## ROTATE

The ROTATE function returns a rotated and/or transposed copy of Array. ROTATE can only rotate arrays in multiples of 90 degrees. To rotate by amounts other than multiples of 90 degrees, use the ROT function. Note, however, that ROTATE is more efficient.

ROTATE can also be used to reverse the order of elements in vectors. For example, to reverse the order of elements in the vector X, use the expression `ROTATE(X,2)`. If X = [0,1,2,3] then `ROTATE(X,2)`yields the resulting array, [3,2,1,0].

 Note
Transposition, if specified, is performed before rotation.

### Syntax

Result = ROTATE(Array, Direction)

### Return Value

Returns the rotated and/or transposed array.

### Arguments

#### Array

The array to be rotated. Array can have only one or two dimensions. The result has the same type as Array. The dimensions of the result are the same as those of Array if Direction is equal to 0 or 2. The dimensions are transposed if the direction is 4 or greater.

#### Direction

Direction specifies the operation to be performed as follows:

Direction
Transpose?
Rotation Counterclockwise
X1
Y1
0 No None X0 Y0
1 No 90° -Y0 X0
2 No 180° -X0 -Y0
3 No 270° Y0 -X0
4 Yes None Y0 X0
5 Yes 90° -X0 Y0
6 Yes 180° -Y0 -X0
7 Yes 270° X0 -Y0

In the table above, (X0, Y0) are the original subscripts, and (X1, Y1) are the subscripts of the resulting array. The notation -Y0 indicates a reversal of the Y axis, Y1 = Ny - Y0 - 1. Direction is taken modulo 8, so a rotation of -1 is the same as 7, 9 is the same as 1, etc.

 Note
The assertion that Array is rotating counterclockwise may cause some confusion. Remember that when arrays are displayed on the screen (using TV or TVSCL, for example), the image is drawn by default with the origin (0,0) at the bottom left corner of the window. (This default can be changed by changing the value of the !ORDER system variable.) When arrays are printed on the console or command log window (using the PRINT command, for example), the (0,0) element is drawn in the upper left corner of the array. This means that while an image displayed in a graphics window appears to rotate counterclockwise, an array printed in the command log appears to rotate clockwise.

### Examples

Create and display a wedge image by entering:

```F = REPLICATE(1, 256) # FINDGEN(256) & TVSCL, F
```

To display the image rotated 90 degrees counterclockwise, enter:

```TVSCL, ROTATE(F, 1)
```

### Version History

Introduced: Original