Tcl Library Source Code

2014-09-21  Arjen Markus <[email protected]>
	* optimize.tcl: Solve a problem with the detection of the exceptions in solving linear programs. Version 1.0.1
	* optimize.test: Added tests to distnguish infeasible and unbounded linear programs
	* pkgIndex.tcl: Bumping version of math::optimize package to 1.0.1

2014-08-21  Arjen Markus <[email protected]>
	* calculus.tcl: Bumping version to 0.8
	* pkgIndex.tcl: Bumping version of math::calculus package to 0.8

2014-08-21  Arjen Markus <[email protected]>
	* calculus.man: Describe the qk15 procedure implementing Gauss-Kronrod 15 points quadrature rule
	* calculus.tcl: Implement the qk15 procedure for Gauss-Kronrod quadrature

        #
        # Now determine which one should leave
        # TODO: is a lack of a proper row indeed an
        #       indication of the infeasibility?
        #
        set nextrow [SimplexFindNextRow $tableau $nextcol]
        if { $nextrow == -1 } {
            return "unbounded"
        }

        #
        # Make the vector for sweeping through the tableau
        #
        set vector [SimplexMakeVector $tableau $nextcol $nextrow]

    set nvars     [expr {[llength $tableau]-2}]
    for {set i 0} {$i < $nvars } { incr i } {
        lappend result 0.0
    }

    set idx 0
    foreach col [lrange $firstcol 0 end-1] {
        set value [lindex $secondcol $idx]
        if { $value >= 0.0 } {
            set result [lreplace $result $col $col [lindex $secondcol $idx]]
            incr idx
        } else {
            # If a negative component, then the problem was not feasible
            return "infeasible"
        }
    }

    return $result
}

# SimplexFindNextColumn --
#    Find the next column - the one with the largest negative

        lappend newtableau $newcol
    }

    return $newtableau
}

# Now we can announce our presence
package provide math::optimize 1.0.1

if { ![info exists ::argv0] || [string compare $::argv0 [info script]] } {
    return
}

namespace import math::optimize::min_bound_1d
namespace import math::optimize::maximum

	     ! [within_range [lindex $result 1]  0.333300 0.333360] } {
	      set ok 0
	}
	set ok
    } \
    -result 1





test linprog-2.1 "Unbounded program 1" \
    -body {
	set result [solveLinearProgram {3.0 4.0} {{1.0 -2.0 1.0} {-2.0 1.0 1.0}} ]
    } \
    -result "unbounded"

test linprog-2.2 "Unbounded program 2" \
    -body {
	set result [::math::optimize::solveLinearProgram {2.0 1.0} {{3.0 0.0 6.0} {1.0  0.0 2.0}}]
    } \
    -result "unbounded"

test linprog-2.3 "Infeasible program" \
    -body {
	set result [::math::optimize::solveLinearProgram {2.0 1.0} {{3.0 1.0 6.0} {1.0 -1.0 2.0} {0.0 1.0 -3.0}}]
    } \
    -result "infeasible"

test linprog-2.4 "Degenerate program" \
    -body {
	# Solution: {1.0 3.0}
	set result [::math::optimize::solveLinearProgram {2.0 1.0} {{3.0 1.0 6.0} {1.0 -1.0 2.0} {0.0 1.0 3.0}}]
	set ok 1
	if { ! [within_range [lindex $result 0]  0.99999  1.00001] ||
	     ! [within_range [lindex $result 1]  2.99999  3.00001] } {
	      set ok 0
	}
	set ok

    } \
    -result 1

test linprog-3.1 "Simple 3D program" \
   -body {
	set result [solveLinearProgram \
	   {1.0 1.0 1.0} \
	   {{1.0  1.0  2.0  1.0}
	    {1.0  2.0  1.0  1.0}

if {![package vsatisfies [package provide Tcl] 8.3]} {return}
package ifneeded math::roman             1.0   [list source [file join $dir romannumerals.tcl]]

if {![package vsatisfies [package provide Tcl] 8.4]} {return}
# statistics depends on linearalgebra (for multi-variate linear regression).
package ifneeded math::statistics        0.9   [list source [file join $dir statistics.tcl]]
package ifneeded math::optimize          1.0.1 [list source [file join $dir optimize.tcl]]
package ifneeded math::calculus          0.8   [list source [file join $dir calculus.tcl]]
package ifneeded math::interpolate       1.1   [list source [file join $dir interpolate.tcl]]
package ifneeded math::linearalgebra     1.1.4 [list source [file join $dir linalg.tcl]]
package ifneeded math::bignum            3.1.1 [list source [file join $dir bignum.tcl]]
package ifneeded math::bigfloat          1.2.2 [list source [file join $dir bigfloat.tcl]]
package ifneeded math::machineparameters 0.1   [list source [file join $dir machineparameters.tcl]]