GramSchmidt: The Gram-Schmidt algorithm

In rgl: 3D Visualization Using OpenGL

The Gram-Schmidt algorithm

Description

Generate a 3x3 orthogonal matrix using the Gram-Schmidt algorithm.

Usage

GramSchmidt(v1, v2, v3, order = 1:3)

Arguments

v1, v2, v3	Three length 3 vectors (taken as row vectors).
order	The precedence order for the vectors; see Details.

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.

Value

A 3x3 matrix whose rows are the orthogonalization of the original row vectors.

Author(s)

Duncan Murdoch

Examples

# 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))

rgl documentation built on Oct. 28, 2024, 5:07 p.m.