#*****************************************************************************80
#
## zero_test() tests zero().
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    28 May 2021
#
#  Author:
#
#    John Burkardt
#
cat ( date ( ), "\n" )
cat ( "\n" )
cat ( "zero_test():\n" )
cat ( " ", version$version.string, "\n" )
cat ( "  zero() seeks the root of a function using Brent's method.\n" )

source ( "/home/burkardt/public_html/r_src/zero/zero.R" )  

a <- 1.0
b <- 2.0
t <- 1.0E-07
f <- function ( x ) { sin(x) - x/2.0 }
cat ( "\n" )
cat ( "  f(x) = sin(x) - x/2\n" )
cat ( "  Interval = [", a, ",", b, "]\n" )
cat ( "  f(a) =", f(a), ", f(b) = ", f(b), "\n" )
output <- zero ( a, b, t, f )
x = output[1]
calls = output[2]
cat ( "  zero() returns x = ", x, "\n" );
cat ( "  f(",x,") = ", f(x), "\n" )
cat ( "  The function was evaluated ", calls, " times.\n" )

a <- 0.0
b <- 1.0
t <- 1.0E-07
f <- function ( x ) { 2.0 * x - exp ( - x ) }
cat ( "\n" )
cat ( "  f(x) = 2 x - exp ( -x )\n" )
cat ( "  Interval = [", a, ",", b, "]\n" )
cat ( "  f(a) =", f(a), ", f(b) = ", f(b), "\n" )
output <- zero ( a, b, t, f )
x = output[1]
calls = output[2]
cat ( "  zero() returns x = ", x, "\n" );
cat ( "  f(",x,") = ", f(x), "\n" )
cat ( "  The function was evaluated ", calls, " times.\n" )

a <- -1.0
b <- 0.5
t <- 1.0E-07
f <- function ( x ) {  x * exp ( - x ) }
cat ( "\n" )
cat ( "  f(x) = x * exp ( -x )\n" )
cat ( "  Interval = [", a, ",", b, "]\n" )
cat ( "  f(a) =", f(a), ", f(b) = ", f(b), "\n" )
output <- zero ( a, b, t, f )
x = output[1]
calls = output[2]
cat ( "  zero() returns x = ", x, "\n" );
cat ( "  f(",x,") = ", f(x), "\n" )
cat ( "  The function was evaluated ", calls, " times.\n" )

a <- 0.0001
b <- 20.0
t <- 1.0E-07
f <- function ( x ) {  exp ( x ) - 1 / ( 100 * x * x ) }
cat ( "\n" )
cat ( "  f(x) = exp ( x ) - 1 / ( 100 * x * x )\n" )
cat ( "  Interval = [", a, ",", b, "]\n" )
cat ( "  f(a) =", f(a), ", f(b) = ", f(b), "\n" )
output <- zero ( a, b, t, f )
x = output[1]
calls = output[2]
cat ( "  zero() returns x = ", x, "\n" );
cat ( "  f(",x,") = ", f(x), "\n" )
cat ( "  The function was evaluated ", calls, " times.\n" )

a <- -5.0
b <- +2.0
t <- 1.0E-07
f <- function ( x ) { (x+3)*(x-1)*(x-1) }
cat ( "\n" )
cat ( "  f(x) = (x+3)*(x-1)*(x-1)\n" )
cat ( "  Interval = [", a, ",", b, "]\n" )
cat ( "  f(a) =", f(a), ", f(b) = ", f(b), "\n" )
output <- zero ( a, b, t, f )
x = output[1]
calls = output[2]
cat ( "  zero() returns x = ", x, "\n" );
cat ( "  f(",x,") = ", f(x), "\n" )
cat ( "  The function was evaluated ", calls, " times.\n" )
#
#  Terminate.
#
cat ( "\n" )
cat ( "zero_test():\n" )
cat ( "  Normal end of execution.\n" )
cat ( date ( ), "\n" )

quit ( )