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# calculus.test --
# Test cases for the Calculus package
#
source calculus.tcl
#
# Simple test functions - exact result predictable!
#
proc const_func { x } {
return 1
}
proc linear_func { x } {
return $x
}
proc downward_linear { x } {
return [expr {100.0-$x}]
}
proc downward_linear { x } {
return [expr {100.0-$x}]
}
#
# Test the Integral proc
#
puts "[::Calculus::Integral 0 100 100 const_func] - expected: 100"
puts "[::Calculus::Integral 0 100 100 linear_func] - expected: 5000"
puts "[::Calculus::Integral 0 100 100 downward_linear] - expected: 5000"
puts "[::Calculus::Integral 0 100 100 downward_linear] - expected: 5000"
puts "[::Calculus::IntegralExpr 0 100 100 {100.0-$x}] - expected: 5000"
proc const_func2d { x y } {
return 1
}
proc linear_func2d { x y } {
return $x
}
puts "[::Calculus::Integral2D { 0 100 10 } { 0 50 1 } const_func2d] - \
expected 5000"
puts "[::Calculus::Integral2D { 0 100 1 } { 0 50 1 } const_func2d] - \
expected 5000"
puts "[::Calculus::Integral2D { 0 100 10 } { 0 50 1 } linear_func2d] - \
expected 250000"
# xvec should one long!
proc const_func { t xvec } { return 1.0 }
# xvec should be two long!
proc dampened_oscillator { t xvec } {
set x [lindex $xvec 0]
set x1 [lindex $xvec 1]
return [list $x1 [expr {-$x1-$x}]]
}
foreach method {EulerStep HeunStep} {
puts "Method: $method"
set xvec 0.0
set t 0.0
set tstep 1.0
for { set i 0 } { $i < 10 } { incr i } {
set result [::Calculus::$method $t $tstep $xvec const_func]
puts "Result ($t): $result"
set t [expr {$t+$tstep}]
set xvec $result
}
set xvec { 1.0 0.0 }
set t 0.0
set tstep 0.1
for { set i 0 } { $i < 20 } { incr i } {
set result [::Calculus::$method $t $tstep $xvec dampened_oscillator]
puts "Result ($t): $result"
set t [expr {$t+$tstep}]
set xvec $result
}
}
#
# Boundary value problems:
# use simple functions
#
proc coeffs { x } { return {1.0 0.0 0.0} }
proc forces { x } { return 0.0 }
puts [::Calculus::BoundaryValueSecondOrder coeffs forces {0.0 1.0} {100.0 0.0} 10]
puts [::Calculus::BoundaryValueSecondOrder coeffs forces {0.0 0.0} {100.0 1.0} 10]
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