SROTI/DROTI

 

Apply sparse Givens rotation

 

indx

Array containing the indices {ki} of the interesting

 

 

elements of x. The indices must satisfy the following:

 

 

1 ≤ indx(i) ≤ n, i = 1, 2, …, m

 

 

indx(i) ≠ indx( j), 1 ≤ i ≠ j ≤ m

 

 

where n is the length of y.

 

y

Array containing the elements of y, y(i) = yi.

 

c

The scalar c.

 

s

The scalar s.

Output

x and y

If m ≤ 0 or if c = 1 and s = 0, then x and y are

 

 

unchanged. Otherwise, the result vectors overwrite the

 

 

input. Only the elements of y whose indices are

 

 

included in indx are changed.

Notes The result is unspecified if any element of indx is out of range, if any two elements of indx have the same value, or if x, indx, and y overlap such that any index or any element of x or y share a memory location.

Fortran Equivalent

SUBROUTINE SROTI (M, X,INDX, Y, C,S) REAL*4 C,S,TEMP,X(*),Y(*)

INTEGER*4 INDX(*)

IF ( M .LE. 0 ) RETURN

IF ( C .EQ. 1.0 .AND. S .EQ. 0.00 ) RETURN DO 10 I = 1, M

TEMP = C * X(I) + S * Y(INDX(I)) Y(INDX(I)) = C * Y(INDX(I)) - S * X(I) X(I) = TEMP

10CONTINUE RETURN END

Example Apply a Givens rotation to x and y, where x is a sparse vector with interesting elements x1, x4, x5, and x9 stored in one-dimensional array X, and y is stored in a

one-dimensional array Y of dimension 20.

INTEGER*4

M,INDX(4)

REAL*8

X(4),Y(20),C,S

DATA

INDX / 1, 4, 5, 9 /

M = 4

 

CALL DROTI (M,X,INDX,Y,C,S)

122HP MLIB User’s Guide