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test.q
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test.q
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/ delete from`.simplex
\l simplex.q
round:{x*floor .5+y%x};
assertAnswer:{(~). round/:[x;(y;z)]};
assertFullAnswer:{assertAnswer[x;y;@[z;`X;count[y`X]#]]};
///////////////////////////////////////////////////////////////////////////////
.simplex.answer .simplex.solveStd[(2 1;1 2);4 3;1 1;0]
.simplex.answer .simplex.solveStd[(2 1;1 2);4 3;1 .5;0]
.simplex.answer .simplex.solveStd[(2 1;2 3);8 12;3 1;0]
.simplex.answer .simplex.solveStd[(1 0 3;3 1 3);6 9;4 1 -1;0]
.simplex.answer .simplex.solveStd[(2 1 1;1 2 1;0 0 1);4 7 5;2 3 2;0]
.simplex.answer .simplex.solveStd[(3 1;1 -1;0 1);6 2 3;2 1;0]
@[.simplex.answer .simplex.solveStd .;((-1 1;1 -2);1 2;2 1;0);::] /unbounded
.simplex.Optimize
.simplex.LessEq [5 3 6;15]
.simplex.LessEq [1 1 1; 6]
.simplex.Maximize[5 3 1; 0]
// Maximize 2x + 3y + 2z
// Such that x,y,z >= 0
// 2x + y + z <= 4
// x + 2y + z <= 7
// z <= 5
X:
.simplex.Optimize
.simplex.LessEq [0 0 1;5]
.simplex.LessEq [1 2 1;7]
.simplex.LessEq [2 1 1;4]
.simplex.Maximize[2 3 2;0]
;assertAnswer[1e-15;X;`obj`X!(11.;0 3 1.)]
///////////////////////////////////////////////////////////////////////////////
//@see https://www.math.ucla.edu/~tom/LP.pdf
X:
.simplex.Optimize
.simplex.LessEq [-1 1; 1]
.simplex.LessEq [ 4 2;12]
.simplex.LessEq [ 1 2; 4]
.simplex.Maximize[ 1 1; 0]
;assertAnswer[1e-15;X;`obj`X!(10;8 2)%3]
///////////////////////////////////////////////////////////////////////////////
//@see https://ocw.mit.edu/courses/sloan-school-of-management/15-053-optimization-methods-in-management-science-spring-2013/tutorials/MIT15_053S13_tut06.pdf
.simplex.Optimize
.simplex.Eq [ 1 1 0;10]
.simplex.GreaterEq[-1 -1 1; 2]
.simplex.LessEq [ 1 -2 -1; 3]
.simplex.Minimize [ 1 1 1; 0]
.simplex.Optimize
.simplex.GreaterEq[2 1;5]
.simplex.GreaterEq[1 2;3]
.simplex.Minimize [1 1;0]
///////////////////////////////////////////////////////////////////////////////
//@see https://jeremykun.com/2014/12/01/linear-programming-and-the-simplex-algorithm/
X:
.simplex.Optimize
.simplex.LessEq [1 -1;1]
.simplex.LessEq [1 2;4]
.simplex.Maximize[3 2;0]
;assertAnswer[1e-15;X;`obj`X!(8.;2 1.)]
///////////////////////////////////////////////////////////////////////////////
//@see http://12000.org/my_notes/simplex/index.htm
X:
.simplex.Optimize
.simplex.LessEq [1 2;9] /silver (oz.)
.simplex.LessEq [3 1;8] /gold (oz.)
.simplex.Maximize[4 5;0] /profit
;assertAnswer[1e-15;X;`obj`X!(24.6;1.4 3.8)]
X:
.simplex.Optimize
.simplex.GreaterEq[ -1.5 1; 0]
.simplex.GreaterEq[ 2 2; 4]
.simplex.LessEq [ 2 2;10]
.simplex.Maximize [1%30 15; 0]
;assertAnswer[1e-12;X;`obj`X!(1%3.;0 5.)]
.simplex.Optimize
.simplex.GreaterEq[1 4; 6]
.simplex.GreaterEq[4 2;12]
.simplex.Minimize [2 3; 0]
///////////////////////////////////////////////////////////////////////////////
//@see https://sourceforge.net/projects/phpsimplexsolve/files/
X:
.simplex.Optimize
.simplex.GreaterEq[3 2;3]
.simplex.GreaterEq[1 2;4]
.simplex.Minimize [2 5;0]
;assertAnswer[1e-11;X;`obj`X!(8.;4 0.)]
///////////////////////////////////////////////////////////////////////////////
//@see http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s2.pdf
X:
.simplex.Optimize
.simplex.LessEq [ 2 5;90]
.simplex.LessEq [ 1 1;27]
.simplex.LessEq [-1 1;11]
.simplex.Maximize[ 4 6; 0]
;assertAnswer[1e-15;X;`obj`X!(132.;15 12.)]
X:
.simplex.Optimize
.simplex.LessEq [ 2 5;27]
.simplex.LessEq [-1 1; 4]
.simplex.LessEq [ 3 -1;15]
.simplex.GreaterEq[ 2 3; 6]
.simplex.Minimize [ 5 7; 0]
;assertAnswer[1e-15;X;`obj`X!(14.;0 2.)]
.simplex.Optimize
.simplex.LessEq [4 1;16]
.simplex.LessEq [1 3;15]
.simplex.Minimize[3 2; 0]
;
.simplex.Optimize
.simplex.LessEq [4 1;16]
.simplex.LessEq [1 3;15]
.simplex.Maximize[3 2; 0]
.simplex.Optimize
.simplex.LessEq [1 5;20]
.simplex.LessEq [3 -2; 9]
.simplex.GreaterEq[2 3; 6]
.simplex.Minimize [4 3; 0]
;
.simplex.Optimize
.simplex.LessEq [1 5;20]
.simplex.LessEq [3 -2; 9]
.simplex.GreaterEq[2 3; 6]
.simplex.Maximize [4 3; 0]
X:
.simplex.Optimize
.simplex.LessEq [250 400;70000] /total investment
.simplex.LessEq [ 1 1; 250] /total demand
.simplex.Maximize[ 45 50; 0] /profit
;assertAnswer[1e-15;X;`obj`X!(11500.;200 50.)]
X:
.simplex.Optimize
.simplex.LessEq [ .3 .1; 30] /days for picking
.simplex.LessEq [ 1 2 ;240] /days for trimming
.simplex.LessEq [ 1 1 ;150] /land area
.simplex.Maximize[140 235 ; 0] /profit
;assertAnswer[1e-15;X;`obj`X!(29550.;60 90.)]
X:
.simplex.Optimize
.simplex.GreaterEq[ 2 3;24] /nutrition C
.simplex.GreaterEq[ 2 9;36] /nutrition B
.simplex.GreaterEq[ 2 1;12] /nutrition A
.simplex.Minimize [25 20; 0] /cost
;assertAnswer[1e-15;X;`obj`X!(195.;3 6.)]
X:
.simplex.Optimize
.simplex.Eq [ 1 1 ; 1] /proportion
.simplex.GreaterEq[80 92 ;90] /octane rating
.simplex.Minimize [ .83 .98; 0] /cost
;assertAnswer[1e-10;X;`obj`X!(.955;1 5%6.)]
///////////////////////////////////////////////////////////////////////////////
//@see http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s3.pdf
X:
.simplex.Optimize
.simplex.LessEq [0 0 2; 5]
.simplex.LessEq [1 2 -2;20]
.simplex.LessEq [2 1 0;10]
.simplex.Maximize[2 -1 2; 0]
;assertAnswer[1e-15;X;`obj`X!(15.;5 0 2.5)]
X:
.simplex.Optimize
.simplex.LessEq [1 2 3;40]
.simplex.LessEq [2 3 1;60]
.simplex.Eq [4 1 1;30]
.simplex.Maximize[3 2 1; 0]
;assertAnswer[1e-15;X;`obj`X!(45.;3 18 0.)]
X:
.simplex.Optimize
.simplex.LessEq [1%2 3 2 ; 2400] /packaging
.simplex.LessEq [ 2 2 3%3; 4600] /trimming
.simplex.LessEq [ 2 4 3%2;12000] /molding
.simplex.Maximize[ 11 16 15 ; 0] /profit
;assertAnswer[1e-15;X;`obj`X!(100200.;600 5100 800.)]
X:
.simplex.Optimize
.simplex.LessEq [ -9 1 1 ; 0] /TV ads priority
.simplex.GreaterEq[ 1 1 -1 ; 0] /radio ads balance
.simplex.LessEq [ 0 1 0 ; 10] /newspaper ads limit
.simplex.LessEq [2000 600 300 ;18200] /total budget
.simplex.Maximize [ 100 40 18*1e3; 0] /viewership
;assertAnswer[1e-15;X;`obj`X!(1052*1e3;4 10 14.)]
@[.simplex.Optimize;;::]
.simplex.LessEq [-1 2;4]
.simplex.LessEq [ 1 -3;1]
.simplex.Maximize[ 1 2;0]
@[.simplex.Optimize;;::]
.simplex.LessEq [-2 1;50]
.simplex.LessEq [-1 1;20]
.simplex.Maximize[ 1 3; 0]
X:
.simplex.Optimize
.simplex.LessEq [5 2;10]
.simplex.LessEq [3 5;15]
.simplex.Maximize[2.5 1; 0]
;assertAnswer[1e-15;X;`obj`X!(5.;2 0.)]
X:
.simplex.Optimize
.simplex.LessEq [1 3 ;35]
.simplex.LessEq [2 1 ;20]
.simplex.Maximize[1 .5; 0]
;assertAnswer[1e-15;X;`obj`X!(10.;10 0.)]
.simplex.Optimize
.simplex.LessEq [ .5 .7 1.2 .4;80]
.simplex.LessEq [1.2 1 1 1.2;96]
.simplex.LessEq [1 1 .83 .5;65]
.simplex.Maximize[2 7 6 4 ; 0]
.simplex.Optimize
.simplex.LessEq [ .5 .7 1.2 .4;80]
.simplex.LessEq [1.2 1 1 1.2;96]
.simplex.LessEq [1 1 .83 .5;65]
.simplex.Maximize[1.2 1 1 1 ; 0]
///////////////////////////////////////////////////////////////////////////////
//@see http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s4.pdf
X:
.simplex.Optimize
.simplex.GreaterEq[10 30 ; 90] /vitamin C
.simplex.GreaterEq[12 6 ; 36] /vitamin A
.simplex.GreaterEq[60 60 ;300] /calories
.simplex.Minimize [ .12 .15; 0] /cost
;assertAnswer[1e-9;X;`obj`X!(.66;3 2.)]
///////////////////////////////////////////////////////////////////////////////
//@see http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s5.pdf
X:
.simplex.Optimize
.simplex.GreaterEq[1 0 1;10]
.simplex.GreaterEq[2 1 0;36]
.simplex.LessEq [2 1 1;50]
.simplex.Maximize [1 1 2; 0]
;assertAnswer[1e-15;X;`obj`X!(64.;0 36 14.)]
X:
.simplex.Optimize
.simplex.GreaterEq[2 1 1; 4]
.simplex.LessEq [4 2 3;16]
.simplex.LessEq [3 2 5;18]
.simplex.Maximize [3 2 4; 0]
;assertAnswer[1e-15;X;`obj`X!(17.;0 6.5 1)]
X:
.simplex.Optimize
.simplex.GreaterEq[1 4 3; 6]
.simplex.GreaterEq[3 1 5; 4]
.simplex.LessEq [2 3 4;14]
.simplex.Minimize [4 2 1; 0]
;assertAnswer[1e-11;X;`obj`X!(2.;0 0 2.)]
X:
.simplex.Optimize
.simplex.LessEq [ 0 1; 300] /customer 2
.simplex.LessEq [ 1 0; 200] /customer 1
.simplex.GreaterEq[ 1 1; 200] /factory 2 (derived)
.simplex.LessEq [ 1 1; 400] /factory 1
.simplex.Minimize [-6 -5;16200] /shipment cost
;assertAnswer[1e-15;X;`obj`X!(14000.;200 200.)]
X:
.simplex.Optimize
.simplex.GreaterEq[ 0 1 0 1;300] /customer 2
.simplex.GreaterEq[ 1 0 1 0;200] /customer 1
.simplex.LessEq [ 0 0 1 1;300] /factory 2
.simplex.LessEq [ 1 1 0 0;400] /factory 1
.simplex.Minimize [30 25 36 30; 0] /shipment cost
;assertAnswer[1e-15;X;`obj`X!(14000.;200 200 0 100.)]
.simplex.Optimize
.simplex.GreaterEq[ 0 1 0 1;300] /customer 2
.simplex.GreaterEq[ 1 0 1 0;200] /customer 1
.simplex.LessEq [ 0 0 1 1;300] /factory 2
.simplex.LessEq [ 1 1 0 0;400] /factory 1
.simplex.Minimize [36 30 30 25; 0] /shipment cost
.simplex.Optimize
.simplex.GreaterEq[ 0 1 0 1;300] /customer 2
.simplex.GreaterEq[ 1 0 1 0;200] /customer 1
.simplex.LessEq [ 0 0 1 1;300] /factory 2
.simplex.LessEq [ 1 1 0 0;400] /factory 1
.simplex.Minimize [25 30 35 30; 0] /shipment cost
.simplex.Optimize
.simplex.GreaterEq[ 0 1 ; 4 ] /newspaper ads
.simplex.GreaterEq[ 1 0 ; 6 ] /TV ads
.simplex.LessEq [60 15*1e3;600*1e3] /budget
.simplex.Maximize [15 3*1e6; 0 ] /viewership
.simplex.Optimize
.simplex.GreaterEq[ 0 1 ; 4 ] /newspaper ads
.simplex.GreaterEq[ 1 0 ; 6 ] /TV ads
.simplex.LessEq [60 30*1e3;600*1e3] /budget
.simplex.Maximize [15 3*1e6; 0 ] /viewership
///////////////////////////////////////////////////////////////////////////////
//@see https://www.utdallas.edu/~scniu/OPRE-6201/documents/LP10-Special-Situations.pdf
X:
.simplex.Optimize
.simplex.LessEq [4 2; 8]
.simplex.LessEq [4 1; 8]
.simplex.LessEq [4 3;12]
.simplex.Maximize[2 1; 0]
;assertAnswer[1e-15;X;`obj`X!(4.;2 0.)]
@[.simplex.Optimize;;::]
.simplex.LessEq [2 -1;40]
.simplex.LessEq [1 -1;10]
.simplex.Maximize[2 1; 0]
X:
.simplex.Optimize
.simplex.LessEq [7 2;21]
.simplex.LessEq [2 7;21]
.simplex.Maximize[4 14; 0]
;assertAnswer[1e-15;X;`obj`X!(42.;0 3.)]
///////////////////////////////////////////////////////////////////////////////
//@see https://www.youtube.com/watch?v=bAlFmzqWLl8
X:
.simplex.Optimize
.simplex.LessEq [ 1 1;41]
.simplex.GreaterEq[ 1 4;22]
.simplex.Maximize [12 10; 0]
;assertAnswer[1e-15;X;`obj`X!(492.;41 0.)]
///////////////////////////////////////////////////////////////////////////////
//@see https://www.youtube.com/watch?v=upgpVkAkFkQ
X:
.simplex.Optimize
.simplex.GreaterEq[0 1 1;10]
.simplex.Eq [1 0 1; 5]
.simplex.LessEq [1 1 0;20]
.simplex.Maximize [1 -1 3; 0]
;assertAnswer[1e-15;X;`obj`X!(10.;0 5 5.)]
Y:
.simplex.Optimize
.simplex.GreaterEq[ 0 1 1; 10]
.simplex.Eq [ 1 0 1; 5]
.simplex.GreaterEq[-1 -1 0;-20]
.simplex.Maximize [ 1 -1 3; 0]
;assertFullAnswer[1e-15;Y;X]
///////////////////////////////////////////////////////////////////////////////
//@see https://www.youtube.com/watch?v=MZ843Vvia0A
X:
.simplex.Optimize
.simplex.GreaterEq[3 9 6;30]
.simplex.GreaterEq[2 4 6;24]
.simplex.Minimize [7 15 20; 0]
;assertAnswer[1e-15;X;`obj`X!(82.;6 0 2.)]
///////////////////////////////////////////////////////////////////////////////
//@see https://stackoverflow.com/questions/3956950/c-c-implementation-of-simplex-method
X:
.simplex.Optimize
.simplex.LessEq [ 0 1 0 -1;10]
.simplex.LessEq [-2 -1 1 1;10]
.simplex.LessEq [ 1 1 1 1;40]
.simplex.Maximize[ .5 3 1 4; 0]
;assertAnswer[1e-15;X;`obj`X!(145.;0 15 0 25.)]
Y:
.simplex.answer .simplex.solveStd[
(1 1 1 1;-2 -1 1 1;0 1 0 -1);
40 10 10;
.5 3 1 4;
0]
;assertFullAnswer[1e-15;X;Y]
///////////////////////////////////////////////////////////////////////////////
//@see http://www.purplemath.com/modules/linprog.htm
X:
.simplex.Optimize
.simplex.LessEq [1 -1; 2]
.simplex.GreaterEq[3 -1; 0]
.simplex.LessEq [1 2;14]
.simplex.Maximize [3 4; 0]
;assertAnswer[1e-15;X;`obj`X!(34.;6 4.)]
X:
.simplex.Optimize
.simplex.LessEq [1 -1; 2]
.simplex.GreaterEq[3 -1; 0]
.simplex.LessEq [1 2;14]
.simplex.Minimize [3 4; 0]
;assertAnswer[1e-15;X;`obj`X!(0.;0 0.)]
///////////////////////////////////////////////////////////////////////////////
//@see http://www.purplemath.com/modules/linprog2.htm
X:
.simplex.Optimize
.simplex.LessEq [ 1 0 ;5]
.simplex.LessEq [-1 1 ;5]
.simplex.GreaterEq[ 1 2 ;4]
.simplex.LessEq [ 1 1 ;7]
.simplex.Maximize [-.4 3.2;0]
;assertAnswer[1e-15;X;`obj`X!(18.8;1 6.)]
X:
.simplex.Optimize
.simplex.LessEq [ 1 0 ;5]
.simplex.LessEq [-1 1 ;5]
.simplex.GreaterEq[ 1 2 ;4]
.simplex.LessEq [ 1 1 ;7]
.simplex.Minimize [-.4 3.2;0]
;assertAnswer[1e-15;X;`obj`X!(-2.;5 0.)]
X:
.simplex.Optimize
.simplex.LessEq [ 1 0 ;6.4e6] /gallons of gasoline
.simplex.GreaterEq[ 0 1 ;3e6 ] /gallons of fuel oil
.simplex.GreaterEq[ 1 -2 ;0 ]
.simplex.Maximize [ 1.9 1.5;0 ]
;assertAnswer[1e-15;X;`obj`X!(16.96e6;6.4e6 3.2e6)]
///////////////////////////////////////////////////////////////////////////////
//@see http://www.purplemath.com/modules/linprog3.htm
X:
.simplex.Optimize
.simplex.GreaterEq[ 1 1;200]
.simplex.LessEq [ 0 1;170]
.simplex.GreaterEq[ 0 1; 80] /# graphing calculators
.simplex.LessEq [ 1 0;200]
.simplex.GreaterEq[ 1 0;100] /# scientific calculators
.simplex.Maximize [-2 5; 0]
;assertAnswer[1e-15;X;`obj`X!(650.;100 170.)]
X:
.simplex.Optimize
.simplex.LessEq [ 6 8; 72] /space
.simplex.LessEq [10 20;140] /cost
.simplex.Maximize[ 8 12; 0] /storage
;assertAnswer[1e-15;X;`obj`X!(100.;8 3.)]
Y:
.simplex.answer .simplex.solveStd[
(10 20;6 8);
140 72;
8 12;
0]
;assertFullAnswer[1e-15;X;Y]
///////////////////////////////////////////////////////////////////////////////
//@see http://www.purplemath.com/modules/linprog4.htm
X:
.simplex.Optimize
.simplex.LessEq [ 1 1 ; 5] /total weight
.simplex.GreaterEq[ 2 1 ; 4] /protein
.simplex.GreaterEq[12 12 ;36] /carbohydrates
.simplex.GreaterEq[ 8 12 ;24] /fat
.simplex.Minimize [ .2 .3; 0]
;assertAnswer[1e-11;X;`obj`X!(.6;3 0.)]
X:
.simplex.Optimize
.simplex.GreaterEq[1 -3 0 ; 0] /municipal bond / bank CD
.simplex.LessEq [0 0 1 ; 2000] /high-risk account
.simplex.LessEq [1 1 1 ;12000] /basis
.simplex.Maximize [.07 .08 .12; 0]
;assertAnswer[1e-8;X;`obj`X!(965.;7500 2500 2000.)]
///////////////////////////////////////////////////////////////////////////////
//@see http://www.purplemath.com/modules/linprog5.htm
X:
.simplex.Optimize
.simplex.LessEq [0 1 0 1 ;45] /west-side warehouse
.simplex.LessEq [1 0 1 0 ;80] /east-side warehouse
.simplex.Eq [0 0 1 1 ;70] /customer B
.simplex.Eq [1 1 0 0 ;50] /customer A
.simplex.Minimize[.5 .4 .6 .55; 0]
;assertAnswer[1e-15;X;`obj`X!(62.5;5 45 70 0.)]
///////////////////////////////////////////////////////////////////////////////
//@see https://www.zweigmedia.com/RealWorld/simplex.html
// (interactive solver)
X:
.simplex.Optimize
.simplex.GreaterEq[3 1;4]
.simplex.LessEq [1 1;2]
.simplex.Maximize [1 1;0]
;assertAnswer[1e-15;X;`obj`X!(2.;1 1.)]
///////////////////////////////////////////////////////////////////////////////
// Portfolio optimization test
pw_index:0 55 77 204 525 687 1062 1593 1764 1909;
a:raze{con:(2305)#0f;(con pw_index x):1f;(con x+2295):-1f;enlist con}each til count pw_index;
a:((neg a),enlist (2295#1f),10#-1f);
b:0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0;
c:"F"$read0`:test_c.txt
LG:11#1f;
s:`A`b`c`LG!(a;b;c;LG);
S1:.simplex.answer .simplex.solveStd[a;b;neg c;0]
S2:.simplex.Optimize{[x;y;a;b].simplex.LessEq[a y;b y] x}[;;a;b]/[.simplex.Minimize[c;0];til count b]
(count[c]#S1[`X])~S2[`X]