Conjugate gradients (CG) method is an iterative algorithm for solving linear systems
 with positive definite coefficient matrices.

algebra

array

Small set of functions to fast computation of some matrices and operations
useful in statistics and econometrics. Currently, there are functions for efficient
computation of duplication, commutation and symmetrizer matrices with minimal storage
requirements. Some commonly used matrix decompositions (LU and LDL), basic matrix
operations (for instance, Hadamard, Kronecker products and the Sherman-Morrison formula)
and iterative solvers for linear systems are also available. In addition, the package
includes a number of common statistical procedures such as the sweep operator, weighted
mean and covariance matrix using an online algorithm, linear regression (using Cholesky,
QR, SVD, sweep operator and conjugate gradients methods), ridge regression (with optimal
selection of the ridge parameter considering several procedures), omnibus tests for
univariate normality, functions to compute the multivariate skewness, kurtosis, the
Mahalanobis distance (checking the positive defineteness), and the Wilson-Hilferty
transformation of gamma variables. Furthermore, the package provides interfaces
to C code callable by another C code from other R packages.

Felipe Osorio

fastmatrix

Fast Computation of some Matrices Useful in Statistics

Alonso Ogueda

cg function

<dl> <dt>a</dt>
<dd>a symmetric positive definite matrix containing the coefficients of
 the linear system.</dd> <dt>b</dt>
<dd>a vector of right-hand sides of the linear system.</dd> <dt>maxiter</dt>
<dd>the maximum number of iterations. Defaults to <code>200</code></dd> <dt>tol</dt>
<dd>tolerance level for stopping iterations.</dd></dl>

Arguments

The underlying <code>C</code> code does not check for symmetry nor positive definitiveness.

Warning

Solve linear systems using the conjugate gradients method — cg

<dl>

 <dt>a</dt>
<dd>a symmetric positive definite matrix containing the coefficients of
 the linear system.</dd>

 <dt>b</dt>
<dd>a vector of right-hand sides of the linear system.</dd>

 <dt>maxiter</dt>
<dd>the maximum number of iterations. Defaults to <code>200</code></dd>

 <dt>tol</dt>
<dd>tolerance level for stopping iterations.</dd>

</dl>

cg: Solve linear systems using the conjugate gradients method

Description

Usage

Value

Arguments

Warning

References

See Also

Examples