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Originally, I entitled this package Fast Matrix Algebra with ‘Eigen’, because I expected it to be faster than R base. But this is not the case. So I entitled it Complex Matrix Algebra with ‘Eigen’, because it supports some operations on complex matrices which are not supported by R base: determinant, Cholesky decomposition, and linear least-squares problems.
set.seed(666L)
M <- matrix(rnorm(300L*300L, mean = 1), 300L, 300L)
M[sample.int(300L*300L, 300L*270L)] <- 0 # 90% of zeros
Ms <- asSparseMatrix(M)
microbenchmark(
base = det(M),
EigenR = Eigen_det(M),
EigenR_sparse = Eigen_det(Ms), # :-(
times = 200L
)
## Unit: milliseconds
## expr min lq mean median uq max neval cld
## base 6.9588 7.90125 9.475266 8.90305 10.01820 24.8761 200 a
## EigenR 2.4274 3.20710 3.913163 3.68080 4.44480 7.0813 200 b
## EigenR_sparse 4.9384 5.73910 6.760806 6.36535 7.52195 12.4549 200 cDeterminants of complex matrices are supported:
set.seed(666L)
Mr <- matrix(rnorm(100L*100L, mean = 1), 100L, 100L)
Mi <- matrix(rnorm(100L*100L, mean = 1), 100L, 100L)
M <- Mr + 1i * Mi
library(complexplus)
microbenchmark(
EigenR = Eigen_det(M), # :-)
complexplus = Det(M),
times = 30L
)
## Unit: microseconds
## expr min lq mean median uq max neval cld
## EigenR 744.8 879.6 1152.00 1017.95 1281.3 2035.1 30 a
## complexplus 16028.3 17791.2 19376.53 19287.40 20139.6 27735.5 30 bset.seed(666L)
M <- matrix(rnorm(100L*100L), 100L, 100L)
microbenchmark(
base = solve(M),
EigenR = Eigen_inverse(M), # :-)
times = 500L
)
## Unit: microseconds
## expr min lq mean median uq max neval cld
## base 1470.2 1699.55 2779.189 2191.10 2829.25 24528.5 500 a
## EigenR 952.3 1060.65 1907.809 1360.75 1884.10 34256.2 500 bset.seed(666L)
M <- matrix(rnorm(100L*70L), 100L, 70L)
library(MASS)
library(pracma)
microbenchmark(
MASS = ginv(M),
pracma = pinv(M),
EigenR = Eigen_pinverse(M), # :-)
times = 500L
)
## Unit: microseconds
## expr min lq mean median uq max neval cld
## MASS 2982.4 3380.50 4535.176 3882.15 5018.55 34714.0 500 a
## pracma 2935.6 3372.45 4470.872 3875.75 4960.50 43498.4 500 a
## EigenR 663.2 928.75 1229.255 1014.30 1421.85 8672.9 500 bset.seed(666L)
M <- matrix(rpois(10000L, 25), 100L, 100L)
A <- crossprod(M)
microbenchmark(
base = chol(A),
EigenR = Eigen_chol(A),
times = 1000L
)
## Unit: microseconds
## expr min lq mean median uq max neval cld
## base 179.2 232.70 285.8752 243.35 281.55 7893.7 1000 a
## EigenR 132.2 185.25 267.9837 200.15 260.15 8256.3 1000 aCholesky decomposition of complex matrices is supported.
set.seed(666L)
M <- matrix(rgamma(202L*199L, 10), 202L, 199L)
M <- cbind(M, M[, 1L] + 3*M[, 2L])
A <- crossprod(M)
microbenchmark(
base = chol(A, pivot = TRUE),
EigenR = Eigen_UtDU(A), # :-)
times = 1000L
)
## Unit: microseconds
## expr min lq mean median uq max neval cld
## base 1449.0 1759.35 2258.477 1993.10 2475.95 13592.7 1000 a
## EigenR 695.9 1002.00 1344.194 1195.45 1554.65 10752.2 1000 bPivoted Cholesky decomposition of complex matrices is supported.
set.seed(666L)
M <- matrix(rpois(10000L, 25), 100L, 100L)
A <- cbind(M, M)
At <- t(A)
library(MASS)
microbenchmark(
MASS = Null(At),
EigenR_LU = Eigen_kernel(A, method = "LU"), # :-)
EigenR_COD = Eigen_kernel(A, method = "COD"),
times = 100L
)
## Unit: milliseconds
## expr min lq mean median uq max neval cld
## MASS 7.6587 9.73635 12.529576 10.4438 11.49775 154.0598 100 a
## EigenR_LU 1.6315 2.04355 2.782136 2.8114 3.25520 6.6788 100 b
## EigenR_COD 3.7744 5.05930 6.742621 6.4258 7.34365 20.8925 100 cset.seed(666L)
n <- 700L; p <- 200L
A <- matrix(rnorm(n * p), n, p)
b <- rnorm(n)
microbenchmark(
stats = lm.fit(A, b),
EigenR_svd = Eigen_lsSolve(A, b, method = "svd"), # :-(
EigenR_cod = Eigen_lsSolve(A, b, method = "cod"), # :-)
times = 100L
)
## Unit: milliseconds
## expr min lq mean median uq max neval cld
## stats 26.2811 28.80175 32.88743 32.01755 36.12695 48.3139 100 a
## EigenR_svd 46.7250 53.45475 62.50637 59.51725 71.55925 116.0388 100 b
## EigenR_cod 9.4010 10.84750 13.85632 12.80600 15.69025 45.6681 100 cComplex matrices A and b are supported.
set.seed(666L)
M <- matrix(rnorm(40L*40L, mean = 1), 40L, 40L)
microbenchmark(
expm = expm::expm(M),
EigenR = Eigen_exp(M), # :-)
times = 500L
)
## Unit: microseconds
## expr min lq mean median uq max neval cld
## expm 992.7 1315.20 1654.1064 1387.95 1646.0 11770.1 500 a
## EigenR 214.2 236.85 308.5246 261.65 305.9 2188.7 500 bExponential of complex matrices is supported:
set.seed(666L)
Mr <- matrix(rnorm(40L*40L, mean = 1), 40L, 40L)
Mi <- matrix(rnorm(40L*40L, mean = 1), 40L, 40L)
M <- Mr + 1i * Mi
library(complexplus)
microbenchmark(
complexplus = matexp(M),
EigenR = Eigen_exp(M), # :-)
times = 500L
)
## Unit: microseconds
## expr min lq mean median uq max neval cld
## complexplus 7037.9 8469.85 11674.841 10282.9 13375.75 196628.8 500 a
## EigenR 934.4 1137.00 1652.693 1630.9 1945.55 10435.8 500 bset.seed(666L)
M <- matrix(rnorm(200L*200L, mean = 1), 200L, 200L)
library(Matrix)
microbenchmark(
Matrix = Schur(M),
EigenR = Eigen_realSchur(M), # :-)
times = 50L
)
## Unit: milliseconds
## expr min lq mean median uq max neval cld
## Matrix 89.2812 91.9326 107.39999 101.5227 120.2015 153.9915 50 a
## EigenR 69.7336 74.0251 87.22316 78.9152 92.7015 139.6560 50 bUse Eigen_complexSchur for the complex Schur decomposition.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.