## library(appell)
## The following code compares results with those published in
## Colavecchia et al. (2001), tables 2-5.
## It also illustrates the very minor differences between results
## obtained with the hyp2f1 algorithm by R. Forrey and or that by
## N. Michel and M. Stoitsov, with the exception of no convergence
## problems with the latter. Therefore it is used as default algorithm.
## --------------------
## read the original table 2
table2orig <- read.table(file=
system.file(file.path("extdata", "table2.dat"),
package="appell"),
col.names=c("x", "y", "absf1", "exact", "relError"))
table2orig
## compute the values here
table2orig <- cbind(table2orig,
absf1.forrey=0,
absf1.michel.stoitsov=0)
for(case in seq_len(nrow(table2orig)))
{
table2orig[case, "absf1.forrey"] <-
abs(appellf1(a=1,
b1=2+1i,
b2=1.5-0.5i,
c=1,
x=table2orig[case, "x"],
y=table2orig[case, "y"],
debug=TRUE, # test debugging info as well
userflag=1L,
hyp2f1="forrey")$val)
table2orig[case, "absf1.michel.stoitsov"] <-
abs(appellf1(a=1,
b1=2+1i,
b2=1.5-0.5i,
c=1,
x=table2orig[case, "x"],
y=table2orig[case, "y"],
userflag=1L,
hyp2f1="michel.stoitsov")$val)
}
table2orig
## look at the (small) differences:
table2orig$absf1 - table2orig$absf1.forrey
table2orig$absf1 - table2orig$absf1.michel.stoitsov
## here no difference between the hyp2f1 choices:
identical(table2orig$absf1.forrey,
table2orig$absf1.michel.stoitsov)
## --------------------
## read the original table 3
table3orig <- read.table(file=
system.file(file.path("extdata", "table3.dat"),
package="appell"),
col.names=
c("x", "y", "f1ser", "f1int", "f1exact", "relErrorser",
"relErrorint"))
## compute the values here
table3orig <- cbind(table3orig,
f1ser.forrey=0,
f1int.forrey=0,
f1ser.michel.stoitsov=0,
f1int.michel.stoitsov=0)
for(case in seq_len(nrow(table3orig)))
{
## first everything with Forrey's algorithm for hyp2f1
f1ser.forrey <- try(appellf1(a=1,
b1=3+1i,
b2=2-0.5i,
c=5+0.5i,
x=table3orig[case, "x"],
y=table3orig[case, "y"],
userflag=2L,
debug=TRUE,
hyp2f1="forrey"))
table3orig[case, "f1ser.forrey"] <-
if(inherits(f1ser.forrey, "try-error"))
NA
else
abs(f1ser.forrey$val)
table3orig[case, "f1int.forrey"] <- abs(appellf1(a=1,
b1=3+1i,
b2=2-0.5i,
c=5+0.5i,
x=table3orig[case, "x"],
y=table3orig[case, "y"],
userflag=1L,
debug=TRUE,
hyp2f1="forrey")$val)
## then everything with the algorithm by Michel and Stoitsov for hyp2f1
f1ser.michel.stoitsov <- try(appellf1(a=1,
b1=3+1i,
b2=2-0.5i,
c=5+0.5i,
x=table3orig[case, "x"],
y=table3orig[case, "y"],
userflag=2L,
debug=TRUE,
hyp2f1="michel.stoitsov"))
table3orig[case, "f1ser.michel.stoitsov"] <-
if(inherits(f1ser.michel.stoitsov, "try-error"))
NA
else
abs(f1ser.michel.stoitsov$val)
table3orig[case, "f1int.michel.stoitsov"] <- abs(appellf1(a=1,
b1=3+1i,
b2=2-0.5i,
c=5+0.5i,
x=table3orig[case, "x"],
y=table3orig[case, "y"],
userflag=1L,
debug=TRUE,
hyp2f1="michel.stoitsov")$val)
}
table3orig
## look at the (small) differences:
table3orig$f1ser - table3orig$f1ser.michel.stoitsov
table3orig$f1int - table3orig$f1int.michel.stoitsov
## so we have no missing values for Michel & Stoitsov
## besides that, only very small differences between the two methods:
table3orig$f1ser.michel.stoitsov - table3orig$f1ser.forrey
table3orig$f1int.michel.stoitsov - table3orig$f1int.forrey
## --------------------
## read the original table 4
table4orig <- read.table(file=
system.file(file.path("extdata", "table4.dat"),
package="appell"),
col.names=
c("x", "y", "f1", "hypergeo", "exact", "relErrorf1",
"relErrorhypergeo"))
## compute the values here
table4orig <- cbind(table4orig,
f1.forrey=0,
f1.michel.stoitsov=0,
flag=0)
for(case in seq_len(nrow(table4orig)))
{
## get Forrey result and flag
thisRes <- appellf1(a=-0.5,
b1=2,
b2=1,
c=3,
x=table4orig[case, "x"],
y=table4orig[case, "y"],
hyp2f1="forrey")
table4orig[case, "f1.forrey"] <- abs(thisRes$val)
table4orig[case, "flag"] <- thisRes$algoflag
## get Michel & Stoitsov result
table4orig[case, "f1.michel.stoitsov"] <-
abs(appellf1(a=-0.5,
b1=2,
b2=1,
c=3,
x=table4orig[case, "x"],
y=table4orig[case, "y"],
hyp2f1="michel.stoitsov")$val)
}
table4orig
## look at the (small) differences:
table4orig$f1 - table4orig$f1.forrey
## very small errors all over the place!
## and extremely small differences between Forrey and Michel & Stoitsov:
table4orig$f1.michel.stoitsov - table4orig$f1.forrey
## look at the flags
subset(table4orig,
select=c(x, y, flag))
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