Constructs a modified Givens transformation.
BLAS Library (libblas.a)
The SROTMG or DROTMG subroutine constructs a modified Givens transformation. The input quantities D1, D2, X1, and X2 define a 2-vector in partitioned form:
--- --- --- --- --- ---
| a1 | | sqrt(D1) 0 | | X1 |
| | = | | | |
| a2 | | 0 sqrt(D2) | | X2 |
--- --- --- --- --- ---
The subroutines determine the modified Givens rotation matrix H that transforms X2 and, thus, a2 to 0. A representation of this matrix is stored in the array PARAM as follows:
Case 1: PARAM(1) = 1.0
PARAM(2) = H(1,1)
PARAM(5) = H(2,2)
Case 2: PARAM(1) = 0.0
PARAM(3) = H(2,1)
PARAM(4) = H(1,2)
Case 3: PARAM(1) = -1.0
H(1,1) = PARAM(2)
H(2,1) = PARAM(3)
H(1,2) = PARAM(4)
H(2,2) = PARAM(5)
Case 4: PARAM(1) = -2.0
H = I (Identity matrix)
Note: Locations in PARAM not listed are left unchanged.
Item | Description |
---|---|
D1 | Nonnegative scalar; modified on exit to reflect the results of the transformation. |
D2 | Scalar; can be negative on entry; modified on exit to reflect the results of the transformation. |
X1 | Scalar; modified on exit to reflect the results of the transformation. |
X2 | Scalar; unchanged on exit. |
PARAM | Vector of dimension (5); values on entry are unused; modified on exit as described above. |