [ 1, 2, 3] ans = 2 5 3```

### Indices of Largest Elements

Create matrix `A`. Find the largest element in each column and its index.

```A = 1./sym(magic(3)) [Cc,Ic] = max(A)```
```A = [ 1/8, 1, 1/6] [ 1/3, 1/5, 1/7] [ 1/4, 1/9, 1/2] Cc = [ 1/3, 1, 1/2] Ic = 2 1 3```

Now, find the largest element in each row and its index.

`[Cr,Ir] = max(A,[],2)`
```Cr = 1 1/3 1/2 Ir = 2 1 3```

If `dim` exceeds the number of dimensions of `A`, then the syntax `[C,I] = max(A,[],dim)` returns ```C = A``` and `I = ones(size(A))`.

`[C,I] = max(A,[],3)`
```C = [ 1/8, 1, 1/6] [ 1/3, 1/5, 1/7] [ 1/4, 1/9, 1/2] I = 1 1 1 1 1 1 1 1 1```

### Largest Elements of Two Symbolic Matrices

Create matrices `A` and `B` containing symbolic numbers. Use `max` to compare each element of `A` with the corresponding element of `B`, and return the matrix containing the largest elements of each pair.

```A = sym(pascal(3)) B = toeplitz(sym([pi/3 pi/2 pi])) maxAB = max(A,B)```
```A = [ 1, 1, 1] [ 1, 2, 3] [ 1, 3, 6] B = [ pi/3, pi/2, pi] [ pi/2, pi/3, pi/2] [ pi, pi/2, pi/3] maxAB = [ pi/3, pi/2, pi] [ pi/2, 2, 3] [ pi, 3, 6]```

### Maximum of Complex Numbers

When finding the maximum of these complex numbers, `max` chooses the number with the largest complex modulus.

```modulus = abs([-1 - i, 1 + 1/2*i]) maximum = max(sym([1 - i, 1/2 + i]))```
```modulus = 1.4142 1.1180 maximum = 1 - 1i```

If the numbers have the same complex modulus, `min` chooses the number with the largest phase angle.

```modulus = abs([1 - 1/2*i, 1 + 1/2*i]) phaseAngle = angle([1 - 1/2*i, 1 + 1/2*i]) maximum = max(sym([1 - 1/2*i, 1/2 + i]))```
```modulus = 1.1180 1.1180 phaseAngle = -0.4636 0.4636 maximum = 1/2 + 1i```

## Input Arguments

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Input, specified as a symbolic number, vector, or matrix. All elements of `A` must be convertible to floating-point numbers. If `A` is a scalar, then `max(A)` returns `A`. `A` cannot be a multidimensional array.

Dimension to operate along, specified as a positive integer. The default value is `1`. If `dim` exceeds the number of dimensions of `A`, then `max(A,[],dim)` returns `A`, and `[C,I] = max(A,[],dim)` returns ```C = A``` and `I = ones(size(A))`.

Input, specified as a symbolic number, vector, or matrix. All elements of `B` must be convertible to floating-point numbers. If `A` and `B` are scalars, then `max(A,B)` returns the largest of `A` and `B`.

If one argument is a vector or matrix, the other argument must either be a scalar or have the same dimensions as the first one. If one argument is a scalar and the other argument is a vector or matrix, then `max` expands the scalar into a vector or a matrix of the same length with all elements equal to that scalar.

`B` cannot be a multidimensional array.

## Output Arguments

collapse all

Largest elements, returned as a symbolic number or vector of symbolic numbers.

Indices of largest elements, returned as a symbolic number or vector of symbolic numbers. `[C,I] = max(A,[],dim)` also returns matrix `I = ones(size(A))` if the value `dim` exceeds the number of dimensions of `A`.

## Tips

• Calling `max` for numbers (or vectors or matrices of numbers) that are not symbolic objects invokes the MATLAB® `max` function.

• For complex input `A`, `max` returns the complex number with the largest complex modulus (magnitude), computed with `max(abs(A))`. If complex numbers have the same modulus, `max` chooses the number with the largest phase angle, `max(angle(A))`.

• `max` ignores `NaN`s.