matrixGaussianSubstitute

 

 

Description

The matrixGaussianSubstitute function returns the M coefficient number vector from a triangulated array representing the solution of a triangulated system of M simultaneous linear equations in M variables.

The input argument {NumMatrix} must be an M by M+1 matrix representing the original independent variable observations with the dependent variable in the last column all having been triangulated via the Gaussian elimination in the form of::

x x x x... x y

0 x x x... x y

0 0 x x... x y

....

0 0 0 0... x y

The output will be the M coefficient number vector representing the solution to the original system of M simultaneous equations in M unknowns.

When to use

The matrixGaussianSubstitute function is a non-destructive function useful when you want to solve a system of M simultaneous equations in M variables from a triangulated matrix. See Sedgewick[2] chap 37.

 

Syntax

(matrixGaussianSubstitute NumMatrix)



Name Description AIS Types
NumMatrix Matrix containing the triangulated original independent and dependent observationsNumMatrix


Returns:

A new number Vector containing the M coefficients of the solution.

 

Examples

Here are a number of links to Lambda coding examples which contain this instruction in various use cases.

Example_NumMatrix_matrixGaussianSubstitute_001

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

 

Argument Types

Here are the links to the data types of the function arguments.

NumMatrix

Here are also a number of links to functions having arguments with any of these data types.

binaryInsert(CpxVector) binaryInsert(FltVector) binaryInsert(IntVector) binaryInsert(Matrix)
binaryInsert(NumMatrix) binaryInsert(NumVector) binaryInsert(ShortVector) binaryInsert(Structure)
binaryInsert(Vector) boolean(Boolean) cdr(BitVector) cdr(Brick)
cdr(CpxVector) cdr(Dictionary) cdr(Directory) cdr(FltVector)
cdr(IntVector) cdr(List) cdr(Matrix) cdr(NumMatrix)
cdr(NumVector) cdr(ObjVector) cdr(ShortVector) cdr(Structure)
cdr(Vector) character(Character) compareEQ(BitVector) compareEQ(Boolean)
compareEQ(Brick) compareEQ(Character) compareEQ(Complex) compareEQ(CpxVector)
compareEQ(Date) compareEQ(Dictionary) compareEQ(Directory) compareEQ(FltVector)
compareEQ(Function) compareEQ(IntVector) compareEQ(Lambda) compareEQ(List)
compareEQ(Matrix) compareEQ(NumMatrix) compareEQ(NumVector) compareEQ(Number)
compareEQ(ObjVector) compareEQ(ObjectRepository) compareEQ(Pair) compareEQ(ShortVector)
compareEQ(String) compareEQ(Structure) compareEQ(Symbol) compareEQ(Vector)
compareEQ(Void) compareLE(BitVector) compareLE(Boolean) compareLE(Brick)
compareLE(Character) compareLE(Complex) compareLE(CpxVector) compareLE(Date)
compareLE(Dictionary) compareLE(Directory) compareLE(FltVector) compareLE(Function)
compareLE(IntVector) compareLE(Lambda) compareLE(List) compareLE(Matrix)
compareLE(NumMatrix) compareLE(NumVector) compareLE(Number) compareLE(ObjVector)
compareLE(ObjectRepository) compareLE(Pair) compareLE(ShortVector) compareLE(String)
compareLE(Structure) compareLE(Symbol) compareLE(Vector) compareLE(Void)
compareLT(BitVector) compareLT(Boolean) compareLT(Brick) compareLT(Character)
compareLT(Complex) compareLT(CpxVector) compareLT(Date) compareLT(Dictionary)
compareLT(Directory) compareLT(FltVector) compareLT(Function) compareLT(IntVector)
compareLT(Lambda) compareLT(List) compareLT(Matrix) compareLT(NumMatrix)
compareLT(NumVector) compareLT(Number) compareLT(ObjVector) compareLT(ObjectRepository)
compareLT(Pair) compareLT(ShortVector) compareLT(String) compareLT(Structure)
compareLT(Symbol) compareLT(Vector) compareLT(Void) compareNE(BitVector)
compareNE(Boolean) compareNE(Brick) compareNE(Character) compareNE(Complex)
compareNE(CpxVector) compareNE(Date) compareNE(Dictionary) compareNE(Directory)
compareNE(FltVector) compareNE(Function) compareNE(IntVector) compareNE(Lambda)
compareNE(List) compareNE(Matrix) compareNE(NumMatrix) compareNE(NumVector)
compareNE(Number) compareNE(ObjVector) compareNE(ObjectRepository) compareNE(Pair)
compareNE(ShortVector) compareNE(String) compareNE(Structure) compareNE(Symbol)
compareNE(Vector) compareNE(Void) compare(BitVector) compare(Boolean)
compare(Brick) compare(Character) compare(Complex) compare(CpxVector)
compare(Date) compare(Dictionary) compare(Directory) compare(FltVector)
compare(Function) compare(IntVector) compare(Lambda) compare(List)
compare(Matrix) compare(NumMatrix) compare(NumVector) compare(Number)
compare(ObjVector) compare(ObjectRepository) compare(Pair) compare(ShortVector)
compare(String) compare(Structure) compare(Symbol) compare(Vector)
compare(Void) cons(Pair) copy(BitVector) copy(Brick)
copy(CpxVector) copy(Dictionary) copy(Directory) copy(FltVector)
copy(IntVector) copy(Lambda) copy(List) copy(Matrix)
copy(NumMatrix) copy(NumVector) copy(ObjVector) copy(Pair)
copy(PcodeVector) copy(ShortVector) copy(Structure) copy(Vector)
delete(Dictionary) delete(Directory) delete(FltVector) delete(IntVector)
delete(List) delete(Matrix) delete(NumMatrix) delete(NumVector)
delete(ObjVector) delete(ObjectRepository) delete(Pair) delete(ShortVector)
delete(Structure) delete(Vector) display(ByteVector) display(FileIO)
insert(Dictionary) insert(Directory) insert(FltVector) insert(IntVector)
insert(Matrix) insert(NumMatrix) insert(NumVector) insert(ObjVector)
insert(ShortVector) insert(Structure) insert(Vector) inside(BitVector)
inside(Dictionary) inside(Directory) inside(IntVector) inside(List)
inside(Matrix) inside(NumMatrix) inside(NumVector) inside(ShortVector)
inside(Structure) inside(Vector) integer(Integer) isAtom(BitVector)
isAtom(Brick) isAtom(Dictionary) isAtom(Directory) isAtom(FltVector)
isAtom(IntVector) isAtom(List) isAtom(Matrix) isAtom(NumMatrix)
isAtom(NumVector) isAtom(ObjVector) isAtom(Pair) isAtom(PcodeVector)
isAtom(ShortVector) isAtom(Structure) isAtom(Vector) isBitVector(BitVector)
isBoolean(Boolean) isByteVector(ByteVector) isChar(String) isCharacter(Character)
isComplex(Complex) isDate(Date) isDictionary(Dictionary) isDirectory(Directory)
isEqual(BitVector) isEqual(Boolean) isEqual(Brick) isEqual(Character)
isEqual(Complex) isEqual(Date) isEqual(Dictionary) isEqual(Directory)
isEqual(FltVector) isEqual(Function) isEqual(IntVector) isEqual(List)
isEqual(Matrix) isEqual(NumMatrix) isEqual(NumVector) isEqual(Number)
isEqual(ObjVector) isEqual(Pair) isEqual(ShortVector) isEqual(String)
isEqual(Structure) isEqual(Vector) isEqual(Void) isError(Error)
isFloatVector(FltVector) isIdentical(BitVector) isIdentical(Boolean) isIdentical(Brick)
isIdentical(Character) isIdentical(Complex) isIdentical(Date) isIdentical(Dictionary)
isIdentical(Directory) isIdentical(Error) isIdentical(FltVector) isIdentical(Function)
isIdentical(IntVector) isIdentical(List) isIdentical(Matrix) isIdentical(NumMatrix)
isIdentical(NumVector) isIdentical(Number) isIdentical(ObjVector) isIdentical(ObjectRepository)
isIdentical(Pair) isIdentical(PcodeVector) isIdentical(ShortVector) isIdentical(Structure)
isIdentical(Vector) isIdentical(Void) isInside(BitVector) isInside(Dictionary)
isInside(Directory) isInside(IntVector) isInside(List) isInside(Matrix)
isInside(NumMatrix) isInside(NumVector) isInside(ObjVector) isInside(Pair)
isInside(ShortVector) isInside(Structure) isInside(Vector) isIntegerVector(IntVector)
isInteger(Integer) isMatrix(Matrix) isMember(BitVector) isMember(Dictionary)
isMember(Directory) isMember(IntVector) isMember(List) isMember(Matrix)
isMember(NumMatrix) isMember(NumVector) isMember(ObjVector) isMember(Pair)
isMember(ShortVector) isMember(Structure) isMember(Vector) isMoney(Number)
isNumberMatrix(NumMatrix) isNumberVector(NumVector) isNumber(Number) isObjectVector(ObjVector)
isObject(BitVector) isObject(Brick) isObject(ByteVector) isObject(Dictionary)
isObject(Directory) isObject(FltVector) isObject(IntVector) isObject(List)
isObject(Matrix) isObject(NumMatrix) isObject(NumVector) isObject(ObjVector)
isObject(Pair) isObject(PcodeVector) isObject(ShortVector) isObject(String)
isObject(Structure) isObject(Symbol) isObject(Vector) isPair(List)
isPair(Pair) isPcodeVector(PcodeVector) isString(String) isStructure(Structure)
isSymbol(Symbol) isText(String) isType(BitVector) isType(Boolean)
isType(Brick) isType(Character) isType(Complex) isType(Date)
isType(Dictionary) isType(Directory) isType(FltVector) isType(Function)
isType(IntVector) isType(Matrix) isType(NumMatrix) isType(NumVector)
isType(Number) isType(ObjVector) isType(ObjectRepository) isType(Pair)
isType(ShortVector) isType(String) isType(Structure) isType(Symbol)
isType(Vector) isType(Void) isVector(Vector) length(BitVector)
length(Brick) length(Dictionary) length(Directory) length(FltVector)
length(IntVector) length(List) length(Matrix) length(NumMatrix)
length(NumVector) length(ObjVector) length(ObjectRepository) length(Pair)
length(PcodeVector) length(ShortVector) length(String) length(Structure)
length(Symbol) length(Vector) list(List) macroReplace(String)
makeGaussianMatrix(NumMatrix) makeGramMatrix(NumMatrix) makeQuotedList(List) map(Dictionary)
map(Directory) map(FltVector) map(IntVector) map(List)
map(Matrix) map(NumMatrix) map(NumVector) map(Pair)
map(ShortVector) map(Structure) map(Vector) mapc(Dictionary)
mapc(Directory) mapc(FltVector) mapc(IntVector) mapc(List)
mapc(Matrix) mapc(NumMatrix) mapc(NumVector) mapc(Pair)
mapc(ShortVector) mapc(Structure) mapc(Vector) matrixGaussianEliminate(NumMatrix)
matrixGaussianSubstitute(NumMatrix) member(BitVector) member(Dictionary) member(Directory)
member(IntVector) member(List) member(Matrix) member(NumMatrix)
member(NumVector) member(ObjVector) member(ShortVector) member(Structure)
member(Vector) money(Number) new(BitVector) new(Brick)
new(ByteVector) new(CpxVector) new(Dictionary) new(Directory)
new(FltVector) new(IntVector) new(Lambda) new(Matrix)
new(NumMatrix) new(NumVector) new(ObjVector) new(ObjectRepository)
new(PcodeVector) new(ShortVector) new(String) new(Structure)
new(Symbol) new(Vector) number(Number) pair(Pair)
parse(String) ref(BitVector) ref(Boolean) ref(Brick)
ref(Character) ref(Complex) ref(Date) ref(Dictionary)
ref(Directory) ref(FltVector) ref(Function) ref(IntVector)
ref(Lambda) ref(List) ref(Matrix) ref(NumMatrix)
ref(NumVector) ref(Number) ref(ObjVector) ref(ObjectRepository)
ref(PcodeVector) ref(ShortVector) ref(String) ref(Structure)
ref(Symbol) ref(Vector) ref(Void) remove(BitVector)
remove(Dictionary) remove(Directory) remove(IntVector) remove(Matrix)
remove(NumMatrix) remove(NumVector) remove(ObjVector) remove(ShortVector)
remove(Structure) remove(Vector) resize(BitVector) resize(Dictionary)
resize(Directory) resize(FltVector) resize(IntVector) resize(Matrix)
resize(NumMatrix) resize(NumVector) resize(ObjVector) resize(ShortVector)
resize(Structure) resize(Vector) reverse(BitVector) reverse(FltVector)
reverse(IntVector) reverse(List) reverse(Matrix) reverse(NumMatrix)
reverse(NumVector) reverse(ObjVector) reverse(ShortVector) reverse(Vector)
saveObject(ByteVector) saveObject(Integer) send(BitVector) send(Boolean)
send(Brick) send(Character) send(CpxVector) send(Date)
send(Dictionary) send(Directory) send(FltVector) send(Function)
send(IntVector) send(Lambda) send(List) send(Matrix)
send(NumMatrix) send(NumVector) send(Number) send(ObjectRepository)
send(Pair) send(ShortVector) send(String) send(Structure)
send(Symbol) send(Vector) send(Void) setCar(List)
setCar(Pair) setCdr(BitVector) setCdr(Brick) setCdr(Dictionary)
setCdr(Directory) setCdr(FltVector) setCdr(IntVector) setCdr(List)
setCdr(Matrix) setCdr(NumMatrix) setCdr(NumVector) setCdr(ObjVector)
setCdr(Pair) setCdr(ShortVector) setCdr(Structure) setCdr(Vector)
setLastCdr(BitVector) setLastCdr(FltVector) setLastCdr(IntVector) setLastCdr(List)
setLastCdr(Matrix) setLastCdr(NumMatrix) setLastCdr(NumVector) setLastCdr(ObjVector)
setLastCdr(Structure) setLastCdr(Vector) setq(BitVector) setq(Boolean)
setq(Brick) setq(Character) setq(Date) setq(Dictionary)
setq(Directory) setq(FltVector) setq(IntVector) setq(Lambda)
setq(List) setq(Matrix) setq(NumVector) setq(Number)
setq(ObjVector) setq(ObjectRepository) setq(PcodeVector) setq(ShortVector)
setq(String) setq(Structure) setq(Symbol) setq(Vector)
setq(Void) sizeof(BitVector) sizeof(Boolean) sizeof(Brick)
sizeof(ByteVector) sizeof(Character) sizeof(Complex) sizeof(Date)
sizeof(Dictionary) sizeof(Directory) sizeof(FltVector) sizeof(Function)
sizeof(IntVector) sizeof(List) sizeof(Matrix) sizeof(NumMatrix)
sizeof(NumVector) sizeof(Number) sizeof(ObjVector) sizeof(ObjectRepository)
sizeof(Pair) sizeof(PcodeVector) sizeof(ShortVector) sizeof(String)
sizeof(Structure) sizeof(Symbol) sizeof(Vector) sizeof(Void)
sort(BitVector) sort(Dictionary) sort(Directory) sort(FltVector)
sort(IntVector) sort(List) sort(Matrix) sort(NumMatrix)
sort(NumVector) sort(ObjVector) sort(ShortVector) sort(Structure)
sort(Vector) string(Complex) string(String) type(BitVector)
type(Boolean) type(Brick) type(ByteVector) type(Character)
type(Complex) type(Date) type(Dictionary) type(Directory)
type(FltVector) type(Function) type(IntVector) type(Lambda)
type(Matrix) type(NumMatrix) type(NumVector) type(Number)
type(ObjVector) type(ObjectRepository) type(Pair) type(PcodeVector)
type(ShortVector) type(String) type(Structure) type(Symbol)
type(Vector) type(Void) uniqueInsert(FltVector) uniqueInsert(IntVector)
uniqueInsert(Matrix) uniqueInsert(NumMatrix) uniqueInsert(NumVector) uniqueInsert(ObjVector)
uniqueInsert(ShortVector) uniqueInsert(Structure) uniqueInsert(Vector) vectorFill(BitVector)
vectorFill(FltVector) vectorFill(IntVector) vectorFill(Matrix) vectorFill(NumMatrix)
vectorFill(NumVector) vectorFill(ObjVector) vectorFill(ShortVector) vectorFill(Vector)
writeln(ByteVector) writeln(String) writeln(Text)

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