Calculates the Givens rotation matrix.
| p | The value which can rotate to any number. |
| q | The value which rotates to zero. |
| return value | Rotation matrix zeroing out q. |
An entry in the offdiagonal of a matrix M can be eliminted by a rotation G: G*M will have a prescribed zero offdiagonal element. The parameter p is the corresponding diagonal element in the same column, and q is the offdiagonal in question.
M = [1,2,3;4,5,6;7,8,9]
col = 2
row = 1
G = eye(numRows(M));
G[col,row;col,row] = givens(M[col;col], M[row;col]);
G*M
M = [1,2,3;4,5,6;7,8,9]
col = 1
row = 2
G = eye(numCols(M));
G[row,col;row,col] = givens(M[row;row]', M[row;col]');
M*G'