The Gram-Schmidt algorithm
Generate a 3x3 orthogonal matrix using the Gram-Schmidt algorithm.
GramSchmidt(v1, v2, v3, order = 1:3)
v1, v2, v3 |
Three length 3 vectors (taken as row vectors). |
order |
The precedence order for the vectors; see Details. |
This function orthogonalizes the matrix rbind(v1, v2, v3)
using the Gram-Schmidt algorithm. It can handle rank 2 matrices
(returning a rank 3 matrix). If the original is rank 1, it is likely
to fail.
The order vector determines the precedence of the original
vectors. For example, if it is c(i, j, k), then row i
will be unchanged (other than normalization); row j will
normally be transformed within the span of rows i and j.
Row k will be transformed orthogonally to the span of
the others.
A 3x3 matrix whose rows are the orthogonalization of the original row vectors.
Duncan Murdoch
# Proceed through the rows in order print(A <- matrix(rnorm(9), 3, 3)) GramSchmidt(A[1, ], A[2, ], A[3, ]) # Keep the middle row unchanged print(A <- matrix(c(rnorm(2), 0, 1, 0, 0, rnorm(3)), 3, 3, byrow = TRUE)) GramSchmidt(A[1, ], A[2, ], A[3, ], order = c(2, 1, 3))
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