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calculate-givens-rotation

calculate-givens-rotation

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Compute the components of a Givens rotation matrix in order to zero an element

Introduction

This module implements Algorithm 5.1.3 of Golub and Van Loan's Matrix Computations, 4th Edition. The goal is to calculate the components of a rotation matrix that, when applied to vector [a,b]^T, will zero out the second component.

[  c  s  ] T     [ a ]     [ r ]
[        ]    *  [   ]  =  [   ]
[ -s  c  ]       [ b ]     [ 0 ]

Note that it also applies to the transposed case,

             [  c  s  ]
[ a  b ]  *  [        ]  =  [ r  0 ]
             [ -s  c  ]

Sample usage:

var givens = require('calculate-givens-rotation')
 
var cs = givens(1,2)    //  --> cs = [ -0.4472135954999579, 0.8944271909999159 ] 
 
// Alternate form: 
var output = []
givens( 1, 2, output )  //  --> output = [ -0.4472135954999579, 0.8944271909999159 ] 

Install

$ npm install calculate-givens-rotation

API

require('calculate-givens-rotation')( a, b )

Given two elements of a vector, compute the rotation matrix that zeros the second element.

  • a,b: the elements of the vector. b is the element to be zeroed.

Returns a two-element list [c,s] containing c and s as defined above.

require('calculate-givens-rotation')( a, b, output )

An alternate form that passes output values through array output

  • a,b: as specified previously
  • output: an array that receives the output values, output[0] = c and output[1] = s

Returns output

Credits

(c) 2015 Ricky Reusser. MIT License