Example Matrix matrixGaussianSubstitute 001

 

 

Description

This example triangulates a Number Matrix to its Gaussian Matrix and returns number Vector containing the M coefficients of the solution.

 

Details

Solve a triangulated number Matrix for its M coefficient solution values: 

 (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 and solve:

(setq T (matrixGaussianEliminate X) Returns: #<NumMatrix 234567>
(setq C (matrixGaussianSubstitute T) Returns: #<NumVector 123456>
(display #<NumVector 123456> ) Returns: #(num| 1.0 1.0 1.0 )

Notes and Hints

Note1, See Sedgewick[2] chap 37, assumes input matrix is triangulated.

 

Related Examples

Here are examples of the matrixGaussianSubstitute function at work.

Matrix matrixGaussianSubstitute 001 NumMatrix matrixGaussianSubstitute 001

 

Function Links

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

matrixGaussianSubstitute

Here are a number of links to other related functions.

makeGramMatrix(#void) makeGaussianMatrix(#void) matrixGaussianEliminate(#void)

 

Argument Types

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

Matrix Vector Integer

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

BitVector bitToIntegerVector 001 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 apply 010 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 objectToDictionary 001 Dictionary objectToDictionary 002 Dictionary objectToDictionary 003 Dictionary objectToDictionary 004
Dictionary ref 007 Dictionary ref 008 Dictionary ref 009 Dictionary refAttributes 002
Dictionary refValues 002 Dictionary resize 002 Dictionary setAttributes 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 objectToDirectory 001 Directory objectToDirectory 002
Directory objectToDirectory 003 Directory objectToDirectory 004 Directory ref 011 Directory ref 012
Directory refAttributes 003 Directory refValues 003 Directory resize 003 Directory setAttributes 003
Directory setq 010 Directory sizeof 005 FltVector binaryInsert 004 FltVector compare 014
FltVector compareLE 014 FltVector compareLT 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 bitToIntegerVector 002
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 compareGT 007 Matrix compareLE 007
Matrix compareLT 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 svmRegression 001 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 stringToBVector 001 String stringToBVector 002 String stringToBVector 003
String stringToVector 001 String stringToVector 002 String stringToVector 003 String stringToVector 004
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 objectToStructure 001 Structure objectToStructure 002
Structure objectToStructure 003 Structure objectToStructure 004 Structure ref 004 Structure ref 006
Structure refAttributes 001 Structure refValues 001 Structure resize 001 Structure setAttributes 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 addMethod 007
Vector append 006 Vector appendWriteln 001 Vector apply 003 Vector apply 004
Vector binaryInsert 002 Vector binaryInsert 003 Vector binarySearch 003 Vector binarySearch 004
Vector cdr 005 Vector cdr 006 Vector compare 006 Vector compareEQ 006
Vector compareGE 006 Vector compareGT 006 Vector compareLE 006 Vector compareLT 006
Vector compareNE 006 Vector comparison functions 006 Vector copy 004 Vector copy 005
Vector count 004 Vector defmethod 008 Vector delete 007 Vector delete 008
Vector insert 004 Vector inside 004 Vector isAtom 004 Vector isEqual 004
Vector isIdentical 004 Vector isMember 004 Vector isObject 006 Vector isType 008
Vector isVector 001 Vector length 007 Vector map 004 Vector mapc 004
Vector member 004 Vector methodsOf 009 Vector new 007 Vector new 008
Vector objectToVector 001 Vector ref 013 Vector ref 014 Vector refAttributes 004
Vector refValues 004 Vector remove 004 Vector resize 004 Vector reverse 001
Vector send 006 Vector setAttributes 004 Vector setAttributes 005 Vector setBlock 001
Vector setCdr 004 Vector setLastCdr 002 Vector setq 012 Vector setq 013
Vector sizeof 006 Vector sort 010 Vector sort 011 Vector type 009
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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