PrimitiveTwoDimensionalArray(S)

u32vec.spad line 364 [edit on github]

• S : Type

This is a low-level domain which implements matrices (two dimensional arrays) of general values. Indexing is 0 based, there is no bound checking (unless provided by lower level).

# : % -> NonNegativeInteger

from Aggregate

* : (%, %) -> % if S has AbelianMonoid and S has SemiRng

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

* : (%, S) -> % if S has AbelianMonoid and S has SemiRng

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

* : (S, %) -> % if S has AbelianMonoid and S has SemiRng

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

* : (Integer, %) -> % if S has AbelianMonoid and S has AbelianGroup

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

* : (%, PrimitiveArray(S)) -> PrimitiveArray(S) if S has AbelianMonoid and S has SemiRng

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

* : (PrimitiveArray(S), %) -> PrimitiveArray(S) if S has AbelianMonoid and S has SemiRng

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

+ : (%, %) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

- : % -> % if S has AbelianMonoid and S has AbelianGroup

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

- : (%, %) -> % if S has AbelianMonoid and S has AbelianGroup

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

/ : (%, S) -> % if S has AbelianMonoid and S has Field

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

= : (%, %) -> Boolean if S has BasicType

from BasicType

Pfaffian : % -> S if S has AbelianMonoid and S has CommutativeRing

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

^ : (%, Integer) -> % if S has AbelianMonoid and S has Field

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

antisymmetric? : % -> Boolean if S has AbelianMonoid and S has AbelianGroup

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from HomogeneousAggregate(S)

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

coerce : PrimitiveArray(S) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

coerce : % -> OutputForm if S has CoercibleTo(OutputForm)

from CoercibleTo(OutputForm)

colSlice : % -> Segment(Integer)

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

column : (%, Integer) -> PrimitiveArray(S)

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

columnSpace : % -> List(PrimitiveArray(S)) if S has AbelianMonoid and S has EuclideanDomain

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

copy : % -> %

from Aggregate

count : (S, %) -> NonNegativeInteger if S has BasicType

from HomogeneousAggregate(S)

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

from HomogeneousAggregate(S)

determinant : % -> S if S has AbelianMonoid and S has CommutativeRing

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

diagonal? : % -> Boolean if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

diagonalMatrix : List(%) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

diagonalMatrix : List(S) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

empty : () -> %

from Aggregate

empty? : % -> Boolean

from Aggregate

eq? : (%, %) -> Boolean

from Aggregate

eval : (%, S, S) -> % if S has Evalable(S) and S has SetCategory

from InnerEvalable(S, S)

eval : (%, Equation(S)) -> % if S has Evalable(S) and S has SetCategory

from Evalable(S)

eval : (%, List(S), List(S)) -> % if S has Evalable(S) and S has SetCategory

from InnerEvalable(S, S)

eval : (%, List(Equation(S))) -> % if S has Evalable(S) and S has SetCategory

from Evalable(S)

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

from HomogeneousAggregate(S)

exquo : (%, S) -> Union(%, "failed") if S has AbelianMonoid and S has IntegralDomain

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

fill! : (%, S) -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

hash : % -> SingleInteger if S has Hashable

from Hashable

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

from Hashable

horizConcat : (%, %) -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

horizConcat : List(%) -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

inverse : % -> Union(%, "failed") if S has AbelianMonoid and S has Field

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

kroneckerProduct : (%, %) -> % if S has AbelianMonoid and S has SemiRng

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

kroneckerProduct : List(%) -> % if S has AbelianMonoid and S has SemiRng

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

kroneckerSum : (%, %) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

kroneckerSum : List(%) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

kronecker_prod1 : (%, Integer, List(List(NonNegativeInteger)), List(%), NonNegativeInteger, NonNegativeInteger, Union(S, "one")) -> Void if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

latex : % -> String if S has SetCategory

from SetCategory

less? : (%, NonNegativeInteger) -> Boolean

from Aggregate

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

matrix : List(List(S)) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

matrix : (NonNegativeInteger, NonNegativeInteger, Mapping(S, Integer, Integer)) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

max : % -> S if S has OrderedSet

from HomogeneousAggregate(S)

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

from HomogeneousAggregate(S)

maxColIndex : % -> Integer

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

maxRowIndex : % -> Integer

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

member? : (S, %) -> Boolean if S has BasicType

from HomogeneousAggregate(S)

members : % -> List(S)

from HomogeneousAggregate(S)

min : % -> S if S has OrderedSet

from HomogeneousAggregate(S)

minColIndex : % -> Integer

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

minRowIndex : % -> Integer

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

minordet : % -> S if S has AbelianMonoid and S has CommutativeRing

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

more? : (%, NonNegativeInteger) -> Boolean

from Aggregate

ncols : % -> NonNegativeInteger

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

nrows : % -> NonNegativeInteger

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

nullSpace : % -> List(PrimitiveArray(S)) if S has AbelianMonoid and S has IntegralDomain

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

nullity : % -> NonNegativeInteger if S has AbelianMonoid and S has IntegralDomain

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

parts : % -> List(S)

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

positivePower : (%, Integer) -> % if S has AbelianMonoid and S has SemiRng

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

qnew : (NonNegativeInteger, NonNegativeInteger) -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

rank : % -> NonNegativeInteger if S has AbelianMonoid and S has IntegralDomain

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

row : (%, Integer) -> PrimitiveArray(S)

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

rowEchelon : % -> % if S has AbelianMonoid and S has EuclideanDomain

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

rowSlice : % -> Segment(Integer)

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

sample : () -> %

from Aggregate

scalarMatrix : (NonNegativeInteger, S) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

setColumn! : (%, Integer, PrimitiveArray(S)) -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

setRow! : (%, Integer, PrimitiveArray(S)) -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

size? : (%, NonNegativeInteger) -> Boolean

from Aggregate

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

from Comparable

square? : % -> Boolean if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

squareTop : % -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

symmetric? : % -> Boolean if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

transpose : % -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

transpose : PrimitiveArray(S) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

vertConcat : (%, %) -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

vertConcat : List(%) -> %

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

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

from TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

zero : (NonNegativeInteger, NonNegativeInteger) -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

zero? : % -> Boolean if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

~= : (%, %) -> Boolean if S has BasicType

from BasicType

Comparable

MatrixCategory(S, PrimitiveArray(S), PrimitiveArray(S))

TwoDimensionalArrayCategory(S, PrimitiveArray(S), PrimitiveArray(S))

shallowlyMutable

Aggregate

BasicType

InnerEvalable(S, S)

SetCategory

HomogeneousAggregate(S)

Evalable(S)

CoercibleTo(OutputForm)

Hashable

finiteAggregate