# R/trapz.R In pracma: Practical Numerical Math Functions

#### Documented in cumtrapztrapztrapzfun

```##
##  t r a p z . R  Numerical integration by trapezoidal rule
##

trapz <- function(x, y) {
if (missing(y)) {
if (length(x) == 0) return(0)
y <- x
x <- seq(along=x)
}
if (length(x) == 0 && length(y) == 0) return(0)
if (!(is.numeric(x) || is.complex(x)) ||
!(is.numeric(y) || is.complex(y)) )
stop("Arguments 'x' and 'y' must be real or complex vectors.")
m <- length(x)
if (length(y) != m)
stop("Arguments 'x', 'y' must be vectors of the same length.")
if (m <= 1) return(0.0)

# z <- sum((x[2:m] - x[1:(m-1)]) * (y[1:(m-1)] + y[2:m]))
# return(0.5 * z)

xp <- c(x, x[m:1])
yp <- c(numeric(m), y[m:1])
n <- 2*m
p1 <- sum(xp[1:(n-1)]*yp[2:n]) + xp[n]*yp[1]
p2 <- sum(xp[2:n]*yp[1:(n-1)]) + xp[1]*yp[n]

return(0.5*(p1-p2))
}

cumtrapz <- function(x, y) {
if (missing(y)) {
if (length(x) == 0) return(0)
y <- x
x <- 1:length(x)
}
if (length(x) == 0) return(0)
if (!(is.numeric(x) || is.complex(x)) ||
!(is.numeric(y) || is.complex(y)))
stop("Arguments 'x' and 'y' must be real or complex.")

x <- as.matrix(c(x))
m <- length(x)
if (is.vector(y)) y <- as.matrix(y)
if (nrow(y) != m)
stop("Arguments 'x' and 'y' are not compatible: nrow(y) != length(x).")

n  <- ncol(y)
dt <- repmat(diff(x)/2, 1, n)
ct <- apply(dt * (y[1:(m-1), ] + y[2:m, ]), 2, cumsum)

return(rbind(zeros(1, n), ct))
}

trapzfun <- function(f, a, b, maxit = 25, tol = 1e-07, ...) {
stopifnot(is.numeric(a), length(a) == 1, is.finite(a),
is.numeric(b), length(b) == 1, is.finite(b))

fun <- match.fun(f)
f <- function(x) fun(x, ...)

if (a == b) return(list(area = 0.0, iter = 0, error = 0))

n <- 1
h <- b - a
T <- h * (f(a) + f(b)) / 2.0

for (i in 1:maxit) {
M <- 0
for (j in 0:(n-1)) {
M <- M + f(a + (j + 0.5) * h)
}
M <- h * M
T <- (T + M) / 2.0
h <- h / 2.0
n <- 2 * n
err <- abs(T - M)
if (err < tol) break
}

return(list(value = T, iter = i, rel.err = err))
}
```

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pracma documentation built on March 18, 2022, 5:12 p.m.