/usr/share/axiom-20170501/src/algebra/MATSTOR.spad is in axiom-source 20170501-3.
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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 | )abbrev package MATSTOR StorageEfficientMatrixOperations
++ Author: Clifton J. Williamson
++ Date Created: 18 July 1990
++ Date Last Updated: 18 July 1990
++ Description:
++ This package provides standard arithmetic operations on matrices.
++ The functions in this package store the results of computations
++ in existing matrices, rather than creating new matrices. This
++ package works only for matrices of type Matrix and uses the
++ internal representation of this type.
StorageEfficientMatrixOperations(R) : SIG == CODE where
R : Ring
M ==> Matrix R
NNI ==> NonNegativeInteger
ARR ==> PrimitiveArray R
REP ==> PrimitiveArray PrimitiveArray R
SIG ==> with
copy_! : (M,M) -> M
++ \spad{copy!(c,a)} copies the matrix \spad{a} into the matrix c.
++ Error: if \spad{a} and c do not have the same
++ dimensions.
plus_! : (M,M,M) -> M
++ \spad{plus!(c,a,b)} computes the matrix sum \spad{a + b} and stores the
++ result in the matrix c.
++ Error: if \spad{a}, b, and c do not have the same dimensions.
minus_! : (M,M) -> M
++ \spad{minus!(c,a)} computes \spad{-a} and stores the result in the
++ matrix c.
++ Error: if a and c do not have the same dimensions.
minus_! : (M,M,M) -> M
++ \spad{!minus!(c,a,b)} computes the matrix difference \spad{a - b}
++ and stores the result in the matrix c.
++ Error: if \spad{a}, b, and c do not have the same dimensions.
leftScalarTimes_! : (M,R,M) -> M
++ \spad{leftScalarTimes!(c,r,a)} computes the scalar product
++ \spad{r * a} and stores the result in the matrix c.
++ Error: if \spad{a} and c do not have the same dimensions.
rightScalarTimes_! : (M,M,R) -> M
++ \spad{rightScalarTimes!(c,a,r)} computes the scalar product
++ \spad{a * r} and stores the result in the matrix c.
++ Error: if \spad{a} and c do not have the same dimensions.
times_! : (M,M,M) -> M
++ \spad{times!(c,a,b)} computes the matrix product \spad{a * b}
++ and stores the result in the matrix c.
++ Error: if \spad{a}, b, and c do not have
++ compatible dimensions.
power_! : (M,M,M,M,NNI) -> M
++ \spad{power!(a,b,c,m,n)} computes m ** n and stores the result in
++ \spad{a}. The matrices b and c are used to store intermediate results.
++ Error: if \spad{a}, b, c, and m are not square
++ and of the same dimensions.
"**" : (M,NNI) -> M
++ \spad{x ** n} computes the n-th power
++ of a square matrix. The power n is assumed greater than 1.
CODE ==> add
rep : M -> REP
rep m == m pretend REP
copy_!(c,a) ==
m := nrows a; n := ncols a
not((nrows c) = m and (ncols c) = n) =>
error "copy!: matrices of incompatible dimensions"
aa := rep a; cc := rep c
for i in 0..(m-1) repeat
aRow := qelt(aa,i); cRow := qelt(cc,i)
for j in 0..(n-1) repeat
qsetelt_!(cRow,j,qelt(aRow,j))
c
plus_!(c,a,b) ==
m := nrows a; n := ncols a
not((nrows b) = m and (ncols b) = n) =>
error "plus!: matrices of incompatible dimensions"
not((nrows c) = m and (ncols c) = n) =>
error "plus!: matrices of incompatible dimensions"
aa := rep a; bb := rep b; cc := rep c
for i in 0..(m-1) repeat
aRow := qelt(aa,i); bRow := qelt(bb,i); cRow := qelt(cc,i)
for j in 0..(n-1) repeat
qsetelt_!(cRow,j,qelt(aRow,j) + qelt(bRow,j))
c
minus_!(c,a) ==
m := nrows a; n := ncols a
not((nrows c) = m and (ncols c) = n) =>
error "minus!: matrices of incompatible dimensions"
aa := rep a; cc := rep c
for i in 0..(m-1) repeat
aRow := qelt(aa,i); cRow := qelt(cc,i)
for j in 0..(n-1) repeat
qsetelt_!(cRow,j,-qelt(aRow,j))
c
minus_!(c,a,b) ==
m := nrows a; n := ncols a
not((nrows b) = m and (ncols b) = n) =>
error "minus!: matrices of incompatible dimensions"
not((nrows c) = m and (ncols c) = n) =>
error "minus!: matrices of incompatible dimensions"
aa := rep a; bb := rep b; cc := rep c
for i in 0..(m-1) repeat
aRow := qelt(aa,i); bRow := qelt(bb,i); cRow := qelt(cc,i)
for j in 0..(n-1) repeat
qsetelt_!(cRow,j,qelt(aRow,j) - qelt(bRow,j))
c
leftScalarTimes_!(c,r,a) ==
m := nrows a; n := ncols a
not((nrows c) = m and (ncols c) = n) =>
error "leftScalarTimes!: matrices of incompatible dimensions"
aa := rep a; cc := rep c
for i in 0..(m-1) repeat
aRow := qelt(aa,i); cRow := qelt(cc,i)
for j in 0..(n-1) repeat
qsetelt_!(cRow,j,r * qelt(aRow,j))
c
rightScalarTimes_!(c,a,r) ==
m := nrows a; n := ncols a
not((nrows c) = m and (ncols c) = n) =>
error "rightScalarTimes!: matrices of incompatible dimensions"
aa := rep a; cc := rep c
for i in 0..(m-1) repeat
aRow := qelt(aa,i); cRow := qelt(cc,i)
for j in 0..(n-1) repeat
qsetelt_!(cRow,j,qelt(aRow,j) * r)
c
copyCol_!: (ARR,REP,Integer,Integer) -> ARR
copyCol_!(bCol,bb,j,n1) ==
for i in 0..n1 repeat qsetelt_!(bCol,i,qelt(qelt(bb,i),j))
times_!(c,a,b) ==
m := nrows a; n := ncols a; p := ncols b
not((nrows b) = n and (nrows c) = m and (ncols c) = p) =>
error "times!: matrices of incompatible dimensions"
aa := rep a; bb := rep b; cc := rep c
bCol : ARR := new(n,0)
m1 := (m :: Integer) - 1; n1 := (n :: Integer) - 1
for j in 0..(p-1) repeat
copyCol_!(bCol,bb,j,n1)
for i in 0..m1 repeat
aRow := qelt(aa,i); cRow := qelt(cc,i)
sum : R := 0
for k in 0..n1 repeat
sum := sum + qelt(aRow,k) * qelt(bCol,k)
qsetelt_!(cRow,j,sum)
c
power_!(a,b,c,m,p) ==
mm := nrows a; nn := ncols a
not(mm = nn) =>
error "power!: matrix must be square"
not((nrows b) = mm and (ncols b) = nn) =>
error "power!: matrices of incompatible dimensions"
not((nrows c) = mm and (ncols c) = nn) =>
error "power!: matrices of incompatible dimensions"
not((nrows m) = mm and (ncols m) = nn) =>
error "power!: matrices of incompatible dimensions"
flag := false
copy_!(b,m)
repeat
if odd? p then
flag =>
times_!(c,b,a)
copy_!(a,c)
flag := true
copy_!(a,b)
(p = 1) => return a
p := p quo 2
times_!(c,b,b)
copy_!(b,c)
m ** n ==
not square? m => error "**: matrix must be square"
a := copy m; b := copy m; c := copy m
power_!(a,b,c,m,n)
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