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|
# -*- tcl -*-
# interpolate.test --
# Test cases for the ::math::interpolate package
#
# -------------------------------------------------------------------------
source [file join \
[file dirname [file dirname [file join [pwd] [info script]]]] \
devtools testutilities.tcl]
testsNeedTcl 8.5
testsNeedTcltest 2.1
support {
use struct/matrix.tcl struct::matrix
useLocal math.tcl math
}
testing {
useLocal interpolate.tcl math::interpolate
}
# -------------------------------------------------------------------------
#
# Compare a list of numbers
#
proc matchNumbers {expected actual} {
set match 1
foreach a $actual e $expected {
if {$e != 0.0} {
if {abs($a-$e) > 0.5e-4*abs($a+$e)} {
set match 0
break
}
} else {
if {abs($a-$e) > 1.0e-5} {
set match 0
break
}
}
}
return $match
}
customMatch numbers matchNumbers
# -------------------------------------------------------------------------
#
# Test cases: interpolation in tables
#
# Add a dummy row to the table - ticket b25b826973edcbb5b3a95f6c284214925a1d5e67
# This makes it possible to use the same table in both 1D and 2D interpolations
#
set t [::math::interpolate::defineTable table1 \
{ x v1 v2 v3 } \
{ - 1 2 3
0 0 10 1
1 1 9 4
2 2 8 9
5 5 5 25
7 7 3 49
10 10 0 100 }]
test "Interpolate-1.1" "Interpolate in a one-dimensional table" \
-match numbers -body {
set result {}
foreach x { -1.0 0.0 3.0 5.0 9.9 11.0 } {
set result [concat $result \
[::math::interpolate::interp-1d-table $t $x]]
}
set result
} -result {
-1 0 10 1
0 0 10 1
3 3 7 14.333333
5 5 5 25
9.9 9.9 0.1 98.3
11 10 0 100 }
# value = x+y
set t2 [::math::interpolate::defineTable table2 \
{ x y1 y2 y3 } \
{ - 0 3 10
1 1 4 11
2 2 5 12
5 5 8 15
7 7 10 17
10 10 13 20 }]
test "Interpolate-1.2" "Interpolate in a two-dimensional table" \
-match numbers -body {
set result {}
foreach y { -1.0 0.0 3.0 5.0 9.9 11.0 } {
foreach x { -1.0 0.0 3.0 5.0 9.9 11.0 } {
set result [concat $result \
$x $y [::math::interpolate::interp-table $t2 $x $y]]
}
}
set result
} -result {
-1.0 -1.0 1.0
0.0 -1.0 1.0
3.0 -1.0 3.0
5.0 -1.0 5.0
9.9 -1.0 9.9
11.0 -1.0 10.0
-1.0 0.0 1.0
0.0 0.0 1.0
3.0 0.0 3.0
5.0 0.0 5.0
9.9 0.0 9.9
11.0 0.0 10.0
-1.0 3.0 4.0
0.0 3.0 4.0
3.0 3.0 6.0
5.0 3.0 8.0
9.9 3.0 12.9
11.0 3.0 13.0
-1.0 5.0 6.0
0.0 5.0 6.0
3.0 5.0 8.0
5.0 5.0 10.0
9.9 5.0 14.9
11.0 5.0 15.0
-1.0 9.9 10.9
0.0 9.9 10.9
3.0 9.9 12.9
5.0 9.9 14.9
9.9 9.9 19.8
11.0 9.9 19.9
-1.0 11.0 11.0
0.0 11.0 11.0
3.0 11.0 13.0
5.0 11.0 15.0
9.9 11.0 19.9
11.0 11.0 20.0
}
test "Interpolate-1.3" "Interpolate with integers" \
-match numbers -body {
set equalResults {}
set table [::math::interpolate::defineTable table3 \
{A B C D E} \
{0 0.00000 0.00000 0.00000 0.0000
1 0.52000 0.52000 0.52000 0.5200
3 0.69831 0.63142 0.67758 0.68457
5 0.86111 0.71690 0.81118 0.80365
7 1.01367 0.78725 0.92891 0.89851}]
foreach A {2 4 6} A2 {2.0 4.0 6.0} {
set intResults [::math::interpolate::interp-1d-table $table $A]
set floatResults [::math::interpolate::interp-1d-table $table $A2]
set equal 1
foreach i $intResults f $floatResults {
if { $i != $f } {
set equal 0
break
}
}
lappend equalResults $equal
}
return $equalResults
} -result {1 1 1}
# linear interpolation: y = x + 1 and y = 2*x, x<5, or 20-2*x, x>5
test "Interpolate-2.1" "Linear interpolation - 1" \
-match numbers -body {
set result {}
set xyvalues { 0.0 1.0 10.0 11.0 }
foreach x { 0.0 4.0 7.0 10.0 101.0 } {
lappend result [::math::interpolate::interp-linear $xyvalues $x]
}
set result
} -result { 1.0 5.0 8.0 11.0 11.0 }
test "Interpolate-2.2" "Linear interpolation - 2" \
-match numbers -body {
set result {}
set xyvalues { 0.0 0.0 5.0 10.0 10.0 0.0 }
foreach x { 0.0 4.0 7.0 10.0 11.0 } {
lappend result [::math::interpolate::interp-linear $xyvalues $x]
}
set result
} -result { 0.0 8.0 6.0 0.0 0.0 }
# Lagrange interpolation: y = x + 1
test "Interpolate-3.1" "Lagrange interpolation - 1" \
-match numbers -body {
set result {}
set xyvalues { 0.0 1.0 10.0 11.0 }
foreach x { 0.0 4.0 7.0 10.0 101.0 } {
lappend result [::math::interpolate::interp-lagrange $xyvalues $x]
}
set result
} -result { 1.0 5.0 8.0 11.0 102.0 }
#Lagrange interpolation (2) - expected: y=10-2*(x-5)**2/5
test "Interpolate-3.2" "Lagrange interpolation - 2" \
-match numbers -body {
set result {}
set xyvalues { 0.0 0.0 5.0 10.0 10.0 0.0 }
foreach x { 0.0 4.0 7.0 10.0 11.0 } {
lappend result [::math::interpolate::interp-lagrange $xyvalues $x]
}
set result
} -result { 0.0 9.6 8.4 0.0 -4.4 }
# Spatial interpolation
test "Interpolate-4.1" "Spatial interpolation - 1" \
-match numbers -body {
set result {}
set xyzvalues { {-1.0 0.0 -2.0 }
{ 1.0 0.0 2.0 } }
foreach coord { {0.0 0.0} {0.0 1.0} {3.0 0.0} {100.0 0.0} } {
lappend result [::math::interpolate::interp-spatial $xyzvalues $coord]
}
set result
} -result { 0.0 0.0 1.2 0.039996 }
test "Interpolate-4.2" "Spatial interpolation - 2" \
-match numbers -body {
set result {}
set xyzvalues { {-1.0 0.0 { -2.0 1.0 } }
{ 1.0 0.0 { 2.0 -1.0 } } }
foreach coord { {0.0 0.0} {0.0 1.0} {3.0 0.0} {100.0 0.0} } {
set result [concat $result \
[::math::interpolate::interp-spatial $xyzvalues $coord]]
}
set result
} -result { 0.0 0.0
0.0 0.0
1.2 -0.6
0.039996 -0.019998 }
test "Interpolate-4.3" "Spatial interpolation - 3 - coincident points" \
-match numbers -body {
set result {}
set xyzvalues { {-1.0 0.0 { -2.0 1.0 } }
{ 1.0 0.0 { 2.0 -1.0 } } }
set coord {-1.0 0.0}
set result [::math::interpolate::interp-spatial $xyzvalues $coord]
set result
} -result { -2.0 1.0 }
#
# Test TODO: parameters for spatial interpolation
#
test interpolate-5.1 "neville algorithm" \
-body {
set problems {}
namespace import ::math::interpolate::neville
set xtable [list 0. 30. 45. 60. 90. 120. 135. 150. 180.]
set ytable [list 0. 0.5 [expr sqrt(0.5)] [expr sqrt(0.75)] 1. \
[expr sqrt(0.75)] [expr sqrt(0.5)] 0.5 0.]
for { set x -15 } { $x <= 195 } { incr x } {
foreach { y error } [neville $xtable $ytable $x] break
set diff [expr { abs( $y - sin( $x*3.1415926535897932/180. ) ) }]
if { $error > 3.e-4 || ( $diff > $error && $diff > 1.e-8 ) } {
append problems \n "interpolating for sine of " $x " degrees" \
\n "value was " $y " +/- " $error \
\n "actual error was " $diff
}
}
set problems
} \
-result {}
proc matchNumbers {expected actual} {
set match 1
foreach a $actual e $expected {
if {abs($a-$e) > 0.1e-6} {
set match 0
break
}
}
return $match
}
customMatch numbers matchNumbers
test "cubic-splines-1.0" "Interpolate linear function" \
-match numbers -body {
set xcoord {1 2 3 4 5}
set ycoord {1 2 3 4 5}
set coeffs [::math::interpolate::prepare-cubic-splines $xcoord $ycoord]
set yvalues {}
foreach x {1.5 2.5 3.5 4.5} {
lappend yvalues [::math::interpolate::interp-cubic-splines $coeffs $x]
}
set yvalues
} -result {1.5 2.5 3.5 4.5}
test "cubic-splines-1.1" "Interpolate quadratic function" \
-match numbers -body {
set xcoord {1 2 3 4 5}
set ycoord {1 4 9 16 25}
set coeffs [::math::interpolate::prepare-cubic-splines $xcoord $ycoord]
set yvalues {}
foreach x $xcoord {
lappend yvalues [::math::interpolate::interp-cubic-splines $coeffs $x]
}
set yvalues
} -result {1 4 9 16 25}
test "cubic-splines-1.2" "Interpolate arbitrary function" \
-match numbers -body {
set coeffs [::math::interpolate::prepare-cubic-splines \
{0.1 0.3 0.4 0.8 1.0} \
{1.0 2.1 2.2 4.11 4.12}]
set yvalues {}
foreach x {0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0} {
lappend yvalues [::math::interpolate::interp-cubic-splines $coeffs $x]
}
set yvalues
} -result {1.0 1.6804411764705884 2.1 2.2 2.5380974264705882
3.1041911764705885 3.695689338235294 4.11 4.2099448529411765 4.12}
test "cubic-splines-2.1" "Too few data" \
-match glob -body {
set xcoord {1 2}
set ycoord {1 4}
set coeffs [::math::interpolate::prepare-cubic-splines $xcoord $ycoord]
} -result "At least *" -returnCodes error
test "cubic-splines-2.2" "Unequal lengths" \
-match glob -body {
set xcoord {1 2 4 5}
set ycoord {1 4 5 5 6}
set coeffs [::math::interpolate::prepare-cubic-splines $xcoord $ycoord]
} -result "Equal number *" -returnCodes error
test "cubic-splines-2.3" "Not-ascending x-coordinates" \
-match glob -body {
set xcoord {1 2 1.5}
set ycoord {1 4 5}
set coeffs [::math::interpolate::prepare-cubic-splines $xcoord $ycoord]
} -result "* ascending" -returnCodes error
test "cubic-splines-2.4" "X too small" \
-match glob -body {
set xcoord {1 2 3}
set ycoord {1 4 5}
set coeffs [::math::interpolate::prepare-cubic-splines $xcoord $ycoord]
set yvalue [::math::interpolate::interp-cubic-splines $coeffs -1]
} -result "* too small" -returnCodes error
test "cubic-splines-2.5" "X too large" \
-match glob -body {
set xcoord {1 2 3}
set ycoord {1 4 5}
set coeffs [::math::interpolate::prepare-cubic-splines $xcoord $ycoord]
set yvalue [::math::interpolate::interp-cubic-splines $coeffs 6]
} -result "* too large" -returnCodes error
# -------------------------------------------------------------------------
testsuiteCleanup
# Local Variables:
# mode: tcl
# End:
|
