Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

SROT, DROT, CROT, ZROT, CSROT, and ZDROT--Apply a Plane Rotation

SROT and DROT apply a real plane rotation to real vectors; CROT and ZROT apply a complex plane rotation to complex vectors; and CSROT and ZDROT apply a real plane rotation to complex vectors. The plane rotation is applied to n points, where the points to be rotated are contained in vectors x and y, and where the cosine and sine of the angle of rotation are c and s, respectively.

Table 49. Data Types

Syntax

On Entry

n

is the number of points to be rotated--that is, the number of elements in vectors x and y. Specified as: a fullword integer; n >= 0.

x

is the vector x of length n, containing the x_i coordinates of the points to be rotated. Specified as: a one-dimensional array of (at least) length 1+(n-1)|incx|, containing numbers of the data type indicated in Table 49.

incx

is the stride for vector x. Specified as: a fullword integer. It can have any value.

y

is the vector y of length n, containing the y_i coordinates of the points to be rotated. Specified as: a one-dimensional array of (at least) length 1+(n-1)|incy|, containing numbers of the data type indicated in Table 49.

incy

is the stride for vector y. Specified as: a fullword integer. It can have any value.

c

the cosine, c, of the angle of rotation. Specified as: a number of the data type indicated in Table 49.

s

the sine, s, of the angle of rotation. Specified as: a number of the data type indicated in Table 49.

On Return

x

is the vector x of length n, containing the rotated x_i coordinates, where:

x_i <-- cx_i+sy_i    for i = 1,

Returned as: a one-dimensional array, containing numbers of the data type indicated in Table 49.

y

is the vector y of length n, containing the rotated y_i coordinates, where:

For SROT, DROT, CSROT, and ZDROT:

y_i <-- -sx_i+cy_i    for i = 1, n

For CROT and ZROT:

Returned as: a one-dimensional array, containing numbers of the data type indicated in Table 49.

Note

The vectors x and y must have no common elements; otherwise, results are unpredictable. See Concepts.

Function

Applying a plane rotation to n points, where the points to be rotated are contained in vectors x and y, is expressed as follows, where c and s are the cosine and sine of the angle of rotation, respectively. For SROT, DROT, CSROT, and ZDROT:

For CROT and ZROT:

See references [57] and [79]. No computation is performed if n is 0 or if c is 1.0 and s is zero. For SROT, CROT, and CSROT, intermediate results are accumulated in long precision.

Error Conditions

Computational Errors

None

Input-Argument Errors

n < 0

Example 1

This example shows how to apply a real plane rotation to real vectors x and y having positive strides.

Call Statement and Input

           N   X  INCX  Y  INCY   C    S
           |   |   |    |   |     |    |
CALL SROT( 5 , X , 1  , Y , 2  , 0.5 , S )
 
X        =  (1.0, 2.0, 3.0, 4.0, 5.0)
Y        =  (-1.0, . , -2.0, . , -3.0, . , -4.0, . , -5.0)

Output

X        =  (-0.366, -0.732, -1.098, -1.464, -1.830)
Y        =  (-1.366, -2.732, -4.098, -5.464, -6.830)

Example 2

This example shows how to apply a real plane rotation to real vectors x and y having strides of opposite sign.

Call Statement and Input

           N   X  INCX  Y   INCY   C    S
           |   |   |    |    |     |    |
CALL SROT( 5 , X , 1  , Y , -1  , 0.5 , S )
 
X        =  (1.0, 2.0, 3.0, 4.0, 5.0)
Y        =  (-5.0, -4.0, -3.0, -2.0, -1.0)

Output

Example 3

This example shows how scalar values in vectors x and y can be processed by specifying 0 strides and the number of elements to be processed, n, equal to 1.

Call Statement and Input

           N   X  INCX  Y  INCY   C    S
           |   |   |    |   |     |    |
CALL SROT( 1 , X , 0  , Y , 0  , 0.5 , S )
 
X        =  (1.0)
Y        =  (-1.0)

Output

X        =  (-0.366)
Y        =  (-1.366)

Example 4

This example shows how to apply a complex plane rotation to complex vectors x and y having positive strides.

Call Statement and Input

           N   X  INCX  Y  INCY   C    S
           |   |   |    |   |     |    |
CALL CROT( 3 , X , 1  , Y , 2  , 0.5 , S )
 
X        =  ((1.0, 2.0), (2.0, 3.0), (3.0, 4.0))
Y        =  ((-1.0, 5.0), . , (-2.0, 4.0), . , (-3.0, 3.0))
S        =  (0.75, 0.50)

Output

X        =  ((-2.750, 4.250), (-2.500, 3.500), (-2.250, 2.750))
Y        =  ((-2.250, 1.500), . , (-4.000, 0.750), . ,
             (-5.750, 0.000))

Example 5

This example shows how to apply a real plane rotation to complex vectors x and y having positive strides.

Call Statement and Input

            N   X  INCX  Y  INCY   C    S
            |   |   |    |   |     |    |
CALL CSROT( 3 , X , 1  , Y , 2  , 0.5 , S )
 
X        =  ((1.0, 2.0), (2.0, 3.0), (3.0, 4.0))
Y        =  ((-1.0, 5.0), . , (-2.0, 4.0), . , (-3.0, 3.0))

Output

X        =  ((-0.366, 5.330), (-0.732, 4.964), (-1.098, 4.598))
Y        =  ((-1.366, 0.768), . , (-2.732, -0.598), . ,
             (-4.098, -1.964))