~o|16
~?!i&32768
~o=295
~$>end_of_copyright
~/!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
~/Copyright (C) Heinz Spiess, CH-2558 Aegerten, 1994.  All rights reserved.
~/
~/The right to use this macro is granted to all EMME/2 users, provided the
~/following conditions are met:
~/   1) The macro cannot be sold for a fee (but it can be used and distributed
~/      without charge within consulting projects).
~/   2) The user is aware that this macro is not a part of the EMME/2 software
~/      licence and there is no explicit or implied warranty or support
~/      provided with this macro.
~/   3) The comments in this macros must not be removed and any additions or
~/      modification must be appropriately identified as such and give at least
~/      date, name and the reason of the modification.
~/!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
~:end_of_copyright
~/=========================================================================
~/BALMPROD 1.4  -  Heinz Spiess, EMME/2 Support Center, CH-2558 Aegerten
~/
~/Perform a 2-dimensional matrix balancing with multiple production types
~/using the matrix calculator module 3.21 only.
~/Up to 4 types of productions and corresponding friction matrices can be
~/specified.  Make sure that the sum of all productions OpX matches the sum
~/of the attractions Dq.
~/
~/Usage: balmprod <Dq> <cpq1> <Op1> <cpq2> <Op2> <cpq3> <Op3> <cpq4> <Op4>
~/
~/where:   <Dq>:  destination matrix containing attractions (mdxx)
~/       <cpq1>:  friction matrix for first type of productions (mfxx)
~/        <Op1>:  origin matrix containing first type of productions (moxx)
~/       <cpq2>:  friction matrix for second type of productions (mfxx)
~/        <Op2>:  origin matrix containing second type of productions (moxx)
~/       <cpq3>:  friction matrix for third type of productions (mfxx)
~/        <Op3>:  origin matrix containing third type of productions (moxx)
~/       <cpq4>:  friction matrix for fourth type of productions (mfxx)
~/        <Op4>:  origin matrix containing fourth type of productions (moxx)
~/
~y=%0%
~?y>2   / check if enough parameters are provided
~$>start_macro
~t9=~*Do you want to see more detailed instructions?
~t9=%t9.1%
~?!t9=y
~$>end_of_macro
~/
~/Results:
~/         mo91:  origin matrix to hold first set multipliers (moxx)
~/         mo92:  origin matrix to hold second set multipliers (moxx)
~/         mo93:  origin matrix to hold thrird set multipliers (moxx)
~/         mo94:  origin matrix to hold fourth set multipliers (moxx)
~/         md91:  destination matrix to hold destination multipliers (mdxx)
~/
~/Temporaries: ms99 is used to save the stopping criteria
~/             md99 is used to save the current attractions
~/
~/Notes:
~/- Omit the parameters <cpq3> <Op3> <cpq4> <Op4> for balancing only two
~/  types of productions, and <cpq4> <Op4> for three types.
~/- The sum of all productions must match the sum of the attractions.
~/- The balanced result matrices for type X are obtained by multiplying
~/  mo9X*<cpqX>*md91.
~/- By default, the number of iterations is limited to 15.  If required,
~/  change the corresponding test near the end of the macro
~/- It is possible to use matrix expression as parameters, e.g. ``2*mo15''
~/  or ``mo10+"produc"'', as long as these do not contain blanks.
~$>end_of_macro
~:start_macro
~/Matrices to balance:  %2% %4% %6% %8%
~/Productions:          %3% %5% %7% %9%
~/Attractions:          %1%
~/=========================================================================
~x=0
c='start macro: balmprod %1% %2% %3% %4% %5% %6% %7% %8% %9%'
~?e
~/log book entry too long!
3.21       /perform a 2-dimensional matrix balancing using matrix calculator
1          /initialize destination multipliers to 1
y
md91
y
betaq
destination multipliers beta q
~?q=1
y
1 

~?e
r
~:next_iteration
~x+1
~/iteration %x%:
1          /compute current productions of type 1
~/... balancing type 1 productions
y
mo91
y
p1-%x%
current productions of type 1
~?q=1
y
0 
md91*(%2%)
 
 
n
+
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
1          /now compute new origin multipliers of type 1
y
mo91
y
a1-%x%
origin multipliers alpha1-p
n
(%3%)/(mo91+(mo91.eq.0))
 
 
n
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
~?y<5
~$do_destinations
1          /compute current productions of type 2
~/... balancing type 2 productions
y
mo92
y
p2-%x%
current productions of type 2
~?q=1
y
0 
md91*(%4%)
 
 
n
+
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
1          /now compute new origin multipliers of type 2
y
mo92
y
a2-%x%
origin multipliers alpha2-p
n
(%5%)/(mo92+(mo92.eq.0))
 
 
n
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
~?y<7
~$do_destinations
1          /compute current productions of type 3
~/... balancing type 3 productions
y
mo93
y
p3-%x%
current productions of type 3
~?q=1
y
0 
md91*(%6%)
 
 
n
+
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
1          /now compute new origin multipliers of type 3
y
mo93
y
a3-%x%
origin multipliers alpha3-p
n
(%7%)/(mo93+(mo93.eq.0))
 
 
n
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
~?y<9
~$do_destinations
1          /compute current productions of type 4
~/... balancing type 4 productions
y
mo94
y
p4-%x%
current productions of type 4
~?q=1
y
0 
md91*(%8%)
 
 
n
+
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
1          /now compute new origin multipliers of type 4
y
mo94
y
a4-%x%
origin multipliers alpha4-p
n
(%9%)/(mo94+(mo94.eq.0))
 
 
n
~?q=2
2
~:do_destinations
1          /compute current attractions
~/... balancing attractions
y
md99
y
a%x%
current attractions
~?q=1
y
0 
(mo91*(%2%)
~?y>4
+mo92*(%4%)
~?y>6
+mo93*(%6%)
~?y>8
+mo94*(%8%)
)
 
 
n
+
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
1          /compute maximum violation
y
md98
y
diff
difference for balancing
~?q=1
y
0
(%1%)-md91*md99


n
~?q=2
2          /send report to print file
1          /compute maximum violation
y
ms99
y
mxdiff
maximum difference for balancing
~?q=1
y
0
abs((%1%)-md91*md99)*1000


n
.max.
~?q=2
2          /send report to print file
1          /now compute new destination multipliers
y
md91
y
b%x%
destination multipliers beta-p
n
(%1%)/(md99+(md99.eq.0))
 
 
n
~?q=2
2          /send report to print file (iter=%x% maxdiff=%ms99%)
~/... maximum constraint violation at iteration %x% is %ms99%/1000
~z=%ms99%
~t9=terminated normally
~?x>15     /maximum number of iterations is limited - change if required
~+|~z=0|~t9=was stopped
~?z>10
~$next_iteration
q
c='end macro: balmprod %1% %2% %3% %4% %5% %6% %7% %8% %9%'
~?e
~/log book entry too long!
~/
~/========================================================================
~/Macro 'balmprod %1% %2% %3% %4% %5% %6% %7% %8% %9%'
~/%t9% after %x% iterations with a maximum constraint
~/violation of %ms99%/1000 trips.  The resulting multipliers are 
~?y=3
~/stored in matrices md91 and mo91.
~?y=5
~/stored in matrices md91, mo91 and mo92.
~?y=7
~/stored in matrices md91, mo91, mo92 and mo93.
~?y=9
~/stored in matrices md91, mo91, mo92, mo93 and mo94.
~/Type 1 trip matrix is:    mo91*md91*%2%
~?y>4
~/Type 2 trip matrix is:    mo92*md91*%4%
~?y>6
~/Type 3 trip matrix is:    mo93*md91*%6%
~?y>8
~/Type 4 trip matrix is:    mo94*md91*%8%
~:end_of_macro
~/=========================================================================
~o=6