89 lines
2.7 KiB
R
89 lines
2.7 KiB
R
## for R_DEFAULT_PACKAGES=NULL :
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library(stats)
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library(Matrix)
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## Matrix Exponential
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source(system.file("test-tools.R", package = "Matrix"))
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## e ^ 0 = 1 - for matrices:
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assert.EQ.mat(expm(Matrix(0, 3,3)), diag(3), tol = 0)# exactly
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## e ^ diag(.) = diag(e ^ .):
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assert.EQ.mat(expm(as(diag(-1:4), "generalMatrix")), diag(exp(-1:4)))
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set.seed(1)
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rE <- replicate(100,
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{ x <- rlnorm(12)
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relErr(as(expm(as(diag(x), "generalMatrix")),
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"matrix"),
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diag(exp(x))) })
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stopifnot(mean(rE) < 1e-15,
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max(rE) < 1e-14)
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summary(rE)
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## Some small matrices
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m1 <- Matrix(c(1,0,1,1), ncol = 2)
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e1 <- expm(m1)
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assert.EQ.mat(e1, cbind(c(exp(1),0), exp(1)))
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(p1 <- pack(m1))
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stopifnot(exprs = {
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is(p1, "dtpMatrix")
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all.equal(pack(e1), expm(p1), tolerance = 2e-15)# failed in Matrix 1.6.1
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})
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m2 <- Matrix(c(-49, -64, 24, 31), ncol = 2)
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e2 <- expm(m2)
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## The true matrix exponential is 'te2':
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e_1 <- exp(-1)
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e_17 <- exp(-17)
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te2 <- rbind(c(3*e_17 - 2*e_1, -3/2*e_17 + 3/2*e_1),
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c(4*e_17 - 4*e_1, -2 *e_17 + 3 *e_1))
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assert.EQ.mat(e2, te2, tol = 1e-13)
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## See the (average relative) difference:
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all.equal(as(e2,"matrix"), te2, tolerance = 0) # 2.22e-14 {was 1.48e-14} on "lynne"
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(dsp <- pack(crossprod(matrix(-2:3, 2,3))))
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stopifnot(all(abs(expm(dsp) - expm(as.matrix(dsp))) <= 0.5)) # failed badly in Matrix 1.6.1
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## The ``surprising identity'' det(exp(A)) == exp( tr(A) )
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## or log det(exp(A)) == tr(A) :
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stopifnot(all.equal(c(determinant(e2)$modulus), sum(diag(m2))))
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## a very simple nilpotent one:
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(m3 <- Matrix(cbind(0,rbind(6*diag(3),0))))# sparse
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stopifnot(all(m3 %*% m3 %*% m3 %*% m3 == 0))# <-- m3 "^" 4 == 0
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e3 <- expm(m3)
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E3 <- expm(Matrix(m3, sparse=FALSE))
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s3 <- symmpart(m3) # dsCMatrix
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es3 <- expm(s3)
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e3. <- rbind(c(1,6,18,36),
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c(0,1, 6,18),
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c(0,0, 1, 6),
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c(0,0, 0, 1))
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stopifnot(is(e3, "triangularMatrix"),
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is(es3, "symmetricMatrix"),
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identical(e3, E3),
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identical(as.mat(e3), e3.),
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all.equal(as(es3,"generalMatrix"),
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expm(as(s3,"generalMatrix")))
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)
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## This used to be wrong {bug in octave-origin code}:
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M6 <- Matrix(c(0, -2, 0, 0, 0, 0,
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10, 0, 0, 0,10,-2,
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0, 0, 0, 0,-2, 0,
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0, 10,-2,-2,-2,10,
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0, 0, 0, 0, 0, 0,
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10, 0, 0, 0, 0, 0), 6, 6)
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exp.M6 <- expm(M6)
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as(exp.M6, "sparseMatrix")# prints a bit more nicely
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stopifnot(all.equal(t(exp.M6),
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expm(t(M6)), tolerance = 1e-12),
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all.equal(exp.M6[,3], c(0,0,1,0,-2,0), tolerance = 1e-12),
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all.equal(exp.M6[,5], c(0,0,0,0, 1,0), tolerance = 1e-12),
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all(exp.M6[3:4, c(1:2,5:6)] == 0)
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)
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cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons''
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