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

SDOT, DDOT, CDOTU, ZDOTU, CDOTC, and ZDOTC--Dot Product of Two Vectors

SDOT, DDOT, CDOTU, and ZDOTU compute the dot product of vectors x and y:

CDOTC and ZDOTC compute the dot product of the complex conjugate of vector x with vector y:

Table 43. Data Types

Syntax

On Entry

n

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. Specified as: a one-dimensional array of (at least) length 1+(n-1)|incx|, containing numbers of the data type indicated in Table 43.

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. Specified as: a one-dimensional array of (at least) length 1+(n-1)|incy|, containing numbers of the data type indicated in Table 43.

incy

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

On Return

Function value

is the result of the dot product computation. Returned as: a number of the data type indicated in Table 43.

Note

Declare this function in your program as returning a value of the data type indicated in Table 43.

Function

SDOT, DDOT, CDOTU, and ZDOTU compute the dot product of the vectors x and y, which is expressed as follows:

CDOTC and ZDOTC compute the dot product of the complex conjugate of vector x with vector y, which is expressed as follows:

See reference [79]. The result is returned as a function value. If n is 0, then zero is returned as the value of the function.

For SDOT, CDOTU, and CDOTC, intermediate results are accumulated in long precision.

Error Conditions

Computational Errors

None

Input-Argument Errors

n < 0

Example 1

This example shows how to compute the dot product of two vectors, x and y, having strides of 1.

Function Reference and Input

             N   X  INCX  Y  INCY
             |   |   |    |   |
DOTT = SDOT( 5 , X , 1  , Y , 1  )
 
X        =  (1.0, 2.0, -3.0, 4.0, 5.0)
Y        =  (9.0, 8.0, 7.0, -6.0, 5.0)

Output

DOTT     =  (9.0 + 16.0 - 21.0 - 24.0 + 25.0) = 5.0

Example 2

This example shows how to compute the dot product of a vector, x, with a stride of 1, and a vector, y, with a stride greater than 1.

Function Reference and Input

             N   X  INCX  Y  INCY
             |   |   |    |   |
DOTT = SDOT( 5 , X , 1  , Y , 2  )
 
X        =  (1.0, 2.0, -3.0, 4.0, 5.0)
Y        =  (9.0, . , 7.0, . , 5.0, . , -3.0, . , 1.0)

Output

DOTT     =  (9.0 + 14.0 - 15.0 - 12.0 + 5.0) = 1.0

Example 3

This example shows how to compute the dot product of a vector, x, with a negative stride, and a vector, y, with a stride greater than 1. For x, processing begins at element X(5), which is 5.0.

Function Reference and Input

             N   X   INCX  Y  INCY
             |   |    |    |   |
DOTT = SDOT( 5 , X , -1  , Y , 2  )
 
X        =  (1.0, 2.0, -3.0, 4.0, 5.0)
Y        =  (9.0, . , 7.0, . , 5.0, . , -3.0, . , 1.0)

Output

DOTT     =  (45.0 + 28.0 - 15.0 - 6.0 + 1.0) = 53.0

Example 4

This example shows how to compute the dot product of a vector, x, with a stride of 0, and a vector, y, with a stride of 1. The result in DOTT is x₁(y₁+...+y_n).

Function Reference and Input

             N   X  INCX  Y  INCY
             |   |   |    |   |
DOTT = SDOT( 5 , X , 0  , Y , 1  )
 
X        =  (1.0, . , . , . , .)
Y        =  (9.0, 8.0, 7.0, -6.0, 5.0)

Output

DOTT     =  (1.0) × (9.0 + 8.0 + 7.0 - 6.0 + 5.0) = 23.0

Example 5

This example shows how to compute the dot product of two vectors, x and y, with strides of 0. The result in DOTT is nx₁y₁.

Function Reference and Input

             N   X  INCX  Y  INCY
             |   |   |    |   |
DOTT = SDOT( 5 , X , 0  , Y , 0  )
 
X        =  (1.0, . , . , . , .)
Y        =  (9.0, . , . , . , .)

Output

DOTT     =  (5) × (1.0) × (9.0) = 45.0

Example 6

This example shows how to compute the dot product of two vectors, x and y, containing complex numbers, where x has a stride of 1, and y has a stride greater than 1.

Function Reference and Input

              N   X  INCX  Y  INCY
              |   |   |    |   |
DOTT = CDOTU( 3 , X , 1  , Y , 2  )
 
X        =  ((1.0, 2.0), (3.0, -4.0), (-5.0, 6.0))
Y        =  ((10.0, 9.0), . , (-6.0, 5.0), . , (2.0, 1.0))

Output

DOTT     =  ((10.0 - 18.0 - 10.0) - (18.0 - 20.0 + 6.0),
             (9.0 + 15.0 - 5.0) + (20.0 + 24.0 + 12.0))
         =  (-22.0, 75.0)

Example 7

This example shows how to compute the dot product of the conjugate of a vector, x, with vector y, both containing complex numbers, where x has a stride of 1, and y has a stride greater than 1.

Function Reference and Input

              N   X  INCX  Y  INCY
              |   |   |    |   |
DOTT = CDOTC( 3 , X , 1  , Y , 2  )
 
X        =  ((1.0, 2.0), (3.0, -4.0), (-5.0, 6.0))
Y        =  ((10.0, 9.0), . , (-6.0, 5.0), . , (2.0, 1.0))

Output

DOTT     =  ((10.0 - 18.0 - 10.0) + (18.0 - 20.0 + 6.0),
             (9.0  +  15.0  -  5.0)  -  (20.0  +  24.0  +  12.0))
         =  (-14.0, -37.0)