/usr/share/axiom-20170501/src/algebra/M3D.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 | )abbrev domain M3D ThreeDimensionalMatrix
++ Author: William Naylor
++ Date Created: 20 October 1993
++ Date Last Updated: 20 May 1994
++ Description:
++ This domain represents three dimensional matrices over a general object type
ThreeDimensionalMatrix(R) : SIG == CODE where
R : SetCategory
L ==> List
NNI ==> NonNegativeInteger
A1AGG ==> OneDimensionalArrayAggregate
ARRAY1 ==> OneDimensionalArray
PA ==> PrimitiveArray
INT ==> Integer
PI ==> PositiveInteger
SIG ==> HomogeneousAggregate(R) with
if R has Ring then
zeroMatrix : (NNI,NNI,NNI) -> $
++ zeroMatrix(i,j,k) create a matrix with all zero terms
identityMatrix : (NNI) -> $
++ identityMatrix(n) create an identity matrix
++ we note that this must be square
plus : ($,$) -> $
++ plus(x,y) adds two matrices, term by term
++ we note that they must be the same size
construct : (L L L R) -> $
++ construct(lll) creates a 3-D matrix from a List List List R lll
elt : ($,NNI,NNI,NNI) -> R
++ elt(x,i,j,k) extract an element from the matrix x
setelt! : ($,NNI,NNI,NNI,R) -> R
++ setelt!(x,i,j,k,s) (or x.i.j.k:=s) sets a specific element
++ of the array to some value of type R
coerce : (PA PA PA R) -> $
++ coerce(p) moves from the representation type
++ (PrimitiveArray PrimitiveArray PrimitiveArray R) to the domain
coerce : $ -> (PA PA PA R)
++ coerce(x) moves from the domain to the representation type
matrixConcat3D : (Symbol,$,$) -> $
++ matrixConcat3D(s,x,y) concatenates two 3-D matrices
++along a specified axis
matrixDimensions : $ -> Vector NNI
++ matrixDimensions(x) returns the dimensions of a matrix
CODE ==> (PA PA PA R) add
import (PA PA PA R)
import (PA PA R)
import (PA R)
import R
matrix1,matrix2,resultMatrix : $
-- function to concatenate two matrices
-- the first argument must be a symbol, which is either i,j or k
-- to specify the direction in which the concatenation is to take place
matrixConcat3D(dir : Symbol,mat1 : $,mat2 : $) : $ ==
^((dir = (i::Symbol)) or (dir = (j::Symbol)) or (dir = (k::Symbol)))_
=> error "the axis of concatenation must be i,j or k"
mat1Dim := matrixDimensions(mat1)
mat2Dim := matrixDimensions(mat2)
iDim1 := mat1Dim.1
jDim1 := mat1Dim.2
kDim1 := mat1Dim.3
iDim2 := mat2Dim.1
jDim2 := mat2Dim.2
kDim2 := mat2Dim.3
matRep1 : (PA PA PA R) := copy(mat1 :: (PA PA PA R))$(PA PA PA R)
matRep2 : (PA PA PA R) := copy(mat2 :: (PA PA PA R))$(PA PA PA R)
retVal : $
if (dir = (i::Symbol)) then
-- j,k dimensions must agree
if (^((jDim1 = jDim2) and (kDim1=kDim2)))
then
error "jxk do not agree"
else
retVal := (coerce(concat(matRep1,matRep2)$(PA PA PA R))$$)@$
if (dir = (j::Symbol)) then
-- i,k dimensions must agree
if (^((iDim1 = iDim2) and (kDim1=kDim2)))
then
error "ixk do not agree"
else
for i in 0..(iDim1-1) repeat
setelt(matRep1,i,(concat(elt(matRep1,i)$(PA PA PA R)_
,elt(matRep2,i)$(PA PA PA R))$(PA PA R))@(PA PA R))$(PA PA PA R)
retVal := (coerce(matRep1)$$)@$
if (dir = (k::Symbol)) then
temp : (PA PA R)
-- i,j dimensions must agree
if (^((iDim1 = iDim2) and (jDim1=jDim2)))
then
error "ixj do not agree"
else
for i in 0..(iDim1-1) repeat
temp := copy(elt(matRep1,i)$(PA PA PA R))$(PA PA R)
for j in 0..(jDim1-1) repeat
setelt(temp,j,concat(elt(elt(matRep1,i)$(PA PA PA R)_
,j)$(PA PA R),elt(elt(matRep2,i)$(PA PA PA R),j)$(PA PA R)_
)$(PA R))$(PA PA R)
setelt(matRep1,i,temp)$(PA PA PA R)
retVal := (coerce(matRep1)$$)@$
retVal
matrixDimensions(mat : $) : Vector NNI ==
matRep : (PA PA PA R) := mat :: (PA PA PA R)
iDim : NNI := (#matRep)$(PA PA PA R)
matRep2 : PA PA R := elt(matRep,0)$(PA PA PA R)
jDim : NNI := (#matRep2)$(PA PA R)
matRep3 : (PA R) := elt(matRep2,0)$(PA PA R)
kDim : NNI := (#matRep3)$(PA R)
retVal : Vector NNI := new(3,0)$(Vector NNI)
retVal.1 := iDim
retVal.2 := jDim
retVal.3 := kDim
retVal
coerce(matrixRep : (PA PA PA R)) : $ == matrixRep pretend $
coerce(mat : $) : (PA PA PA R) == mat pretend (PA PA PA R)
-- i,j,k must be with in the bounds of the matrix
elt(mat : $,i : NNI,j : NNI,k : NNI) : R ==
matDims := matrixDimensions(mat)
iLength := matDims.1
jLength := matDims.2
kLength := matDims.3
((i > iLength) or (j > jLength) or (k > kLength) or (i=0) _
or (j=0) or (k=0)) => _
error "coordinates must be within the bounds of the matrix"
matrixRep : PA PA PA R := mat :: (PA PA PA R)
elt(elt(elt(matrixRep,i-1)$(PA PA PA R),j-1)$(PA PA R),k-1)$(PA R)
setelt!(mat : $,i : NNI,j : NNI,k : NNI,val : R)_
: R ==
matDims := matrixDimensions(mat)
iLength := matDims.1
jLength := matDims.2
kLength := matDims.3
((i > iLength) or (j > jLength) or (k > kLength) or (i=0) _
or (j=0) or (k=0)) => _
error "coordinates must be within the bounds of the matrix"
matrixRep : PA PA PA R := mat :: (PA PA PA R)
row2 : PA PA R := copy(elt(matrixRep,i-1)$(PA PA PA R))$(PA PA R)
row1 : PA R := copy(elt(row2,j-1)$(PA PA R))$(PA R)
setelt(row1,k-1,val)$(PA R)
setelt(row2,j-1,row1)$(PA PA R)
setelt(matrixRep,i-1,row2)$(PA PA PA R)
val
if R has Ring then
zeroMatrix(iLength:NNI,jLength:NNI,kLength:NNI) : $ ==
(new(iLength,_
new(jLength,_
new(kLength,(0$R))$(PA R))$(PA PA R))$(PA PA PA R)) :: $
identityMatrix(iLength:NNI) : $ ==
retValueRep : PA PA PA R := _
zeroMatrix(iLength,iLength,iLength)$$ :: (PA PA PA R)
row1 : PA R
row2 : PA PA R
row1empty : PA R := new(iLength,0$R)$(PA R)
row2empty : PA PA R := new(iLength,copy(row1empty)$(PA R))$(PA PA R)
for count in 0..(iLength-1) repeat
row1 := copy(row1empty)$(PA R)
setelt(row1,count,1$R)$(PA R)
row2 := copy(row2empty)$(PA PA R)
setelt(row2,count,copy(row1)$(PA R))$(PA PA R)
setelt(retValueRep,count,copy(row2)$(PA PA R))$(PA PA PA R)
retValueRep :: $
plus(mat1 : $,mat2 :$) : $ ==
mat1Dims := matrixDimensions(mat1)
iLength1 := mat1Dims.1
jLength1 := mat1Dims.2
kLength1 := mat1Dims.3
mat2Dims := matrixDimensions(mat2)
iLength2 := mat2Dims.1
jLength2 := mat2Dims.2
kLength2 := mat2Dims.3
-- check that the dimensions are the same
(^(iLength1 = iLength2) or ^(jLength1 = jLength2) _
or ^(kLength1 = kLength2))_
=> error "error the matrices are different sizes"
sum : R
row1 : (PA R) := new(kLength1,0$R)$(PA R)
row2 : (PA PA R) := new(jLength1,copy(row1)$(PA R))$(PA PA R)
row3 : (PA PA PA R) := new(iLength1,copy(row2)$(PA PA R))$(PA PA PA R)
for i in 1..iLength1 repeat
for j in 1..jLength1 repeat
for k in 1..kLength1 repeat
sum := (elt(mat1,i,j,k)::R +$R_
elt(mat2,i,j,k)::R)
setelt(row1,k-1,sum)$(PA R)
setelt(row2,j-1,copy(row1)$(PA R))$(PA PA R)
setelt(row3,i-1,copy(row2)$(PA PA R))$(PA PA PA R)
resultMatrix := (row3 pretend $)
resultMatrix
construct(listRep : L L L R) : $ ==
(#listRep)$(L L L R) = 0 => error "empty list"
(#(listRep.1))$(L L R) = 0 => error "empty list"
(#((listRep.1).1))$(L R) = 0 => error "empty list"
iLength := (#listRep)$(L L L R)
jLength := (#(listRep.1))$(L L R)
kLength := (#((listRep.1).1))$(L R)
--first check that the matrix is in the correct form
for subList in listRep repeat
^((#subList)$(L L R) = jLength) => error_
"can not have an irregular shaped matrix"
for subSubList in subList repeat
^((#(subSubList))$(L R) = kLength) => error_
"can not have an irregular shaped matrix"
row1 : (PA R) := new(kLength,((listRep.1).1).1)$(PA R)
row2 : (PA PA R) := new(jLength,copy(row1)$(PA R))$(PA PA R)
row3 : (PA PA PA R) := new(iLength,copy(row2)$(PA PA R))$(PA PA PA R)
for i in 1..iLength repeat
for j in 1..jLength repeat
for k in 1..kLength repeat
element := elt(elt(elt(listRep,i)$(L L L R),j)$(L L R),k)$(L R)
setelt(row1,k-1,element)$(PA R)
setelt(row2,j-1,copy(row1)$(PA R))$(PA PA R)
setelt(row3,i-1,copy(row2)$(PA PA R))$(PA PA PA R)
resultMatrix := (row3 pretend $)
resultMatrix
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