ISBN 0882756494
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)set break resume
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)expose UnittestCount UnittestAux Unittest
UnittestCount is now explicitly exposed in frame initial
UnittestAux is now explicitly exposed in frame initial
Unittest is now explicitly exposed in frame initial
--)co jacdiag
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)expose JACDIAG
JacobiDiagonalisation is already explicitly exposed in frame initial
-- Test Suite
testsuite "Package JacobiDiagonalisation"
All user variables and function definitions have been cleared.
WARNING: string for testsuite should have less than 15 characters!
Type: Void
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-- Cases
testcase "jacobi"
All user variables and function definitions have been cleared.
Type: Void
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-- https://en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm
S:= matrix [[4,-30,60,-35], [-30,300,-675,420],
[60,-675,1620,-1050],[-35,420,-1050,700]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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ev1:= vector [0.1666428611_7189046264, 37.1014913651_27658188,
2585.2538109289_223144, 1.4780548447_781369118]
Type: Vector(Float)
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EV1:= matrix [[0.7926082911_6404284196, -0.1791862905_3191911245, _
0.0291933231_7921032382_1, -0.5820756994_9722239026], _
[0.4519231209_0048280218, 0.7419177906_0266858684, _
-0.3287120558_2291241902, 0.3705021850_6710175866], _
[0.3224163985_8196511663, -0.1002281368_8300231266, _
0.7914111458_4119456574, 0.5095786345_0180583406], _
[0.2521611696_891868645, -0.6382825282_3465850686, _
-0.5145527499_457719896, 0.5140482722_2216914813]]
Type: Matrix(Float)
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eps:=0.0000000001
Type: Float
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floatNull(v:Vector Float):Boolean == sqrt dot(v,v) <= eps
Function declaration floatNull : Vector(Float) -> Boolean has been
added to workspace.
Type: Void
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vector members(map(abs,R.EV-EV1))
Type: Vector(Float)
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testEquals("floatNull(R.ev-ev1)", "true")
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Compiling function floatNull with type Vector(Float) -> Boolean
Type: Void
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testEquals("floatNull(vector members(map(abs,R.EV-EV1)))", "true")
Type: Void
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-- Gregory R.T, Karney D.L, A collection of matrices for testing
-- computational algorithms, Krieger, 1978
-- CHAPTER IV, Example 4.1
S:= matrix [[5,4,1,1], [4,5,1,1], [1,1,4,2],[1,1,2,4]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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p:=showParams()
Type: Record(maxit: PositiveInteger
?,
tol: Float)
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p.maxit:=20000
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p.tol:=0.00000000001
Type: Float
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setParams(p)
Type: Record(maxit: PositiveInteger
?,
tol: Float)
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R1:=jacobi(M)
?}}, \: \right.
\
\
\displaystyle
\left.{
\begin{array}{@{}l}
\displaystyle
EV =
\
\
\displaystyle
{\left[
\begin{array}{cccc}
{0.7071067811 \ 865475244}&{0.6324555320 \ 336758664}&{0.0}& -{0.3162277660 \ 168379332}
\
-{0.7071067811 \ 865475244}&{0.6324555320 \ 336758664}&{0.0}& -{0.3162277660 \ 168379332}
\
{0.0}&{0.3162277660 \ 168379332}&{0.7071067811 \ 865475244}&{0.6
324555320 \ 336758664}
\
{0.0}&{0.3162277660 \ 168379332}& -{0.7071067811 \ 86547524
4}&{0.6324555320 \ 336758664}
" class="equation" src="images/3192297519243230694-16.0px.png" align="bottom" Style="vertical-align:text-bottom" width="793" height="155"/> | (14) |
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R1,M)<eps","true")
Type: Void
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-- Example 4.2
S:= matrix [[6,4,4,1], [4,6,1,4], [4,1,6,4],[1,4,4,6]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R2:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R2,M)<eps","true")
Type: Void
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-- Example 4.3
S:= matrix [[2,1,3,4], [1,-3,1,5], [3,1,6,-2],[4,5,-2,-1]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R3:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R3,M)<eps","true")
Type: Void
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-- Example 4.4
S:= matrix [[5,7,6,5], [7,10,8,7], [6,8,10,9],[5,7,9,10]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R4:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R4,M)<eps","true")
Type: Void
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-- Example 4.5
eps:=0.00000001 -- eps from above too small
Type: Float
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M:= matrix [[0.81321,-0.00013,0.00014,0.00011,0.00021], _
[-0.00013,0.93125,0.23567,0.41235,0.41632], _
[0.00014,0.23567,0.18765,0.50632,0.30697], _
[0.00011,0.41235,0.50632,0.27605,0.46322], _
[0.00021,0.41632,0.30697,0.46322,0.41931]]
Type: Matrix(Float)
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R5:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R5,M)<eps","true")
Type: Void
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-- Example 4.6
eps:=0.0000001 -- eps from above too small
Type: Float
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S:= matrix [[5,4,3,2,1],[4,6,0,4,3],[3,0,7,6,5],[2,4,6,8,7],[1,3,5,7,9]]
Type: Matrix(NonNegativeInteger
?)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R6:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R6,M)<eps","true")
Type: Void
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-- Example 4.7
S:= matrix [[10,1,2,3,4],[1,9,-1,2,-3],[2,-1,7,3,-5],[3,2,3,12,-1],_
[4,-3,-5,-1,15]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R7:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R7,M)<eps","true")
Type: Void
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-- Example 4.8
S:= matrix [[5,1,-2,0,-2,5],[1,6,-3,2,0,6],[-2,-3,8,-5,-6,0],[0,2,-5,5,1,-2],_
[-2,0,-6,1,6,-3],[5,6,0,-2,-3,8]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R8:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R8,M)<eps","true")
Type: Void
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-- Example 4.9
S:= matrix [[1,2,3,0,1,2],[2,4,5,-1,0,3],[3,5,6,-2,-3,0],[0,-1,-2,1,2,3],_
[1,0,-3,2,4,5],[2,3,0,3,5,6]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R9:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R9,M)<eps","true")
Type: Void
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-- Example 4.10
eps:=0.00001 -- eps from above too small
Type: Float
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S:= matrix [[611,196,-192,407,-8,-52,-49,29], _
[196,899,113,-192,-71,-43,-8,-44], _
[-192,113,899,196,61,49,8,52], _
[407,-192,196,611,8,44,59,-23],_
[-8,-71,61,8,411,-599,208,208], _
[-52,-43,49,44,-599,411,208,208], _
[-49,-8,8,59,208,208,99,-911], _
[29,-44,52,-23,208,208,-911,99]]
Type: Matrix(Integer)
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R10:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R10,M)<eps","true")
Type: Void
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-- Example 4.11
eps:=0.00001 -- eps from above too small
Type: Float
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S:= diagonalMatrix [5,6,6,6,6,6,6,6,6,6,5]
Type: Matrix(Integer)
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for i in 2..11 repeat S(i-1,i):=S(i,i-1):=3
Type: Void
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for i in 3..11 repeat S(i-2,i):=S(i,i-2):=1
Type: Void
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for i in 4..11 repeat S(i-3,i):=S(i,i-3):=1
Type: Void
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S(1,2):=S(2,1):=S(10,11):=S(11,10):=2
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M:=map(s+->s::Float, S)
Type: Matrix(Float)
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R11:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R11,M)<eps","true")
Type: Void
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-- Example 4.12
M:=matrix [[0.2500,0.06675,0.04000,0.02475,0.07050,0.06375,0.06925,0.02050,_
0.03600, -0.01025,-0.00175,0.02750,0.02300,0.00200], _
[0.06675,0.25000,0.10400,0.07475,0.03625,0.11675,0.11050,0.06225,0.05100, _
0.03250,0.02400,0.03600,0.06350,0.05300], _
[0.04000,0.10400,0.25000,0.14575,0.03725,0.07175,0.07800,0.12200,0.11275, _
0.09375,0.10175,0.09600,0.14300,0.11550], _
[0.02475,0.07475,0.14575,0.25000,0.05375,0.07000,0.05225,0.12800,0.12475, _
0.10550,0.13000,0.14575,0.13975,0.13375], _
[0.07050,0.03625,0.03725,0.05375,0.25000,0.04575,0.05750,0.05700,0.05050, _
0.01475,0.04500,0.07150,0.05300,0.01600], _
[0.06375,0.11675,0.07175,0.07000,0.04575,0.25000,0.08625,0.08800,0.07150, _
0.04850,0.03200,0.04475,0.03300,0.04500], _
[0.06925,0.11050,0.07800,0.05225,0.05750,0.08625,0.25000,0.08725,0.06950, _
0.03725,0.04025,0.04300,0.04075,0.01450], _
[0.02050,0.06225,0.12200,0.12800,0.05700,0.08800,0.08725,0.25000,0.14100, _
0.13275,0.15550,0.13050,0.11825,0.09125], _
[0.03600,0.05100,0.11275,0.12475,0.05050,0.07150,0.06950,0.14100,0.25000, _
0.07425,0.10750,0.09175,0.10725,0.08225], _
[-0.01025,0.03250,0.09375,0.10550,0.01475,0.04850,0.03725,0.13275,0.07425, _
0.25000,0.15500,0.09625,0.09950,0.09425], _
[-0.00175,0.02400,0.10175,0.13000,0.04500,0.03200,0.04025,0.15550,0.10750, _
0.15500,0.25000,0.13350,0.14850,0.13050], _
[0.02750,0.03600,0.09600,0.14575,0.07150,0.04475,0.04300,0.13050,0.09175, _
0.09625,0.13350,0.25000,0.11100,0.10075], _
[0.02300,0.06350,0.14300,0.13975,0.05300,0.03300,0.04075,0.11825,0.10725, _
0.09950,0.14850,0.11100,0.25000,0.14325], _
[0.00200,0.05300,0.11550,0.13375,0.01600,0.04500,0.01450,0.09125,0.08225, _
0.09425,0.13050,0.10075,0.14325,0.25000]]
Type: Matrix(Float)
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R12:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R12,M)<eps","true")
Type: Void
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-- Example 4.13 (Hilbert Matrix)
H(n) == matrix [[1/(i+j-1) for i in 1..n] for j in 1..n]
Type: Void
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M:=H(20);
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Compiling function H with type PositiveInteger -> Matrix(Fraction(
Integer))
Type: Matrix(Fraction(Integer))
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R13:=jacobi(M)
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R13,M)<eps","true")
Type: Void
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-- Example 4.23
M:=matrix [[1 for i in 1..50] for j in 1..50];
Type: Matrix(Integer)
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R23:=jacobi(M);
Type: Record(ev: Vector(Float),EV: Matrix(Float))
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testEquals("checkResult(R23,M)<eps","true")
Type: Void
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-- Results/Statistics
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)set output algebra on
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)version
Value = "FriCAS 1.3.4 compiled at Wed Jun 27 14:53:01 UTC 2018"
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)lisp (lisp-implementation-type)
Value = "SBCL"
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)lisp (lisp-implementation-version)
Value = "1.1.1"
statistics()
=============================================================================
General WARNINGS:
* do not use ')clear completely' before having used 'statistics()'
It clears the statistics without warning!
* do not forget to pass the arguments of the testXxxx functions as Strings!
Otherwise, the test will fail and statistics() will not notice!
* testLibraryError does not prevent FriCAS from aborting the current block.
Thus, if a block contains other test functions, they will not be executed
and statistics() will not notice!
=============================================================================
Testsuite: Package JacobiDiagonalisation
failed (total): 0 (1)
=============================================================================
testsuite | testcases: failed (total) | tests: failed (total)
Package JacobiDiagonalisation 0 (1) 0 (16)
=============================================================================
File summary.
unexpected failures: 0
expected failures: 0
unexpected passes: 0
total tests: 16
Type: Void