HP MLIB User's Guide Vol. 2 7th Ed.

Chapter 6 Correlation and Convolution Subprograms 597

Correlation and convolution SCONV/DCONV

incy Increment for the array y, incy ≠ 0. is stored in

y((k−1)×incy+1). incy will normally be positive whether

computing the correlation or the convolution. Use incy

= 1 if the vector y is stored contiguously in array y, that

is, if is stored in y(k). Refer to “Notes.”

m The length of the y vector. m > 0.

n The length of the w vector. n > 0.

Output y The convolution or correlation vector y of length m.

leny = (m−1)×|incy|+1.

Notes These subprograms do not use the BLAS indexing scheme described in “BLAS

indexing conventions” on page 35. Indexing works the same way as the BLAS

for a positive increment but, for a negative increment, these subprograms

access data backward from the beginning of the array passed to it rather than

from the end. To index backward through an array, as desired for a convolution,

the ending location of the array should be passed to the subprogram. Refer to

“Example 2” on page 598.

To compute the complete correlation or convolution vector, including both tails

as well as the fully engaged portion, append n−1 zeros to each end of the x

vector. The fully engaged portion of the correlation or convolution of the

resulting vector is the complete correlation or convolution corresponding to the

original x vector. Refer to“Example 2” on page 598

Example 1 Compute the fully engaged portion of the discrete correlation of the REAL*4

vectors x = (4, 1, 3, 5, 2) and w = (2, 1) stored in arrays X and W,

respectively. In this instance, n = 2 and m+n−1 = 5, so m =4.

INTEGER*4 INCX,INCW,INCY,M,N

REAL*4 X(5),W(2),Y(4)

DATA X / 4.0 , 1.0 , 3.0 , 5.0, 2.0 /

DATA W / 2.0 , 1.0 /

M = 4

N = 2

INCX = 1

INCW = 1

INCY = 1

CALL SCONV (X,INCX,W,INCW,Y,INCY,M,N)

The result is y = (9, 5, 11, 12).