Example NumMatrix makeGramMatrix 001

 

 

Description

This example converts a Number Matrix to a Gram Matrix.

 

Details

Create a number Matrix containing the original independent observations:

(define X #(nummat[4 3]| 1 2 3 4
5 6 7 8
9 10 11 12))
Returns: #<NumMatrix 123456>

Convert the observation matrix to its Gaussian matrix:

(setq G (makeGramMatrix X)) Returns: #<NumMatrix 234567>

The contents of the Gaussian matrix:

(display #<NumMatrix 234567> ) Returns: #(nummat[4 4]| 14 32 50 68
32 77 122 167
50 122 194 266
68 167 266 365)

Notes and Hints

Note, the Gram matrix is always square, symmetric, and positive definite (has positive Eigenvalues).

 

Related Examples

Here are examples of the makeGramMatrix function at work.

Matrix makeGramMatrix 001 NumMatrix makeGramMatrix 001

 

Function Links

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

makeGramMatrix

Here are a number of links to other related functions.

makeGaussianMatrix(NumMatrix) matrixGaussianEliminate(NumMatrix) matrixGaussianSubstitute(NumMatrix)

 

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 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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