h_is_positive_definite

<a href="https://lifecycle.r-lib.org/articles/stages.html#experimental"><img src="figures/lifecycle-experimental.svg?package=crmPack&version=2.0.0" alt="[Experimental]"></a>
This helper function checks whether a given numerical matrix <code>x</code> is a
positive-definite square matrix of a given size, without any missing
values. This function is used to test if a given matrix is a covariance
matrix, since every symmetric positive semi-definite matrix is a covariance
matrix.

Implements a wide range of dose escalation
designs. The focus is on model-based designs, ranging from classical and
modern continual reassessment methods (CRMs) based on dose-limiting toxicity
endpoints to dual-endpoint designs taking into account a biomarker/efficacy
outcome. Bayesian inference is performed via MCMC sampling in JAGS, and it is easy
to setup a new design with custom JAGS code. However, it is also possible to
implement 3+3 designs for comparison or models with non-Bayesian estimation.
The whole package is written in a modular form in the S4 class system, making it
very flexible for adaptation to new models, escalation or stopping rules.
Further details are presented in
Sabanes Bove et al. (2019) <doi:10.18637/jss.v089.i10>.

Daniel Sabanes Bove

crmPack

Object-Oriented Implementation of Dose Escalation Designs

Wai Yin Yeung

Burak Kuersad Guenhan

Giuseppe Palermo

Thomas Jaki

Jiawen Zhu

Ziwei Liao

Dimitris Kontos

Marlene Schulte-Goebel

Doug Kelkhoff

Oliver Boix

Robert Adams

Clara Beck

John Kirkpatrick

Wojciech Wójciak

Guanya Peng

Prerana Chandratre

F. Hoffmann-La Roche AG 

Merck Healthcare KGaA 

Bayer AG 

RPACT GmbH 

h_is_positive_definite function

<dl><dt>x</dt>
<dd>(<code>matrix</code>) a matrix to be checked.</dd>
<dt>size</dt>
<dd>(<code>integer</code>) a size of the square matrix <code>x</code> to be checked
against for.</dd>
<dt>tol</dt>
<dd>(<code>number</code>) a given tolerance number used to check whether
an eigenvalue is positive or not. An eigenvalue is considered
as positive if and only if it is greater than the <code>tol</code>.</dd></dl>

Arguments

<a href='https://lifecycle.r-lib.org/articles/stages.html#experimental'><img src='figures/lifecycle-experimental.svg' alt='[Experimental]' /></a>
This helper function checks whether a given numerical matrix <code>x</code> is a
positive-definite square matrix of a given size, without any missing
values. This function is used to test if a given matrix is a covariance
matrix, since every symmetric positive semi-definite matrix is a covariance
matrix.

Testing Matrix for Positive Definiteness — h_is_positive_definite

<dl>

<dt>x</dt>
<dd>(<code>matrix</code>) a matrix to be checked.</dd>


<dt>size</dt>
<dd>(<code>integer</code>) a size of the square matrix <code>x</code> to be checked
against for.</dd>


<dt>tol</dt>
<dd>(<code>number</code>) a given tolerance number used to check whether
an eigenvalue is positive or not. An eigenvalue is considered
as positive if and only if it is greater than the <code>tol</code>.</dd>

</dl>

Testing Matrix for Positive Definiteness

h_is_positive_definite: Testing Matrix for Positive Definiteness

Description

Usage

Value

Arguments

Details