Example Matrix matrixGaussianEliminate 001

 

 

Description

This example triangulates a Number Matrixto its Gaussian Matrix.

 

Details

Create a triangulated number Matrix ready for Gaussian substitution: 

 (define X  #(nummat[3 4]| 12 2 3 17
                                                          1 5  -3 3
                                                          9  5 -3 11))
Returns: #<NumMatrix 123456>

Triangulate the observation matrix to its Gaussian matrix:

(setq T (matrixGaussianEliminate X) Returns: #<NumMatrix 234567>
(display #<NumMatrix 234567> ) Returns: 
#(nummat[3 4]| 12.0 2.0   3.0 17.0
                                      0.0 4.833 -3.25 1.583
                                      0.0 0.0 -2.896 -2.896
)

Notes and Hints

Note1, See Sedgewick[2] chap 37, uses row swapping.
Note2, This function implements an approximate form of Gaussian elimination by fudging around singular conditions where dividing by zero would be a problem..

 

Related Examples

Here are examples of the matrixGaussianEliminate function at work.

Matrix matrixGaussianEliminate 001 NumMatrix matrixGaussianEliminate 001

 

Function Links

Here is the link to the current function used in this example.

matrixGaussianEliminate

Here are a number of links to other related functions.

makeGramMatrix(#void) makeGaussianMatrix(#void) matrixGaussianSubstitute(#void)

 

Argument Types

Here are the links to the data types of the arguments used in this example.

Matrix Integer

Here are a number of links to examples having similar argument types.

BitVector compare 018 BitVector findBlock 001 BitVector freeBlock 001 BitVector inside 007
BitVector isBitVector 001 BitVector isMember 008 BitVector isObject 012 BitVector length 013
BitVector member 008 BitVector ref 027 BitVector resize 010 BitVector sizeof 019
BitVector vectorFill 007 Boolean bcompareEQ 001 Boolean bcompareGE 001 Boolean bcompareGT 001
Boolean bcompareLE 001 Boolean bcompareLT 001 Boolean bcompareNE 001 Boolean boolean 001
Boolean compare 009 Boolean isBoolean 001 Boolean sizeof 009 ByteVector isByteVector 001
ByteVector isObject 013 ByteVector sizeof 020 Character cadd 001 Character ccompareEQ 001
Character ccompareGE 001 Character ccompareGT 001 Character ccompareLE 001 Character ccompareLT 001
Character ccompareNE 001 Character cdiv 001 Character character 001 Character cmod 001
Character cmul 001 Character compare 010 Character csub 001 Character isCharacter 001
Character sizeof 010 Complex compare 021 Complex cos 002 Complex exp 002
Complex expt 002 Complex log 002 Complex log10 002 Complex log2 002
Complex logbase 002 Complex sin 002 Complex sqrt 002 Complex tan 002
Context globalBinding 001 CpxVector avg 002 CpxVector binaryInsert 008 CpxVector binarySearch 008
CpxVector compare 020 CpxVector compareEQ 020 CpxVector compareGE 020 CpxVector compareGT 020
CpxVector compareLE 020 CpxVector compareLT 020 CpxVector compareNE 020 Date compare 012
Date date 001 Date day 001 Date days360 001 Date hour 001
Date minute 001 Date month 001 Date second 001 Date sizeof 012
Date time 001 Date time 002 Date year 001 Dictionary compare 004
Dictionary count 002 Dictionary delete 003 Dictionary delete 004 Dictionary insert 002
Dictionary isBound 002 Dictionary isDictionary 001 Dictionary isObject 004 Dictionary length 005
Dictionary member 002 Dictionary new 004 Dictionary ref 007 Dictionary ref 008
Dictionary ref 009 Dictionary refAttributes 002 Dictionary refValues 002 Dictionary resize 002
Dictionary setq 007 Dictionary setq 008 Dictionary sizeof 004 Dictionary sort 003
Directory compare 005 Directory count 003 Directory delete 005 Directory delete 006
Directory insert 003 Directory inside 003 Directory isBound 003 Directory isObject 005
Directory length 006 Directory new 005 Directory new 006 Directory ref 011
Directory ref 012 Directory refAttributes 003 Directory refValues 003 Directory resize 003
Directory setq 010 Directory sizeof 005 FltVector binaryInsert 004 FltVector compare 014
FltVector delete 009 FltVector insert 005 FltVector isFloatVector 001 FltVector isObject 007
FltVector length 008 FltVector ref 022 FltVector resize 006 FltVector sizeof 014
FltVector uniqueInsert 004 FltVector vectorFill 003 Function compare 013 Function sizeof 013
IntVector binaryInsert 005 IntVector compare 015 IntVector delete 010 IntVector insert 006
IntVector inside 005 IntVector isIntegerVector 001 IntVector isMember 005 IntVector isObject 008
IntVector length 009 IntVector member 005 IntVector ref 023 IntVector resize 007
IntVector sizeof 015 IntVector uniqueInsert 005 IntVector vectorFill 004 Integer binaryNot 001
Integer bitwiseNot 001 Integer fact 001 Integer gcd 001 Integer iadd 001
Integer icompareGE 001 Integer icompareGT 001 Integer icompareLE 001 Integer icompareLT 001
Integer icompareNE 001 Integer idiv 001 Integer imod 001 Integer imul 001
Integer integer 001 Integer isub 001 Integer lcm 001 Lambda balance 001
Lambda globalBinding 001 Lambda ref 017 List count 007 List count 008
List length 015 List sizeof 022 Matrix addMethod 008 Matrix append 007
Matrix apply 005 Matrix apply 006 Matrix binaryInsert 004 Matrix binaryInsert 005
Matrix binarySearch 005 Matrix binarySearch 006 Matrix cdr 007 Matrix cdr 008
Matrix compare 007 Matrix compareEQ 007 Matrix compareGE 007 Matrix compareLE 007
Matrix compareNE 007 Matrix comparison functions 007 Matrix copy 006 Matrix copy 007
Matrix count 005 Matrix defMethod 009 Matrix delete 009 Matrix insert 005
Matrix inside 005 Matrix isAtom 005 Matrix isEqual 005 Matrix isIdentical 005
Matrix isMatrix 001 Matrix isMember 005 Matrix isNumberMatrix 001 Matrix isObject 007
Matrix isType 009 Matrix length 008 Matrix makeGaussianMatrix 001 Matrix makeGramMatrix 001
Matrix map 006 Matrix map 007 Matrix mapc 005 Matrix matrixGaussianEliminate 001
Matrix matrixGaussianSubstitute 001 Matrix member 005 Matrix methodsOf 010 Matrix new 009
Matrix new 010 Matrix objectToMatrix 001 Matrix objectToNumMatrix 001 Matrix rank 001
Matrix ref 015 Matrix ref 016 Matrix remove 005 Matrix resize 005
Matrix reverse 002 Matrix send 008 Matrix setCdr 005 Matrix setLastCdr 005
Matrix setq 014 Matrix sizeof 007 Matrix sort 012 Matrix type 010
Matrix uniqueInsert 004 Matrix vectorFill 002 NumMatrix binaryInsert 007 NumMatrix cdr 011
NumMatrix compare 023 NumMatrix count 009 NumMatrix delete 014 NumMatrix insert 009
NumMatrix inside 009 NumMatrix isMember 010 NumMatrix isNumberMatrix 001 NumMatrix isObject 014
NumMatrix length 017 NumMatrix makeGaussianMatrix 001 NumMatrix makeGramMatrix 001 NumMatrix matrixGaussianEliminate 001
NumMatrix matrixGaussianSubstitute 001 NumMatrix member 009 NumMatrix rank 002 NumMatrix ref 035
NumMatrix resize 011 NumMatrix reverse 004 NumMatrix sizeof 028 NumMatrix uniqueInsert 005
NumMatrix vectorFill 008 NumVector binaryInsert 006 NumVector compare 016 NumVector delete 011
NumVector insert 007 NumVector inside 006 NumVector isMember 006 NumVector isNumberVector 001
NumVector isObject 009 NumVector length 010 NumVector member 006 NumVector objectToNumVector 001
NumVector ref 024 NumVector resize 008 NumVector sizeof 016 NumVector uniqueInsert 006
NumVector vectorFill 005 Number asin 001 Number atan 001 Number avg 001
Number compare 011 Number cos 001 Number cosh 001 Number deg 001
Number exp 001 Number floor 001 Number kurtosis 001 Number log 001
Number log10 001 Number log2 001 Number logbase 001 Number max 001
Number median 001 Number min 001 Number mod 001 Number modi 001
Number nadd 001 Number ncompareGE 001 Number ncompareGT 001 Number ncompareLE 001
Number ncompareLT 001 Number ndiv 001 Number nmod 001 Number nmul 001
Number nsub 001 Number number 001 Number pi 001 Number product 001
Number rad 001 Number random 001 Number randomize 001 Number range 001
Number round 001 Number sign 001 Number sin 001 Number sinh 001
Number sizeof 011 Number skew 001 Number sqrt 001 Number srandom 001
Number stdev 001 Number stdevp 001 Number sumsqr 001 Number tan 001
Number tanh 001 Number var 001 Number varp 001 ObjVector compare 017
ObjVector delete 012 ObjVector insert 008 ObjVector isMember 007 ObjVector isObject 010
ObjVector isObjectVector 001 ObjVector length 011 ObjVector member 007 ObjVector ref 025
ObjVector resize 009 ObjVector sizeof 017 ObjVector uniqueInsert 007 ObjVector vectorFill 006
ObjectRepository delete 013 Pair compare 019 Pair compareEQ 019 Pair compareGE 019
Pair compareGT 019 Pair compareLE 019 Pair compareLT 019 Pair compareNE 019
Pair comparison 019 Pair count 006 Pair length 014 Pair sizeof 021
PcodeVector isObject 011 PcodeVector isPcodeVector 001 PcodeVector length 012 PcodeVector ref 026
PcodeVector sizeof 018 ShortVector binaryInsert 006 ShortVector compare 016 ShortVector delete 011
ShortVector insert 007 ShortVector inside 006 ShortVector isMember 006 ShortVector isObject 009
ShortVector length 010 ShortVector member 006 ShortVector ref 024 ShortVector resize 008
ShortVector sizeof 016 ShortVector uniqueInsert 007 ShortVector vectorFill 005 String code 001
String compare 001 String compareEQ 001 String compareGE 001 String compareGT 001
String compareLE 001 String compareLT 001 String compareNE 001 String find 001
String find 002 String hashString 001 String isChar 001 String isCharAlphabetic 001
String isCharAlphanumeric 001 String isCharLowercase 001 String isCharName 001 String isCharNumeric 001
String isCharUppercase 001 String isCharWhitespace 001 String isEqual 001 String isEqual 002
String isObject 001 String isString 001 String isText 001 String isType 001
String isType 002 String isType 003 String left 001 String length 001
String length 002 String mid 001 String new 001 String parse 001
String ref 001 String ref 002 String replace 001 String rept 001
String right 001 String sizeof 001 String string 001 String string 002
String string 003 String stringCiEQ 001 String stringCiGE 001 String stringCiGT 001
String stringCiLE 001 String stringCiLT 001 String stringCiNE 001 String substitute 001
String substitute 002 String substring 001 String substring 002 String substringCiEQ 001
String substringCiGE 001 String substringCiGT 001 String substringCiLE 001 String substringCiLT 001
String substringCiNE 001 String text 001 String type 001 Structure apply 001
Structure binaryInsert 001 Structure binarySearch 001 Structure compareGE 003 Structure compareGT 003
Structure compareLE 003 Structure compareLT 003 Structure compareNE 003 Structure count 001
Structure defstruct 001 Structure delete 001 Structure insert 001 Structure inside 001
Structure isBound 001 Structure isObject 003 Structure length 004 Structure member 001
Structure new 003 Structure ref 004 Structure ref 006 Structure refAttributes 001
Structure refValues 001 Structure resize 001 Structure setq 004 Structure setq 005
Structure setq 006 Structure sizeof 003 Structure uniqueInsert 001 Structure uniqueInsert 002
Symbol compare 002 Symbol compareEQ 002 Symbol compareGE 002 Symbol compareGT 002
Symbol compareLE 002 Symbol compareLT 002 Symbol compareNE 002 Symbol hashString 002
Symbol isCharName 002 Symbol isCharNumeric 002 Symbol isObject 002 Symbol isSymbol 001
Symbol isType 004 Symbol length 003 Symbol new 002 Symbol sizeof 002
Symbol type 002 Vector binaryInsert 002 Vector binaryInsert 003 Vector compare 006
Vector count 004 Vector delete 007 Vector delete 008 Vector insert 004
Vector inside 004 Vector isMember 004 Vector isObject 006 Vector isVector 001
Vector length 007 Vector member 004 Vector objectToVector 001 Vector ref 013
Vector ref 014 Vector refAttributes 004 Vector refValues 004 Vector resize 004
Vector setBlock 001 Vector sizeof 006 Vector uniqueInsert 003 Vector vectorFill 001
Void compare 008 Void compareEQ 008 Void compareGT 008 Void compareNE 008
Void ref 017 Void sizeof 008 substringEQ 001 substringGE 001
substringGT 001 substringLE 001 substringLT 001 substringNE 001

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