IndexedMatrix(R, mnRow, mnCol)

matrix.spad line 1 [edit on github]

• R : AbelianMonoid
• mnRow : Integer
• mnCol : Integer

An IndexedMatrix is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function minRowIndex. The index of the 'first' column may be obtained by calling the function minColIndex. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa.

# : % -> NonNegativeInteger

from Aggregate

* : (%, %) -> % if R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

* : (%, R) -> % if R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

* : (R, %) -> % if R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

* : (Integer, %) -> % if R has AbelianGroup

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

* : (IndexedVector(R, mnCol), %) -> IndexedVector(R, mnCol) if R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

* : (%, IndexedVector(R, mnRow)) -> IndexedVector(R, mnRow) if R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

+ : (%, %) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

- : % -> % if R has AbelianGroup

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

- : (%, %) -> % if R has AbelianGroup

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

/ : (%, R) -> % if R has Field

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

= : (%, %) -> Boolean

from BasicType

Pfaffian : % -> R if R has CommutativeRing

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

^ : (%, Integer) -> % if R has Field

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

^ : (%, NonNegativeInteger) -> % if R has Monoid and R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

antisymmetric? : % -> Boolean if R has AbelianGroup

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

any? : (Mapping(Boolean, R), %) -> Boolean

from HomogeneousAggregate(R)

array2 : List(List(R)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

blockConcat : List(List(%)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

blockSplit : (%, List(NonNegativeInteger), List(NonNegativeInteger)) -> List(List(%))

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

blockSplit : (%, PositiveInteger, PositiveInteger) -> List(List(%))

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

coerce : IndexedVector(R, mnRow) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

colSlice : % -> Segment(Integer)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

column : (%, Integer) -> IndexedVector(R, mnRow)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

columnSpace : % -> List(IndexedVector(R, mnRow)) if R has EuclideanDomain

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

copy : % -> %

from Aggregate

count : (R, %) -> NonNegativeInteger

from HomogeneousAggregate(R)

count : (Mapping(Boolean, R), %) -> NonNegativeInteger

from HomogeneousAggregate(R)

determinant : % -> R if R has CommutativeRing

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

diagonal? : % -> Boolean

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

diagonalMatrix : List(%) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

diagonalMatrix : List(R) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, Integer, List(Integer)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, Integer, List(Segment(Integer))) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, List(Integer), Integer) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, List(Integer), List(Integer)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, List(Integer), Segment(Integer)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, List(Segment(Integer)), Integer) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, List(Segment(Integer)), List(Segment(Integer))) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, List(Segment(Integer)), Segment(Integer)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, Segment(Integer), List(Integer)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, Segment(Integer), List(Segment(Integer))) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, Segment(Integer), Segment(Integer)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, Integer, Integer) -> R

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

elt : (%, Integer, Integer, R) -> R

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

empty : () -> %

from Aggregate

empty? : % -> Boolean

from Aggregate

eq? : (%, %) -> Boolean

from Aggregate

eval : (%, R, R) -> % if R has Evalable(R)

from InnerEvalable(R, R)

eval : (%, Equation(R)) -> % if R has Evalable(R)

from Evalable(R)

eval : (%, List(R), List(R)) -> % if R has Evalable(R)

from InnerEvalable(R, R)

eval : (%, List(Equation(R))) -> % if R has Evalable(R)

from Evalable(R)

every? : (Mapping(Boolean, R), %) -> Boolean

from HomogeneousAggregate(R)

exquo : (%, R) -> Union(%, "failed") if R has IntegralDomain

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

fill! : (%, R) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

hash : % -> SingleInteger if R has Hashable

from Hashable

hashUpdate! : (HashState, %) -> HashState if R has Hashable

from Hashable

horizConcat : (%, %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

horizConcat : List(%) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

horizSplit : (%, List(NonNegativeInteger)) -> List(%)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

horizSplit : (%, PositiveInteger) -> List(%)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

inverse : % -> Union(%, "failed") if R has Field

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

kroneckerProduct : (%, %) -> % if R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

kroneckerProduct : List(%) -> % if R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

kroneckerSum : (%, %) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

kroneckerSum : List(%) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

kronecker_prod1 : (%, Integer, List(List(NonNegativeInteger)), List(%), NonNegativeInteger, NonNegativeInteger, Union(R, "one")) -> Void

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

latex : % -> String

from SetCategory

less? : (%, NonNegativeInteger) -> Boolean

from Aggregate

listOfLists : % -> List(List(R))

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

map : (Mapping(R, R), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

map : (Mapping(R, R, R), %, %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

map : (Mapping(R, R, R), %, %, R) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

map! : (Mapping(R, R), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

matrix : List(List(R)) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

matrix : (NonNegativeInteger, NonNegativeInteger, Mapping(R, Integer, Integer)) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

max : % -> R if R has OrderedSet

from HomogeneousAggregate(R)

max : (Mapping(Boolean, R, R), %) -> R

from HomogeneousAggregate(R)

maxColIndex : % -> Integer

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

maxRowIndex : % -> Integer

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

member? : (R, %) -> Boolean

from HomogeneousAggregate(R)

members : % -> List(R)

from HomogeneousAggregate(R)

min : % -> R if R has OrderedSet

from HomogeneousAggregate(R)

minColIndex : % -> Integer

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

minRowIndex : % -> Integer

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

minordet : % -> R if R has CommutativeRing

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

more? : (%, NonNegativeInteger) -> Boolean

from Aggregate

ncols : % -> NonNegativeInteger

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

new : (NonNegativeInteger, NonNegativeInteger, R) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

nrows : % -> NonNegativeInteger

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

nullSpace : % -> List(IndexedVector(R, mnRow)) if R has IntegralDomain

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

nullity : % -> NonNegativeInteger if R has IntegralDomain

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

parts : % -> List(R)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

positivePower : (%, Integer) -> % if R has SemiRng

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

qelt : (%, Integer, Integer) -> R

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

qnew : (NonNegativeInteger, NonNegativeInteger) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

qsetelt! : (%, Integer, Integer, R) -> R

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

rank : % -> NonNegativeInteger if R has IntegralDomain

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

row : (%, Integer) -> IndexedVector(R, mnCol)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

rowEchelon : % -> % if R has EuclideanDomain

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

rowSlice : % -> Segment(Integer)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

sample : () -> %

from Aggregate

scalarMatrix : (NonNegativeInteger, R) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setColumn! : (%, Integer, IndexedVector(R, mnRow)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setRow! : (%, Integer, IndexedVector(R, mnCol)) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, Integer, List(Integer), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, Integer, List(Segment(Integer)), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, List(Integer), Integer, %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, List(Integer), List(Integer), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, List(Integer), Segment(Integer), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, List(Segment(Integer)), Integer, %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, List(Segment(Integer)), List(Segment(Integer)), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, List(Segment(Integer)), Segment(Integer), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, Segment(Integer), List(Integer), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, Segment(Integer), List(Segment(Integer)), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, Segment(Integer), Segment(Integer), %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setelt! : (%, Integer, Integer, R) -> R

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

setsubMatrix! : (%, Integer, Integer, %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

size? : (%, NonNegativeInteger) -> Boolean

from Aggregate

smaller? : (%, %) -> Boolean if R has Comparable

from Comparable

square? : % -> Boolean

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

squareTop : % -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

subMatrix : (%, Integer, Integer, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

swapColumns! : (%, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

swapRows! : (%, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

symmetric? : % -> Boolean

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

transpose : % -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

transpose : IndexedVector(R, mnCol) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

vertConcat : (%, %) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

vertConcat : List(%) -> %

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

vertSplit : (%, List(NonNegativeInteger)) -> List(%)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

vertSplit : (%, PositiveInteger) -> List(%)

from TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

zero : (NonNegativeInteger, NonNegativeInteger) -> %

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

zero? : % -> Boolean

from MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

~= : (%, %) -> Boolean

from BasicType

Comparable

shallowlyMutable

Aggregate

BasicType

HomogeneousAggregate(R)

SetCategory

TwoDimensionalArrayCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

Hashable

InnerEvalable(R, R)

CoercibleTo(OutputForm)

MatrixCategory(R, IndexedVector(R, mnCol), IndexedVector(R, mnRow))

finiteAggregate

Evalable(R)