SROTM(3dxml) — Subroutines

Digital

Name

srotm, drotm − Apply modified givens transformation

FORMAT

{S,D}ROTM (n, x, incx, y, incy, param)

Arguments

ninteger∗4
On entry, the number of elements in the vectors x and y.
On exit, n is unchanged.

xreal∗4 | real∗8
On entry, a one-dimensional array X of length at least (1+(n-1)∗|incx|), containing the elements of the vector x.
On exit, if n<=0 or if PARAM(1) = (-2.0), x is unchanged. Otherwise, x is overwritten; X contains the rotated vector x.

incxinteger∗4
On entry, the increment for the array X.
If incx > 0, vector x is stored forward in the array, so that x(i) is stored in location X(1+(i-1)∗incx).
If incx < 0, vector x is stored backward in the array, so that x(i) is stored in location X(1+(n-i)∗|incx|).
On exit, incx is unchanged.

yreal∗4 | real∗8
On entry, a one-dimensional array Y of length at least (1+(n-1)∗|incy|). Y contains the n elements of the vector y.
On exit, if n<=0 or if PARAM(1) = (-2.0), y is unchanged. Otherwise, y is overwritten; Y contains the rotated vector y.

incyinteger∗4
On entry, the increment for the array Y.
If incy > 0, vector y is stored forward in the array, so that y(i) is stored in location Y(1+(i-1)∗incy).
If incy < 0, vector y is stored backward in the array, so that y(i) is stored in location Y(1+(n-i)∗|incy|).
On exit, incy is unchanged.

paramreal∗4 | real∗8
On entry, an array defining the type of transform matrix H used:

PARAM(1) specifies the flag characteristic: -1.0, 0.0, 1.0, -2.0

PARAM(2) specifies H(11) value

PARAM(3) specifies H(21) value

PARAM(4) specifies H(12) value

PARAM(5) specifies H(22) value
On exit, param is unchanged.

Description

SROTM and DROTM apply a modified Givens transform to each element in the pair of real vectors, x and y, using the transformation matrix H as follows:

            |-    -|         |-    -|
            | x(i) |         | x(i) |
            |      |   = H ∗ |      |
            | y(i) |         | y(i) |
            |_    _|         |_    _|

Depending on the value of PARAM(1), the transformation matrix is defined as follows:

•PARAM(1)= -1.0
H(11) H(12)
H(21) H(22)

•PARAM(1)= 0.0
1.0 H(12)
H(21) 1.0

•PARAM(1)= 1.0
H(11) 1.0
-1.0 H(22)

•PARAM(1)= -2.0
1.0 0.0
0.0 1.0

The array PARAM is generated by a call to the routine _ROTMG.

Results are unpredictable if either incx or incy are zero.

Example

      INTEGER∗4 INCA, N
      REAL A(10,10), D(10), SPARAM(5)
C
      INCA = 10
C
C INITIALIZE D TO 1.0
C
      DO I = 1, 10
         D(I) = 1.0
      END DO
C
C FOR EACH ROW OF THE MATRIX, ELIMINATE TO UPPER TRIANGULAR FORM
C
      DO I = 2, 10
C
C ELIMINATE A(I,J) USING ELEMENT A(J,J)
C
         JEND = I-1
         DO J = 1, JEND
            N = 10-J
            CALL SROTMG(D(J),D(I),A(J,J),A(I,J),SPARAM)
            CALL SROTM(N,A(J,J+1),INCA,A(I,J+1),INCA,SPARAM)
         ENDDO
C
      END DO
C
C APPLY ACCUMULATED SCALE FACTORS TO THE ROWS OF A
C
      DO I = 1, 10
         CALL SSCAL(11-I, SQRT(D(I)), A(I,I), INCA)
      END DO