Tcl Library Source Code

2019-04-23  Arjen Markus <[email protected]>
	* quasirandom.tcl: New package - generate quasi-random numbers (for instance for estimating multidimensional integrals)
	* quasirandom.test: Tests for the new package
	* quasirandom.man: Documentation for the new package
	* pkgIndex.tcl: Add the new package

2019-04-18  Arjen Markus <[email protected]>

2019-05-07  Arjen Markus <[email protected]>
	* quasirandom.test: Add tests to deal with procedures in a different namespace
	* quasirandom.tcl: Deal with procedures in a different namespace

2019-04-24  Arjen Markus <[email protected]>
	* quasirandom.test: Add support code
	* numtheory.tcl: Add estimation of the number of primes between two limits
	* numtheory.test: Add tests regarding the estimated number of primes

2019-04-23  Arjen Markus <[email protected]>
	* quasirandom.tcl: New package - generate quasi-random numbers (for instance for estimating multidimensional integrals)
	* quasirandom.test: Tests for the new package
	* quasirandom.man: Documentation for the new package
	* pkgIndex.tcl: Add the new package

2019-04-18  Arjen Markus <[email protected]>

[list_end]

[call [cmd math::numtheory::numberPrimesGauss] [arg N]]
Estimate the number of primes according the formula by Gauss.

[list_begin arguments]
[arg_def integer N in]
Number in question
[list_end]

[call [cmd math::numtheory::numberPrimesLegendre] [arg N]]
Estimate the number of primes according the formula by Legendre.

[list_begin arguments]
[arg_def integer N in]
Number in question
[list_end]

[call [cmd math::numtheory::numberPrimesLegendreModified] [arg N]]
Estimate the number of primes according the modified formula by Legendre.

[list_begin arguments]
[arg_def integer N in]
Number in question








[list_end]

[list_end]

[vset CATEGORY {math :: numtheory}]
[include ../common-text/feedback.inc]
[manpage_end]

[list_end]

[call [cmd math::numtheory::numberPrimesGauss] [arg N]]
Estimate the number of primes according the formula by Gauss.

[list_begin arguments]
[arg_def integer N in]
Number in question, should be larger than 0
[list_end]

[call [cmd math::numtheory::numberPrimesLegendre] [arg N]]
Estimate the number of primes according the formula by Legendre.

[list_begin arguments]
[arg_def integer N in]
Number in question, should be larger than 0
[list_end]

[call [cmd math::numtheory::numberPrimesLegendreModified] [arg N]]
Estimate the number of primes according the modified formula by Legendre.

[list_begin arguments]
[arg_def integer N in]
Number in question, should be larger than 0
[list_end]

[call [cmd math::numtheory::differenceNumberPrimesLegendreModified] [arg lower] [arg upper]]
Estimate the number of primes between tow limits according the modified formula by Legendre.

[list_begin arguments]
[arg_def integer lower in] Lower limit for the primes, should be larger than 0
[arg_def integer upper in] Upper limit for the primes, should be larger than 0
[list_end]

[list_end]

[vset CATEGORY {math :: numtheory}]
[include ../common-text/feedback.inc]
[manpage_end]

## 
## This is the file `numtheory.test',
## generated with the SAK utility
## (sak docstrip/regen).
## 
## The original source files were:
## 
## numtheory.dtx  (with options: `test test_common')
## 
## In other words:
## **************************************
## * This Source is not the True Source *
## **************************************
## the true source is the file from which this one was generated.
##
source [file join\
................................................................................
testsNeedTcl     8.5
testsNeedTcltest 2.1

testing {
    useLocal numtheory.tcl math::numtheory
}







test prime_trialdivision-1 "Trial division of 1" -body {
   ::math::numtheory::prime_trialdivision 1
} -returnCodes 2 -result 0
test prime_trialdivision-2 "Trial division of 2" -body {
   ::math::numtheory::prime_trialdivision 2
} -returnCodes 2 -result 1
test prime_trialdivision-3 "Trial division of 6" -body {
................................................................................
   ::math::numtheory::isprime 118670087467 -randommr 500
} -result on -cleanup {
   namespace eval ::math::numtheory {
      rename Miller--Rabin ""
      rename _orig_Miller--Rabin Miller--Rabin
   }
}





















testsuiteCleanup
## 
## 
## End of file `numtheory.test'.

##
## This is the file `numtheory.test',
## generated with the SAK utility
## (sak docstrip/regen).
##
## The original source files were:
##
## numtheory.dtx  (with options: `test test_common')
##
## In other words:
## **************************************
## * This Source is not the True Source *
## **************************************
## the true source is the file from which this one was generated.
##
source [file join\
................................................................................
testsNeedTcl     8.5
testsNeedTcltest 2.1

testing {
    useLocal numtheory.tcl math::numtheory
}

proc compareRounded {expected actual} {
    return [expr {int($expected-$actual) == 0} ]
}

::tcltest::customMatch rounded compareRounded

test prime_trialdivision-1 "Trial division of 1" -body {
   ::math::numtheory::prime_trialdivision 1
} -returnCodes 2 -result 0
test prime_trialdivision-2 "Trial division of 2" -body {
   ::math::numtheory::prime_trialdivision 2
} -returnCodes 2 -result 1
test prime_trialdivision-3 "Trial division of 6" -body {
................................................................................
   ::math::numtheory::isprime 118670087467 -randommr 500
} -result on -cleanup {
   namespace eval ::math::numtheory {
      rename Miller--Rabin ""
      rename _orig_Miller--Rabin Miller--Rabin
   }
}

test numberPrimes-1.0 "Number of primes below 100" -match rounded -body {
   set result [::math::numtheory::numberPrimesLegendre 100]
} -result 28

test numberPrimes-1.1 "Number of primes below 100 (modified)" -match rounded -body {
   set result [::math::numtheory::numberPrimesLegendreModified 100]
} -result 28

test numberPrimes-1.2 "Number of primes below 0 (modified)" -body {
   set result [::math::numtheory::numberPrimesLegendreModified 0]
} -result "The limit must be larger than 1" -returnCodes 1

test numberPrimes-1.3 "Number of primes between 100 and 200" -match rounded -body {
   set result [::math::numtheory::differenceNumberPrimesLegendreModified 100 200]
} -result 19

test numberPrimes-1.4 "Number of primes between 100 and 0 - error expected" -body {
   set result [::math::numtheory::differenceNumberPrimesLegendreModified 100 0]
} -result "The upper limit must be larger than 1" -returnCodes 1

testsuiteCleanup
##
##
## End of file `numtheory.test'.

## 
## This is the file `primes.tcl',
## generated with the SAK utility
## (sak docstrip/regen).
## 
## The original source files were:
## 
## numtheory.dtx  (with options: `pkg_primes pkg_common')
## 
## In other words:
## **************************************
## * This Source is not the True Source *
## **************************************
## the true source is the file from which this one was generated.
##
# Copyright (c) 2010 by Lars Hellstrom.  All rights reserved.
................................................................................
namespace eval ::math::numtheory {
    variable primes {2 3 5 7 11 13 17}
    variable nextPrimeCandidate 19
    variable nextPrimeIncrement  1 ;# Examine numbers 6n+1 and 6n+5

    namespace export firstNprimes primesLowerThan primeFactors uniquePrimeFactors factors \
                     totient moebius legendre jacobi gcd lcm \
                     numberPrimesGauss numberPrimesLegendre numberPrimesLegendreModified

}

# ComputeNextPrime --
#     Determine the next prime
#
# Arguments:
#     None
................................................................................
#
proc ::math::numtheory::numberPrimesLegendreModified {limit} {
    if { $limit <= 1 } {
        return -code error "The limit must be larger than 1"
    }
    expr {$limit / (log($limit) - 1.08366)}
}



























## 
## 
## End of file `primes.tcl'.

##
## This is the file `primes.tcl',
## generated with the SAK utility
## (sak docstrip/regen).
##
## The original source files were:
##
## numtheory.dtx  (with options: `pkg_primes pkg_common')
##
## In other words:
## **************************************
## * This Source is not the True Source *
## **************************************
## the true source is the file from which this one was generated.
##
# Copyright (c) 2010 by Lars Hellstrom.  All rights reserved.
................................................................................
namespace eval ::math::numtheory {
    variable primes {2 3 5 7 11 13 17}
    variable nextPrimeCandidate 19
    variable nextPrimeIncrement  1 ;# Examine numbers 6n+1 and 6n+5

    namespace export firstNprimes primesLowerThan primeFactors uniquePrimeFactors factors \
                     totient moebius legendre jacobi gcd lcm \
                     numberPrimesGauss numberPrimesLegendre numberPrimesLegendreModified \
                     differenceNumberPrimesLegendreModified
}

# ComputeNextPrime --
#     Determine the next prime
#
# Arguments:
#     None
................................................................................
#
proc ::math::numtheory::numberPrimesLegendreModified {limit} {
    if { $limit <= 1 } {
        return -code error "The limit must be larger than 1"
    }
    expr {$limit / (log($limit) - 1.08366)}
}

# differenceNumberPrimesLegendreModified --
#     Return the approximate difference number of primes
#     between a lower and higher limit as given values
#     for approximate number of primes based on the
#     modified formula by Legendre
#
# Arguments:
#     limit1     The lower limit for the interval, largest prime to be included in the l.limit
#     limit2     The upper limit for the interval, largest prime to be included in the u.mlimit
#
# Returns:
#     Approximate difference number of primes
#
proc ::math::numtheory::differenceNumberPrimesLegendreModified {limit1 limit2} {
    if { $limit1 <= 1 } {
        return -code error "The lower limit must be larger than 1"
    }
    if { $limit2 <= 1 } {
        return -code error "The upper limit must be larger than 1"
    }

     set aa [::math::numtheory::numberPrimesLegendreModified [expr ($limit1)]]
     set bb [::math::numtheory::numberPrimesLegendreModified [expr ($limit2)]]
     expr {abs($bb-$aa)}
}

##
##
## End of file `primes.tcl'.

        my variable coord_factors
        my variable evaluations
        my variable use_radius
        my variable effective_dim

        set evals $evaluations



        foreach {key value} $args {
            switch -- $key {
            "-evaluations" {
                 if { ![string is integer -strict $value] || $value <= 0 } {
                     return -code error "The value for the option $key should be a positive integer value"
                 }

................................................................................
    #     -error value        - estimate of the error
    #     -rawvalues list     - list of raw values obtained for the integral
    #
    method integral-detailed {func minmax args} {
        my variable evaluations

        set evals $evaluations



        foreach {key value} $args {
            switch -- $key {
            "-evaluations" {
                 if { ![string is integer -strict $value] || $value <= 0 } {
                     return -code error "The value for the option $key should be a positive integer value"
                 }

        my variable coord_factors
        my variable evaluations
        my variable use_radius
        my variable effective_dim

        set evals $evaluations

        set func [uplevel 1 [list namespace which -command $func]]

        foreach {key value} $args {
            switch -- $key {
            "-evaluations" {
                 if { ![string is integer -strict $value] || $value <= 0 } {
                     return -code error "The value for the option $key should be a positive integer value"
                 }

................................................................................
    #     -error value        - estimate of the error
    #     -rawvalues list     - list of raw values obtained for the integral
    #
    method integral-detailed {func minmax args} {
        my variable evaluations

        set evals $evaluations

        set func [uplevel 1 [list namespace which -command $func]]

        foreach {key value} $args {
            switch -- $key {
            "-evaluations" {
                 if { ![string is integer -strict $value] || $value <= 0 } {
                     return -code error "The value for the option $key should be a positive integer value"
                 }

    set result [simple integral-detailed fxyz4 {{0.0 1.0} {0.0 1.0} {0.0 1.0}}]

    set rawvalues [dict get $result -rawvalues]

} -result {0.0022115062627913935 0.009840104253511376 0.014937934937801888 0.007838969739655276} -cleanup {simple destroy}









































# TODO:
# - func in different namespace
# - implement detailed integration and test the details
# - implement minimization

#

    set result [simple integral-detailed fxyz4 {{0.0 1.0} {0.0 1.0} {0.0 1.0}}]

    set rawvalues [dict get $result -rawvalues]

} -result {0.0022115062627913935 0.009840104253511376 0.014937934937801888 0.007838969739655276} -cleanup {simple destroy}


#
# Test integration procedures in a different namespace
#
test "Quasirandom-6.1" "Integrate ::func::func" -match tolerant -body {
    namespace eval ::func {

        proc func {xy} {
            lassign $xy x y
            expr {$x**2+$y**2}
        }

        ::math::quasirandom::qrpoints create simple 2

        set ::result [simple integral func {{0.0 1.0} {0.0 1.0}}]
    }

    return $result

} -result {0.67353777} -cleanup {::func::simple destroy}


test "Quasirandom-6.2" "Integrate (details) ::func::func" -match tolerant -body {
    namespace eval ::func {

        proc func {xy} {
            lassign $xy x y
            expr {$x**2+$y**2}
        }

        ::math::quasirandom::qrpoints create simple 2

        set ::result [simple integral-detailed func {{0.0 1.0} {0.0 1.0}}]
    }

    return [dict get $result -estimate]

} -result {0.67353777} -cleanup {::func::simple destroy}


# TODO:
# - func in different namespace
# - implement detailed integration and test the details
# - implement minimization

#