diff options
Diffstat (limited to 'src/algebra/array2.spad.pamphlet')
| -rw-r--r-- | src/algebra/array2.spad.pamphlet | 68 |
1 files changed, 20 insertions, 48 deletions
diff --git a/src/algebra/array2.spad.pamphlet b/src/algebra/array2.spad.pamphlet index b21179d5..17fd3a3f 100644 --- a/src/algebra/array2.spad.pamphlet +++ b/src/algebra/array2.spad.pamphlet @@ -32,24 +32,17 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where R : Type Row : FiniteLinearAggregate R Col : FiniteLinearAggregate R - Definition == HomogeneousAggregate(R) with - shallowlyMutable ++ one may destructively alter arrays - finiteAggregate ++ two-dimensional arrays are finite - --% Array creation - new: (NonNegativeInteger,NonNegativeInteger,R) -> % ++ new(m,n,r) is an m-by-n array all of whose entries are r fill!: (%,R) -> % ++ fill!(m,r) fills m with r's - --% Size inquiries - minRowIndex : % -> Integer ++ minRowIndex(m) returns the index of the 'first' row of the array m maxRowIndex : % -> Integer @@ -62,9 +55,7 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where ++ nrows(m) returns the number of rows in the array m ncols : % -> NonNegativeInteger ++ ncols(m) returns the number of columns in the array m - --% Part extractions - elt: (%,Integer,Integer) -> R ++ elt(m,i,j) returns the element in the ith row and jth ++ column of the array m @@ -85,9 +76,7 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where ++ error check to determine if index is in proper ranges parts: % -> List R ++ parts(m) returns a list of the elements of m in row major order - --% Part assignments - setelt: (%,Integer,Integer,R) -> R -- will become setelt! ++ setelt(m,i,j,r) sets the element in the ith row and jth @@ -101,9 +90,7 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where ++ setRow!(m,i,v) sets to ith row of m to v setColumn!: (%,Integer,Col) -> % ++ setColumn!(m,j,v) sets to jth column of m to v - --% Map and Zip - map: (R -> R,%) -> % ++ map(f,a) returns \spad{b}, where \spad{b(i,j) = f(a(i,j))} for all \spad{i, j} map!: (R -> R,%) -> % @@ -117,11 +104,8 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where ++ else \spad{c(i,j) = f(r, b(i,j))} when \spad{a(i,j)} does not exist; ++ else \spad{c(i,j) = f(a(i,j),r)} when \spad{b(i,j)} does not exist; ++ otherwise \spad{c(i,j) = f(r,r)}. - add - --% Predicates - any?(f,m) == for i in minRowIndex(m)..maxRowIndex(m) repeat for j in minColIndex(m)..maxColIndex(m) repeat @@ -135,11 +119,9 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where true --% Size inquiries - # m == nrows(m) * ncols(m) --% Part extractions - elt(m,i,j,r) == i < minRowIndex(m) or i > maxRowIndex(m) => r j < minColIndex(m) or j > maxColIndex(m) => r @@ -289,29 +271,26 @@ InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col):_ Row : FiniteLinearAggregate R Col : FiniteLinearAggregate R - Exports ==> TwoDimensionalArrayCategory(R,Row,Col) - - Implementation ==> add - - Rep := PrimitiveArray PrimitiveArray R + Exports == TwoDimensionalArrayCategory(R,Row,Col) + Implementation == PrimitiveArray PrimitiveArray R add --% Predicates - empty? m == empty?(m)$Rep + empty? m == empty? rep m --% Primitive array creation - empty() == empty()$Rep + empty() == per empty()$Rep new(rows,cols,a) == rows = 0 => error "new: arrays with zero rows are not supported" -- cols = 0 => -- error "new: arrays with zero columns are not supported" - arr : PrimitiveArray PrimitiveArray R := new(rows,empty()) - for i in minIndex(arr)..maxIndex(arr) repeat - qsetelt!(arr,i,new(cols,a)) - arr + arr : Rep := new(rows,empty()) + for i in 0..rows-1 repeat + arr.i := new(cols,a) + per arr --% Size inquiries @@ -319,17 +298,15 @@ InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col):_ minColIndex m == mnCol maxRowIndex m == nrows m + mnRow - 1 maxColIndex m == ncols m + mnCol - 1 - - nrows m == (# m)$Rep - + nrows m == # rep m ncols m == empty? m => 0 - # m(minIndex(m)$Rep) + # rep(m)(minIndex rep m) --% Part selection/assignment qelt(m,i,j) == - qelt(qelt(m,i - minRowIndex m)$Rep,j - minColIndex m) + qelt(qelt(rep m,i - minRowIndex m),j - minColIndex m) elt(m:%,i:Integer,j:Integer) == i < minRowIndex(m) or i > maxRowIndex(m) => @@ -339,7 +316,7 @@ InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col):_ qelt(m,i,j) qsetelt!(m,i,j,r) == - setelt(qelt(m,i - minRowIndex m)$Rep,j - minColIndex m,r) + setelt(qelt(rep m,i - minRowIndex m),j - minColIndex m,r) setelt(m:%,i:Integer,j:Integer,r:R) == i < minRowIndex(m) or i > maxRowIndex(m) => @@ -377,13 +354,10 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where ++ first column in an array and vice versa. R : Type mnRow, mnCol : Integer - Row ==> IndexedOneDimensionalArray(R,mnCol) - Col ==> IndexedOneDimensionalArray(R,mnRow) - - Exports ==> TwoDimensionalArrayCategory(R,Row,Col) - - Implementation ==> - InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col) + macro Row == IndexedOneDimensionalArray(R,mnCol) + macro Col == IndexedOneDimensionalArray(R,mnRow) + Exports == TwoDimensionalArrayCategory(R,Row,Col) + Implementation == InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col) @ \section{domain ARRAY2 TwoDimensionalArray} @@ -393,14 +367,12 @@ TwoDimensionalArray(R):Exports == Implementation where ++ A TwoDimensionalArray is a two dimensional array with ++ 1-based indexing for both rows and columns. R : Type - Row ==> OneDimensionalArray R - Col ==> OneDimensionalArray R - - Exports ==> TwoDimensionalArrayCategory(R,Row,Col) with + macro Row == OneDimensionalArray R + macro Col == OneDimensionalArray R + Exports == TwoDimensionalArrayCategory(R,Row,Col) with shallowlyMutable ++ One may destructively alter TwoDimensionalArray's. - - Implementation ==> InnerIndexedTwoDimensionalArray(R,1,1,Row,Col) + Implementation == InnerIndexedTwoDimensionalArray(R,1,1,Row,Col) @ \section{License} |