library("broadcast")
vc <- datasets::ability.cov$cov
X <- matrix(rnorm(100), 100, ncol(vc))
solve(vc)
## general picture blocks maze reading
## general 0.082259001 -0.0312406436 -7.750932e-03 -0.013309494 -2.061705e-02
## picture -0.031240644 0.2369906996 -2.484938e-02 0.017844845 8.603286e-04
## blocks -0.007750932 -0.0248493822 1.344272e-02 -0.012544830 -3.802671e-05
## maze -0.013309494 0.0178448450 -1.254483e-02 0.101625400 5.508423e-03
## reading -0.020617049 0.0008603286 -3.802671e-05 0.005508423 5.713620e-02
## vocab -0.002420800 0.0019394999 -1.157864e-03 -0.002857265 -2.406969e-02
## vocab
## general -0.002420800
## picture 0.001939500
## blocks -0.001157864
## maze -0.002857265
## reading -0.024069692
## vocab 0.020323179
cinv(vc) # faster than `solve()`, but only works on positive definite matrices
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.082259001 -0.0312406436 -7.750932e-03 -0.013309494 -2.061705e-02
## [2,] -0.031240644 0.2369906996 -2.484938e-02 0.017844845 8.603286e-04
## [3,] -0.007750932 -0.0248493822 1.344272e-02 -0.012544830 -3.802671e-05
## [4,] -0.013309494 0.0178448450 -1.254483e-02 0.101625400 5.508423e-03
## [5,] -0.020617049 0.0008603286 -3.802671e-05 0.005508423 5.713620e-02
## [6,] -0.002420800 0.0019394999 -1.157864e-03 -0.002857265 -2.406969e-02
## [,6]
## [1,] -0.002420800
## [2,] 0.001939500
## [3,] -0.001157864
## [4,] -0.002857265
## [5,] -0.024069692
## [6,] 0.020323179
all(round(solve(vc), 6) == round(cinv(vc), 6)) # they're the same
## [1] TRUE
sd_lc(X, vc)
## [1] 43.4073171 41.2740401 53.3164093 14.0747582 35.2902031 88.2767914
## [7] 24.8157933 12.0439739 7.1861024 28.6209981 40.2412223 41.0418633
## [13] 38.6558326 12.6533232 82.3326336 57.2451051 26.3387797 1.7128853
## [19] 2.3877058 41.7033251 18.5463942 41.1206122 78.3715210 6.5427717
## [25] 17.5723607 27.9348138 27.1992269 5.3123103 37.3107653 15.7389135
## [31] 6.5980134 57.3153458 0.7330632 4.7762495 62.9043613 20.7836610
## [37] 45.5579373 20.9814090 3.5460098 45.2510950 28.2299643 7.5942212
## [43] 13.3682944 1.1903421 13.8945040 14.3375901 19.0916791 30.6113497
## [49] 48.2565760 15.6093831 12.5782772 15.9891274 6.9415761 38.5376621
## [55] 8.9734555 16.5853854 74.5961937 21.8985844 41.4879770 50.5020260
## [61] 66.1121175 15.0897261 6.1982754 50.5433333 25.5922920 12.3721057
## [67] 32.5442976 6.5730409 16.2367350 27.3417614 30.8654273 20.8542828
## [73] 10.0893138 2.8604279 25.8244753 30.8409941 50.0642030 3.8457165
## [79] 33.8713509 4.7644235 23.4079907 7.6901473 17.2559830 21.0487438
## [85] 30.8708882 4.9593600 28.6224839 22.6253557 27.7853181 13.7072525
## [91] 0.3648497 16.6307393 10.5123965 15.5051164 0.1506426 3.8873052
## [97] 54.0974694 5.5698790 10.3838945 37.9336070linear_algebra_stats
Simple Linear Algebra Functions for Statistics
Description
‘broadcast’ provides some simple Linear Algebra Functions for Statistics:
cinv();
sd_lc().
Usage
cinv(x)
sd_lc(X, vc, bad_rp = NaN)
Arguments
x
|
a real symmetric positive-definite square matrix. |
X
|
a numeric (or logical) matrix of multipliers/constants |
vc
|
the variance-covariance matrix for the (correlated) random variables. |
bad_rp
|
if vc is not a Positive (semi-) Definite matrix, give here the value to replace bad standard deviations with. |
Details
cinv()
cinv() computes the Choleski inverse of a real symmetric positive-definite square matrix.
sd_lc()
Given the linear combination X %*% b, where:
-
Xis a matrix of multipliers/constants; -
bis a vector of (correlated) random variables; -
vcis the symmetric variance-covariance matrix forb;
sd_lc(X, vc) computes the standard deviations for the linear combination X %*% b, without making needless copies.
sd_lc(X, vc) will use much less memory than a base ‘R’ approach.
sd_lc(X, vc) may possibly, but not necessarily, be faster than a base ‘R’ approach (depending on the Linear Algebra Library used for base ‘R’).
Value
For cinv():
A matrix.
For sd_lc():
A vector of standard deviations.
References
John A. Rice (2007), Mathematical Statistics and Data Analysis (6th Edition)
See Also
chol, chol2inv