Polynomial regression: Difference between revisions
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Thus we confirm once more that for already sorted sequences the considered quick sort implementation has quadratic dependence on sequence length (see [[Query Performance|'''Example''' section for Python language on ''Query Performance'' page]]). |
Thus we confirm once more that for already sorted sequences the considered quick sort implementation has quadratic dependence on sequence length (see [[Query Performance|'''Example''' section for Python language on ''Query Performance'' page]]). |
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=={{header|Tcl}}== |
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{{libheader|tcllib}}(which includes a package for performing linear algebra operations) |
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<!-- This implementation from Emiliano Gavilan; posted here with his explicit permission --> |
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<lang tcl>package require math::linearalgebra |
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proc build.matrix {xvec degree} { |
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set sums [llength $xvec] |
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for {set i 1} {$i <= 2*$degree} {incr i} { |
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set sum 0 |
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foreach x $xvec { |
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set sum [expr {$sum + pow($x,$i)}] |
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} |
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lappend sums $sum |
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} |
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set order [expr {$degree + 1}] |
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set A [math::linearalgebra::mkMatrix $order $order 0] |
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for {set i 0} {$i <= $degree} {incr i} { |
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set A [math::linearalgebra::setrow A $i [lrange $sums $i $i+$degree]] |
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} |
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return $A |
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} |
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proc build.vector {xvec yvec degree} { |
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set sums [list] |
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for {set i 0} {$i <= $degree} {incr i} { |
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set sum 0 |
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foreach x $xvec y $yvec { |
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set sum [expr {$sum + $y * pow($x,$i)}] |
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} |
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lappend sums $sum |
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} |
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set x [math::linearalgebra::mkVector [expr {$degree + 1}] 0] |
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for {set i 0} {$i <= $degree} {incr i} { |
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set x [math::linearalgebra::setelem x $i [lindex $sums $i]] |
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} |
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return $x |
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} |
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# Now, to solve the example from the top of this page |
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set x {0 1 2 3 4 5 6 7 8 9 10} |
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set y {1 6 17 34 57 86 121 162 209 262 321} |
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# build the system A.x=b |
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set degree 2 |
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set A [build.matrix $x $degree] |
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set b [build.vector $x $y $degree] |
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# solve it |
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set coeffs [math::linearalgebra::solveGauss $A $b] |
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# show results |
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puts $coeffs</lang> |
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This will print: |
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1.0000000000000207 1.9999999999999958 3.0 |
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which is a close approximation to the correct solution. |
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