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# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA
# Copyrights (C)
# for this R-port:
# 1999 - 2008, Diethelm Wuertz, Rmetrics Foundation, GPL
# Diethelm Wuertz <wuertz@itp.phys.ethz.ch>
# www.rmetrics.org
# for the code accessed (or partly included) from other R-ports:
# see R's copyright and license files
# for the code accessed (or partly included) from contributed R-ports
# and other sources
# see Rmetrics's copyright file
################################################################################
# GENERATION: DESCRIPTION:
# matrix R Creates a matrix from the given set of values
# diag R Creates a diagonal matrix or extracts diagonals
# triang M Extracs the lower tridiagonal part from a matrix
# Triang M Extracs the upper tridiagonal part from a matrix
# pascal M Creates a Pascal matrix
# hilbert M Creates a Hilbert matrix
# colVec M Creates a column vector from a data vector
# rowVec M Creates a row vector from a data vector
# as.matrix R Attempts to turn its argument into a matrix
# is.matrix R Tests if its argument is a (strict) matrix
# isPositiveDefinite M Checks if the matrix X is positive definite
# makePositiveDefinite M Forces the matrix x to be positive definite
# dimnames R Retrieves or sets the dimnames of an object
# colnames|rownames R Retrieves or sets the row or column names
# colIds|rowIds M ... use alternatively
# colIds<-|rowIds<- M ... for assignments
# SUBSETS: DESCRIPTION:
# dim R Returns the dimension of a matrix object
# ncol|nrow R Counts columns|rows of a matrix object
# length R Counts elements of a matrix object
# "["|"[[" R Subsets a matrix object
# (Arith) R Elementwise Arithmetic: + - * /
# (Lops) R Elementwise logical Ops: > < >= <= == !=
# cbind|rbind R Augments a matrix object by columns|rows
# na.omit R Removes NA from a matrix object
# BASIC STATISTICS: DESCRIPTION:
# var R Returns the variance matrix
# cov R Returns the covariance matrix
# col|rowStats B calculates column|row statistics
# col|rowMeans R calculates column|row means
# col|rowAvgs B calculates column|row averages
# col|rowVars B calculates column|row variances
# col|rowStdevs B calculates column|row standard deviations
# col|rowSkewness B calculates column|row skewness
# col|rowKurtosis B calculates column|row kurtosis
# col|rowCumsums B calculates column|row cumulated sums
# LINEAR ALGEBRA: DESCRIPTION:
# t R Returns the transposed matrix
# det R Returns the determinant of a matrix
# inv M returns the inverse of a matrix, synonyme
# chol2inv R Returns the inverse of a matrix
# norm M returns the norm of a matrix
# rk M returns the rank of a matrix
# tr M returns the trace of a matrix
# %*% R Returns the product of two matrices
# %x% R Returns the Kronecker product
# kron S returns the Kronecker product
# vec M is the operator that stacks a matrix
# vech M is the operator that stacks the lower triangle
# MORE LINEAR ALGEBRA: DESCRIPTION:
# chol R Returns the Cholesky factor matrix
# eigen R Returns eigenvalues and eigenvectors
# svd R Returns the singular value decomposition
# kappa R Returns the condition number of a matrix
# qr R Returns the QR decomposition of a matrix
# solve R Solves a system of linear equations
# backsolve R ... use when the matrix is upper triangular
# forwardsolve R ... use when the matrix is lower triangular
# TIME SERIES DESCRIPTION:
# tslag R Lagged/leading vector/matrix of selected orders
# .tslag1 Internal Function used by tslag
# pdl R Regressor matrix for polynomial distributed lags
# NOTES: WHERE YOU FIND THE FUCTIONS?
# R Basic R Package
# B Rmetrics fBasics Package
# M This Rmetrics fMultivar Package
################################################################################
test.creation =
function()
{
# Create Pascal Matrix:
P = pascal(3)
P
# Create lower triangle matrix
L = triang(P)
L
# Extract diagonal part
diag(P)
# Return Value:
return()
}
# ------------------------------------------------------------------------------
test.mathOps =
function()
{
# Create Pascal Matrix:
P = pascal(3)
P
# Add/Subtract/Multiply/Divide:
X = P
# Multiply matrix with a constant
3 * X
# Multiply two matrices elementwise
X * P
# Multiplies rows/columns of a matrix by a vector
X %*% diag(P)
diag(P) %*% X
# Return Value:
return()
}
# ------------------------------------------------------------------------------
test.subsets =
function()
{
# Create Pascal Matrix:
P = pascal(3)
P
# Operate on Subsets of a Matrix:
n = 3
i = 2
j = 3
D = diag(1:3)
# Return the dimension of a matrix
dim(P)
# Get the last colum of a matrix
P[, ncol(P)]
# Delete a column of a matrix
P[, -i]
# Permute the columns of a matrix
P[c(3, 1, 2), ]
# Augments matrix horizontally
cbind(P, D)
# Return Value:
return()
}
# ------------------------------------------------------------------------------
test.apply =
function()
{
# Apply a function to all Elements of a Matrix:
# Create Pascal Matrix:
P = pascal(3)
P
# Return square root for each element
sqrt(P)
# Exponentiate the matrix elementwise
exp(P)
# Compute the median of each column
apply(P, 2, "median")
# Test on all elements of a matrix
all( P > 2 )
# test on any element in a matrix
any( P > 2 )
# Return Value:
return()
}
# ------------------------------------------------------------------------------
test.moreOperations =
function()
{
# More Matrix Operations:
# Create Pascal Matrix:
P = pascal(3)
P
# Create Diagonal Matrix:
D = diag(1:3)
# Return the product of two matrices
P %*% D
# Return the Kronecker Product
P %x% D
# Return the transposed matrix
t(P)
# Return the inverse of a matrix
inv(P)
# Return the norm of a matrix
norm(P)
# Return the determinante of a matrix
det(P)
# Return the rank of a matrix
rk(P)
# Return trace of a matrix
tr(P)
# Return the variance matrix
var(P)
# Return the covariance matrix
cov(P)
# Stack a matrix
vec(P)
# Stack the lower triangle
vech(P)
# Return Value:
return()
}
# ------------------------------------------------------------------------------
test.linearAlgebra =
function()
{
# More Linear Algebra:
# Create Pascal Matrix:
P = pascal(3)
P
# Example Matrix and Vector
X = P
b = c(1, 2, 3)
# Return the Cholesky factor matrix
chol(X)
# Return eigenvalues and eigenvectors
eigen(X)
# Return the singular value decomposition
svd(X)
# Return the condition number of a matrix
kappa(X)
# Return the QR decomposition of a matrix
qr(X)
# Solve a system of linear equations
# ... use backsolve when the matrix is upper triangular
# ... use forwardsolve when the matrix is lower triangular
solve(X, b)
backsolve(Triang(X), b)
solve(Triang(X), b)
forwardsolve(triang(X), b)
solve(triang(X), b)
# Return Value:
return()
}
################################################################################
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