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)

*: (%, PrimitiveArray S) -> PrimitiveArray 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)

*: (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 Field and S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from BasicType

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

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)

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

from BasicType

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

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

any?: (S -> Boolean, %) -> 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: % -> OutputForm if S has CoercibleTo OutputForm

from CoercibleTo OutputForm

coerce: PrimitiveArray S -> % if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

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 -> Boolean, %) -> NonNegativeInteger

from HomogeneousAggregate S

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

from HomogeneousAggregate S

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

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, Integer) -> S

from TwoDimensionalArrayCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from TwoDimensionalArrayCategory(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)

empty?: % -> Boolean

from Aggregate

empty: () -> %

from Aggregate

eq?: (%, %) -> Boolean

from Aggregate

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

from Evalable S

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

from InnerEvalable(S, S)

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

from HomogeneousAggregate S

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

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 Field and 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)

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)

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

from TwoDimensionalArrayCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from TwoDimensionalArrayCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from TwoDimensionalArrayCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from TwoDimensionalArrayCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

max: % -> S if S has OrderedSet

from HomogeneousAggregate S

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

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

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

minRowIndex: % -> Integer

from TwoDimensionalArrayCategory(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)

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

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

parts: % -> List S

from TwoDimensionalArrayCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from MatrixCategory(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 IntegralDomain and S has AbelianMonoid

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)

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

setRow!: (%, Integer, PrimitiveArray 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?: % -> Boolean if S has AbelianMonoid

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

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

from MatrixCategory(S, PrimitiveArray S, PrimitiveArray S)

Aggregate

BasicType if S has BasicType

CoercibleTo OutputForm if S has CoercibleTo OutputForm

Comparable if S has Comparable

Evalable S if S has Evalable S and S has SetCategory

finiteAggregate

Hashable if S has Hashable

HomogeneousAggregate S

InnerEvalable(S, S) if S has Evalable S and S has SetCategory

MatrixCategory(S, PrimitiveArray S, PrimitiveArray S) if S has AbelianMonoid

SetCategory if S has SetCategory

shallowlyMutable

TwoDimensionalArrayCategory(S, PrimitiveArray S, PrimitiveArray S)