inst/doc/volume.R

In stokes: The Exterior Calculus

## ----setup, include=FALSE-----------------------------------------------------
knitr::opts_chunk$set(echo = TRUE)
options(rmarkdown.html_vignette.check_title = FALSE)
library("stokes")
set.seed(0)

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volume

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(V <- volume(7))

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f <- as.function(V)
f(diag(7))

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A <- matrix(rnorm(49),7,7)
LHS <- f(A)
RHS <- det(A)
c(LHS=LHS,RHS=RHS,diff=LHS-RHS)

## -----------------------------------------------------------------------------
M1 <- qr.Q(qr(matrix(rnorm(49),7,7)))  # M1: a random orthogonal matrix
M2 <- M1[c(2,1,3,4,5,6,7),]            # M2: (odd) permutation of rows of M1
c(f(M1),f(M2))