Running ‘aaa.R’
Running the tests in ‘tests/aaa.R’ failed.
Complete output:
  > require(elliptic)
  Loading required package: elliptic
  
  Attaching package: 'elliptic'
  
  The following objects are masked from 'package:stats':
  
      sd, sigma
  
  The following object is masked from 'package:base':
  
      is.primitive
  
  > require(MASS)
  Loading required package: MASS
  > 
  > safety.factor <- 100
  > "test" <- function(x,abs.error=1e-6){stopifnot(abs(x)<abs.error*safety.factor)}
  > 
  > 
  > 
  > # equations 16.20.1 to 16.20.3, Jacobi's imaginary transform:
  > u <-  seq(from=1,to=4+1i,len=10)
  Warning message:
  In seq.default(from = 1, to = 4 + (0+1i), len = 10) :
    imaginary parts discarded in coercion
  > m <- 0.1+0.1123312i
  > test(sn(1i*u,m=m) - 1i*sc(u,m=1-m))
  > test(cn(1i*u,m=m) -    nc(u,m=1-m))
  > test(dn(1i*u,m=m) -    dc(u,m=1-m))
  > 
  > 
  > # eqs 16.28.1-16.28.5, p576:
  > test(abs(e16.28.1(z=1:600,m=0.234+0.1i)),abs.error=2e-15)
  > test(abs(e16.28.2(z=1:600,m=0.234+0.1i)),abs.error=2e-15)
  > test(abs(e16.28.3(z=1:600,m=0.234+0.1i)),abs.error=2e-15)
  > test(abs(e16.28.4(z=1:600,m=0.234+0.1i)),abs.error=2e-15)
  > 
  > test(abs(e16.28.5(m=seq(from=-0.234+0.1i, to=0.44-1i,len=100))),abs.error=2e-15)
  Warning messages:
  1: In seq.default(from = -0.234 + (0+0.1i), to = 0.44 - (0+1i), len = 100) :
    imaginary parts discarded in coercion
  2: In seq.default(from = -0.234 + (0+0.1i), to = 0.44 - (0+1i), len = 100) :
    imaginary parts discarded in coercion
  > 
  > #Now, try and get 16.28.6, p576: theta1dash=theta2*theta3*theta4:
  > m <- 0.5
  > derivative <- function(small){(theta1(small,m=m)-theta1(0,m=m))/small}
  > right.hand.side <-  theta2(0,m=m)*theta3(0,m=m)*theta4(0,m=m)
  > test(derivative(1e-7)-right.hand.side)
  > #looks fine.
  > 
  > 
  > 
  > 
  > #now compare e16.37.1 (product form for Neville's theta.s) with
  > #eq 16.36.6:
  > test( e16.37.1(0.5,0.5) - theta.s(0.5,0.5))
  > 
  > 
  > 
  > #now compare   e16.37.2 with eq 16.36.6, part 2:
  > test(e16.37.2(0.75,0.5) - theta.c(0.75,0.5))
  > 
  > # An identity of the form pq= pn/qn:
  > test(theta.c(0.5,0.5)/theta.d(0.5,0.5)- cd(0.5,0.5),abs.error=1e-9)
  > 
  > 
  > 
  > #Now check Laurent series for equianharmonic case, table on p656:
  > page.656 <- ck(g=c(0,1),n=12)-as.vector(t(cbind(0,0,c(1/28,1/10192,1/5422144,3/(5*13^2*19*28^4)))))
  > test(abs(page.656),abs.error=1e-19)
  > 
  > 
  > 
  > # Example 2, p579:
  > test(dn(0.20,0.19)-0.996253, abs.error=1e-6)
  > 
  > # Example 3, p579:
  > test(dn(0.2,0.81)-0.98406, abs.error=1e-5)
  > 
  > # Example 4, p580:
  > test(cn(0.2,0.81)-0.980278, abs.error=1e-6)
  > 
  > # Example 5, p580:
  > test(dc(0.672,0.36)-1.174,abs.error=1e-4)
  > 
  > # Example 6, p580:
  > test(Theta(0.6,m=0.36)-0.97357,abs.error=1e-5)
  > 
  > # Example 7, p581:
  > test(cs(0.5360162,0.09)-1.6918083,abs.error=1e-7)
  > 
  > # Example 8, p581:
  > test(sn(0.61802,0.5)-0.56458,abs.error=1e-5)
  > 
  > #Example 9, p581:
  > test(sc(0.61802,m=0.5)-0.68402,abs.error=1e-5)
  > 
  > #Example 11, p581:
  > test(cs(0.99391,m=0.5)-0.75,abs.error=1e-5)
  > 
  > # Example 8, p666, LHS
  > test(P(z=0.07 + 0.1i, g=c(10,2)) - (-22.97450010 - 63.0532328i),abs.error=1e-7)
  > 
  > # Now check sigma() against some Maple arguments:
  > test(sigma(1+0.4i,g=c(2+0.3i,1-0.99i)) - (1.006555817+0.3865197102i),abs.error=1e-9)
  > test(sigma(10-8i,g=c(1-0.4i,2.1-0.7i))-(-1.033893831e18 + 6.898810975e17i),1e11)
  > test(sigma(4,g=c(2,3)) - (-80.74922381),abs.error=1e-7)
  > 
  > #Now verify that g2.fun() and g3.fun() are in fact unimodular:
  > o <- c(1,1i)
  >  test(abs(unimodularity(7,o,FUN=g2.fun, maxiter=100)-g2.fun(o)),abs.error=1e-9)
  >  test(abs(unimodularity(7,o,FUN=g3.fun, maxiter=100)-g3.fun(o)),abs.error=2e-9)
  > 
  > M <- congruence(c(4,9))
  > test(abs(g.fun(o) - g.fun(M %*% o,maxiter=840)),2e-13)
  > 
  > # Verify Jacobi's formula numerically:
  > test(theta1dash(z=0,q=0.1+0.2i) -  theta1.dash.zero.q(0.1+0.2i),abs.error=3e-16)
  > 
  > #Now verify theta1.dashdash etc:
  > 
  > #d/dz (theta1) == theta1dash:
  > m <- 0.3+0.31i
  > z <- seq(from=1,to=2+1i,len=7)
  Warning message:
  In seq.default(from = 1, to = 2 + (0+1i), len = 7) :
    imaginary parts discarded in coercion
  > delta <- 0.001
  > deriv.numer <- (theta1(z=z+delta,m=m) - theta1(z=z,m=m))/delta
  > deriv.exact <- theta1dash(z=z+delta/2,m=m)
  > test(deriv.numer-deriv.exact,abs.error=1e-7)
  > 
  > #d/dz (theta1dash) == theta1dashdash:
  > deriv.numer <- (theta1dash(z=z+delta,m=m) - theta1dash(z=z,m=m))/delta
  > deriv.exact <- theta1dashdash(z=z+delta/2,m=m)
  > test(deriv.numer-deriv.exact,abs.error=1e-7)
  > 
  > #d/dz (theta1dashdash) == theta1dashdashdash:
  > deriv.numer <- (theta1dashdash(z=z+delta,m=m) - theta1dashdash(z=z,m=m))/delta
  > deriv.exact <- theta1dashdashdash(z=z+delta/2,m=m)
  > test(deriv.numer-deriv.exact,abs.error=2e-7)
  > 
  > 
  > # Example 13, page 668, LHS:
  > test(sigma.laurent(z=0.4 + 1.3i,g=c(8,4),nmax=8)-(0.278080 + 1.272785i),abs.error=6e-8)
  > 
  > # Example 13, page 668, RHS:
  > test(sigma.laurent(z=0.8 + 0.4i,g=c(7,6),nmax=8)-(0.81465765 + 0.38819473i),abs.error=1e-8)
  > 
  > 
  > # Check  P() against Some Maple outputs (I just made up the arguments):
  > test(P(1+0.3i,g=c(1+1i,2-0.33i),give.all.3=TRUE)-(0.8231651984-0.3567903513i),abs.error=1e-10)
  > test(P(-4-4i,g=c(0.3123+10i,0.1-0.2222i),give.all.3=TRUE)-(-1.118985985-1.038221043i),abs.error=1e-9)
  > test(P(10+2i,g=c(1,4+0i),give.all.3=TRUE)-(2.021264367-0.9875939553i),abs.error=1e-10)
  > 
  > 
  > # check e18.10.9, p650:
  > test(e18.10.9(parameters(g=c(1,3+0.2i))), abs.error=2e-14)
  > test(e18.10.9(parameters(g=c(1,3+  0i))), abs.error=1e-14)
  > test(e18.10.9(parameters(g=c(1,0.1+0i))), abs.error=1e-14)
  > 
  > 
  > # check that P'2=4P^3-g2*P-g3:
  > g <- c(1.44+0.1i, -0.3+0.99i)
  > g2 <- g[1]
  > g3 <- g[2]
  > u <- parameters(g=g)
  > z <- seq(from= 10-14i, to=-10+20i, len=777)
  Warning messages:
  1: In seq.default(from = 10 - (0+14i), to = -10 + (0+20i), len = 777) :
    imaginary parts discarded in coercion
  2: In seq.default(from = 10 - (0+14i), to = -10 + (0+20i), len = 777) :
    imaginary parts discarded in coercion
  > p <- P(z,g)
  > pd <- Pdash(z,g)
  > test(4*p^3-g2*p-g3-pd^2, 2e-11)
  Error: abs(x) < abs.error * safety.factor are not all TRUE
  Execution halted