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View of /pkg/tests/matr-exp.R

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Revision 532 - (download) (annotate)
Mon Feb 7 17:23:54 2005 UTC (14 years, 7 months ago) by maechler
File size: 974 byte(s)
use "true" matrix; also "show" inaccuracy
library(Matrix)

## Matrix Exponential

assert.EQ.mat <- function(M, m, tol = 1e-15)
    stopifnot(all.equal(as(M, "matrix"), m, tol = tol))


m1 <- Matrix(c(1,0,1,1), nc = 2)
e1 <- expm(m1)
assert.EQ.mat(e1, cbind(c(exp(1),0), exp(1)))

m2 <- Matrix(c(-49, -64, 24, 31), nc = 2)
e2 <- expm(m2)
## The true matrix exponential is 'te2':
e_1 <-  exp(-1)
e_17 <- exp(-17)
te2 <- rbind(c(3*e_17 - 2*e_1, -3/2*e_17 + 3/2*e_1),
             c(4*e_17 - 4*e_1, -2  *e_17 + 3  *e_1))
assert.EQ.mat(e2, te2, tol = 1e-13)
## See the (average relative) difference:
all.equal(as(e2,"matrix"), te2, tol = 0) # 1.48e-14 on "lynne"

## The ``surprising identity''      det(exp(A)) == exp( tr(A) )
## or                           log det(exp(A)) == tr(A) :
stopifnot(all.equal(determinant(e2)$modulus, sum(diag(m2))))

m3 <- Matrix(cbind(0,rbind(6*diag(3),0)), nc = 4)
e3 <- expm(m3)
assert.EQ.mat(e3,
	      rbind(c(1,6,18,36),
		    c(0,1, 6,18),
		    c(0,0, 1, 6),
		    c(0,0, 0, 1)))


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