# conjugate-gradient

Conjugate gradient solver

``npm install conjugate-gradient``
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# conjugate-gradient

Solves sparse symmetric positive definite linear systems. These problems arise in many physical applications, like linear elasticity, heat transfer and other diffusion based transport phenomena.

This code implements the conjugate gradient method using a Jacobi preconditioner.

## Install

``````npm install conjugate-gradient
``````

## Example

``````var pcg = require("conjugate-gradient")
, CSRMatrix = require("csr-matrix")

//Create a matrix
var A = CSRMatrix.fromDense([[-2, 1, 0],
[ 1,-2, 1],
[ 0, 1,-2]])

//Create input vector
var B = new Float64Array([1, 0, 0])

//Solve equation:
//
//  A x = B
//
console.log(pcg(A, b))
``````

### `require("conjugate-gradient")(A, b[, x0, tolerance, max_iter])`

Solves the equation Ax = b by conjugate gradient

• `A` is a symmetric positive definite matrix represented as a CSRMatrix
• `b` is an array of length n
• `x0` is an optional initial guess for the solution to the equation. If specified, the result of the solution will also get stored in this array
• `tolerance` is a cutoff tolerance for the solution. (Default is 1e-5)
• `max_iter` is the maximum number of iterations to run the solver. (Default is min(n, 20))

Returns An array encoding the solution to the equation Ax = b

# Credits

(c) 2013 Mikola Lysenko. MIT License

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