Data update
This commit is contained in:
Ingy döt Net
parent
52a6ef48dd
commit
157b70a810
604 changed files with 14253 additions and 2100 deletions
204
Task/Strassens-algorithm/FreeBASIC/strassens-algorithm.basic
Normal file
204
Task/Strassens-algorithm/FreeBASIC/strassens-algorithm.basic
Normal file
|
|
@ -0,0 +1,204 @@
|
|||
Type Matrix
|
||||
As Integer rows
|
||||
As Integer cols
|
||||
As Double dato(Any)
|
||||
End Type
|
||||
|
||||
Function makeMatrix(rows As Integer, cols As Integer) As Matrix
|
||||
Dim As Matrix m
|
||||
m.rows = rows
|
||||
m.cols = cols
|
||||
Redim m.dato(rows * cols - 1)
|
||||
Return m
|
||||
End Function
|
||||
|
||||
Function matrixAdd(m1 As Matrix, m2 As Matrix) As Matrix
|
||||
If m1.rows <> m2.rows Or m1.cols <> m2.cols Then
|
||||
Print "Matrices must have the same dimensions."
|
||||
End
|
||||
End If
|
||||
|
||||
Dim As Matrix result = makeMatrix(m1.rows, m1.cols)
|
||||
For i As Integer = 0 To m1.rows * m1.cols - 1
|
||||
result.dato(i) = m1.dato(i) + m2.dato(i)
|
||||
Next
|
||||
Return result
|
||||
End Function
|
||||
|
||||
Function matrixSub(m1 As Matrix, m2 As Matrix) As Matrix
|
||||
If m1.rows <> m2.rows Or m1.cols <> m2.cols Then
|
||||
Print "Matrices must have the same dimensions."
|
||||
End
|
||||
End If
|
||||
|
||||
Dim As Matrix result = makeMatrix(m1.rows, m1.cols)
|
||||
For i As Integer = 0 To m1.rows * m1.cols - 1
|
||||
result.dato(i) = m1.dato(i) - m2.dato(i)
|
||||
Next
|
||||
Return result
|
||||
End Function
|
||||
|
||||
Function matrixMul(m1 As Matrix, m2 As Matrix) As Matrix
|
||||
If m1.cols <> m2.rows Then
|
||||
Print "Cannot multiply these matrices."
|
||||
End
|
||||
End If
|
||||
|
||||
Dim As Integer i, j, k
|
||||
Dim As Matrix result = makeMatrix(m1.rows, m2.cols)
|
||||
For i = 0 To m1.rows - 1
|
||||
For j = 0 To m2.cols - 1
|
||||
Dim As Double sum = 0
|
||||
For k = 0 To m1.cols - 1
|
||||
sum += m1.dato(i * m1.cols + k) * m2.dato(k * m2.cols + j)
|
||||
Next
|
||||
result.dato(i * result.cols + j) = sum
|
||||
Next
|
||||
Next
|
||||
Return result
|
||||
End Function
|
||||
|
||||
Sub printMatrix(m As Matrix, precision As Integer = 6)
|
||||
Dim As Integer i, j
|
||||
Print "[[";
|
||||
For i = 0 To m.rows - 1
|
||||
If i > 0 Then Print " [";
|
||||
For j = 0 To m.cols - 1
|
||||
Dim As Double valor = m.dato(i * m.cols + j)
|
||||
valor = Int(valor * (10 ^ precision) + 0.5) / (10 ^ precision)
|
||||
If Abs(valor) < 1e-10 Then valor = 0
|
||||
Print Using "&"; valor;
|
||||
If j < m.cols - 1 Then Print " ";
|
||||
Next
|
||||
If i < m.rows - 1 Then Print "]";
|
||||
Next
|
||||
Print "]]"
|
||||
End Sub
|
||||
|
||||
Function getQuarter(m As Matrix, quarter As Integer) As Matrix
|
||||
Dim As Integer i, j
|
||||
Dim As Integer halfRows, halfCols
|
||||
halfRows = m.rows \ 2
|
||||
halfCols = m.cols \ 2
|
||||
Dim As Matrix result = makeMatrix(halfRows, halfCols)
|
||||
|
||||
Dim As Integer rowOffset, colOffset
|
||||
rowOffset = (quarter \ 2) * halfRows
|
||||
colOffset = (quarter Mod 2) * halfCols
|
||||
|
||||
For i = 0 To halfRows - 1
|
||||
For j = 0 To halfCols - 1
|
||||
result.dato(i * halfCols + j) = m.dato((i + rowOffset) * m.cols + j + colOffset)
|
||||
Next
|
||||
Next
|
||||
Return result
|
||||
End Function
|
||||
|
||||
Function combineQuarters(q1 As Matrix, q2 As Matrix, q3 As Matrix, q4 As Matrix) As Matrix
|
||||
Dim As Integer i, j, n
|
||||
n = q1.rows
|
||||
Dim As Matrix result = makeMatrix(n * 2, n * 2)
|
||||
|
||||
For i = 0 To n - 1
|
||||
For j = 0 To n - 1
|
||||
result.dato(i * result.cols + j) = q1.dato(i * n + j)
|
||||
result.dato(i * result.cols + j + n) = q2.dato(i * n + j)
|
||||
result.dato((i + n) * result.cols + j) = q3.dato(i * n + j)
|
||||
result.dato((i + n) * result.cols + j + n) = q4.dato(i * n + j)
|
||||
Next
|
||||
Next
|
||||
Return result
|
||||
End Function
|
||||
|
||||
Function strassen(a As Matrix, b As Matrix) As Matrix
|
||||
If a.rows <> a.cols Or b.rows <> b.cols Or a.rows <> b.rows Then
|
||||
Print "Matrices must be square and of equal size."
|
||||
End
|
||||
End If
|
||||
|
||||
If a.rows = 1 Then Return matrixMul(a, b)
|
||||
|
||||
Dim As Matrix a11 = getQuarter(a, 0)
|
||||
Dim As Matrix a12 = getQuarter(a, 1)
|
||||
Dim As Matrix a21 = getQuarter(a, 2)
|
||||
Dim As Matrix a22 = getQuarter(a, 3)
|
||||
Dim As Matrix b11 = getQuarter(b, 0)
|
||||
Dim As Matrix b12 = getQuarter(b, 1)
|
||||
Dim As Matrix b21 = getQuarter(b, 2)
|
||||
Dim As Matrix b22 = getQuarter(b, 3)
|
||||
|
||||
Dim As Matrix p1 = strassen(matrixSub(a12, a22), matrixAdd(b21, b22))
|
||||
Dim As Matrix p2 = strassen(matrixAdd(a11, a22), matrixAdd(b11, b22))
|
||||
Dim As Matrix p3 = strassen(matrixSub(a11, a21), matrixAdd(b11, b12))
|
||||
Dim As Matrix p4 = strassen(matrixAdd(a11, a12), b22)
|
||||
Dim As Matrix p5 = strassen(a11, matrixSub(b12, b22))
|
||||
Dim As Matrix p6 = strassen(a22, matrixSub(b21, b11))
|
||||
Dim As Matrix p7 = strassen(matrixAdd(a21, a22), b11)
|
||||
|
||||
Dim As Matrix c11 = matrixAdd(matrixSub(matrixAdd(p1, p2), p4), p6)
|
||||
Dim As Matrix c12 = matrixAdd(p4, p5)
|
||||
Dim As Matrix c21 = matrixAdd(p6, p7)
|
||||
Dim As Matrix c22 = matrixSub(matrixAdd(matrixSub(p2, p3), p5), p7)
|
||||
|
||||
Return combineQuarters(c11, c12, c21, c22)
|
||||
End Function
|
||||
|
||||
Sub main()
|
||||
' Matrix A (2x2)
|
||||
Dim As Matrix a = makeMatrix(2, 2)
|
||||
a.dato(0) = 1: a.dato(1) = 2
|
||||
a.dato(2) = 3: a.dato(3) = 4
|
||||
|
||||
' Matrix B (2x2)
|
||||
Dim As Matrix b = makeMatrix(2, 2)
|
||||
b.dato(0) = 5: b.dato(1) = 6
|
||||
b.dato(2) = 7: b.dato(3) = 8
|
||||
|
||||
' Matrix C (4x4)
|
||||
Dim As Matrix c = makeMatrix(4, 4)
|
||||
c.dato(0) = 1: c.dato(1) = 1: c.dato(2) = 1: c.dato(3) = 1
|
||||
c.dato(4) = 2: c.dato(5) = 4: c.dato(6) = 8: c.dato(7) = 16
|
||||
c.dato(8) = 3: c.dato(9) = 9: c.dato(10) = 27: c.dato(11) = 81
|
||||
c.dato(12) = 4: c.dato(13) = 16: c.dato(14) = 64: c.dato(15) = 256
|
||||
|
||||
' Matrix D (4x4)
|
||||
Dim As Matrix d = makeMatrix(4, 4)
|
||||
d.dato(0) = 4: d.dato(1) = -3: d.dato(2) = 4/3: d.dato(3) = -1/4
|
||||
d.dato(4) = -13/3: d.dato(5) = 19/4: d.dato(6) = -7/3: d.dato(7) = 11/24
|
||||
d.dato(8) = 3/2: d.dato(9) = -2: d.dato(10) = 7/6: d.dato(11) = -1/4
|
||||
d.dato(12) = -1/6: d.dato(13) = 1/4: d.dato(14) = -1/6: d.dato(15) = 1/24
|
||||
|
||||
' Matrix E (4x4)
|
||||
Dim As Matrix e = makeMatrix(4, 4)
|
||||
e.dato(0) = 1: e.dato(1) = 2: e.dato(2) = 3: e.dato(3) = 4
|
||||
e.dato(4) = 5: e.dato(5) = 6: e.dato(6) = 7: e.dato(7) = 8
|
||||
e.dato(8) = 9: e.dato(9) = 10: e.dato(10) = 11: e.dato(11) = 12
|
||||
e.dato(12) = 13: e.dato(13) = 14: e.dato(14) = 15: e.dato(15) = 16
|
||||
|
||||
' Matrix F (Identity 4x4)
|
||||
Dim As Matrix f = makeMatrix(4, 4)
|
||||
f.dato(0) = 1: f.dato(1) = 0: f.dato(2) = 0: f.dato(3) = 0
|
||||
f.dato(4) = 0: f.dato(5) = 1: f.dato(6) = 0: f.dato(7) = 0
|
||||
f.dato(8) = 0: f.dato(9) = 0: f.dato(10) = 1: f.dato(11) = 0
|
||||
f.dato(12) = 0: f.dato(13) = 0: f.dato(14) = 0: f.dato(15) = 1
|
||||
|
||||
Print "Using 'normal' matrix multiplication:"
|
||||
Print " a * b = ";
|
||||
printMatrix(matrixMul(a, b))
|
||||
Print " c * d = ";
|
||||
printMatrix(matrixMul(c, d), 6)
|
||||
Print " e * f = ";
|
||||
printMatrix(matrixMul(e, f))
|
||||
|
||||
Print !"\nUsing 'Strassen' matrix multiplication:"
|
||||
Print " a * b = ";
|
||||
printMatrix(strassen(a, b))
|
||||
Print " c * d = ";
|
||||
printMatrix(strassen(c, d), 6)
|
||||
Print " e * f = ";
|
||||
printMatrix(strassen(e, f))
|
||||
End Sub
|
||||
|
||||
main()
|
||||
|
||||
Sleep
|
||||
113
Task/Strassens-algorithm/Jq/strassens-algorithm.jq
Normal file
113
Task/Strassens-algorithm/Jq/strassens-algorithm.jq
Normal file
|
|
@ -0,0 +1,113 @@
|
|||
### Generic utilities
|
||||
def sigma(stream): reduce stream as $x (0; . + $x);
|
||||
|
||||
# Hilbert-Schmidt norm:
|
||||
def frobenius:
|
||||
sigma( flatten[] | .*. ) | sqrt;
|
||||
|
||||
### Matrices
|
||||
# Create an m x n matrix
|
||||
def matrix(m; n; init):
|
||||
if m == 0 then []
|
||||
elif m == 1 then [[range(0;n) | init]]
|
||||
elif m > 0 then
|
||||
matrix(1;n;init) as $row
|
||||
| [range(0;m) | $row ]
|
||||
else error("matrix\(m);_;_) invalid")
|
||||
end;
|
||||
|
||||
# A and B must be (multi-dimensional) vectors of the same shape
|
||||
def vector_add($A;$B):
|
||||
if ($A|type) == "array"
|
||||
then reduce range(0; $A|length) as $i ([];
|
||||
. + [vector_add($A[$i]; $B[$i])] )
|
||||
else $A + $B
|
||||
end;
|
||||
|
||||
def vector_negate:
|
||||
if type == "array"
|
||||
then map(vector_negate)
|
||||
else - .
|
||||
end;
|
||||
|
||||
def vector_subtract($A;$B):
|
||||
vector_add($A; $B|vector_negate);
|
||||
|
||||
# A should be m by n; and B n by p
|
||||
# Pre-allocating the resultant matrix results in a very small net speedup.
|
||||
def multiply($A; $B):
|
||||
($A|length) as $m
|
||||
| ($A[0]|length) as $n
|
||||
| ($B[0]|length) as $p
|
||||
| reduce range(0; $m) as $i
|
||||
(matrix($m; $p; 0); # initialize to avoid resizing
|
||||
reduce range(0;$p) as $j (.;
|
||||
.[$i][$j] = reduce range(0;$n) as $k
|
||||
(0;
|
||||
# Cij = innerproduct of row i, column j
|
||||
. + $A[$i][$k] * $B[$k][$j] ))) ;
|
||||
|
||||
def submatrix($m1; $m2; $n1; $n2):
|
||||
.[$m1:$m2] | map( .[$n1:$n2]);
|
||||
|
||||
def submatrix($A; $m1; $m2; $n1; $n2):
|
||||
$A | submatrix($m1; $m2; $n1; $n2);
|
||||
|
||||
def rowwise_extend($A;$B):
|
||||
reduce range(0; $A|length) as $i ([]; . + [$A[$i] + $B[$i]]);
|
||||
|
||||
### Strassen multiplication of n*n square matrices where n is a power of 2.
|
||||
def Strassen($A; $B):
|
||||
($A[0]|length) as $n
|
||||
| if $n == 1 then multiply($A; $B)
|
||||
else
|
||||
submatrix($A; 0; $n/2; 0; $n/2) as $A11
|
||||
| submatrix($A; 0; $n/2; $n/2; $n) as $A12
|
||||
| submatrix($A; $n/2; $n; 0; $n/2) as $A21
|
||||
| submatrix($A; $n/2; $n; $n/2; $n) as $A22
|
||||
| submatrix($B; 0; $n/2; 0; $n/2) as $B11
|
||||
| submatrix($B; 0; $n/2; $n/2; $n) as $B12
|
||||
| submatrix($B; $n/2; $n; 0; $n/2) as $B21
|
||||
| submatrix($B; $n/2; $n; $n/2+0; $n) as $B22
|
||||
|
||||
| Strassen( vector_subtract($A12; $A22); vector_add($B21; $B22)) as $P1
|
||||
| Strassen( vector_add($A11; $A22); vector_add($B11; $B22)) as $P2
|
||||
| Strassen( vector_subtract($A11; $A21); vector_add($B11; $B12)) as $P3
|
||||
| Strassen( vector_add($A11; $A12); $B22) as $P4
|
||||
| Strassen( $A11; vector_subtract($B12; $B22)) as $P5
|
||||
| Strassen( $A22; vector_subtract($B21; $B11) ) as $P6
|
||||
| Strassen( vector_add($A21; $A22); $B11) as $P7
|
||||
|
||||
| vector_add(vector_subtract(vector_add($P1; $P2); $P4); $P6) as $C11
|
||||
| vector_add($P4; $P5) as $C12
|
||||
| vector_add($P6; $P7) as $C21
|
||||
| vector_add(vector_subtract($P2; $P3); vector_subtract($P5;$P7)) as $C22
|
||||
# [C11 C12; C21 C22]
|
||||
| rowwise_extend($C11; $C12) + rowwise_extend($C21; $C22)
|
||||
end
|
||||
;
|
||||
|
||||
# ## Examples
|
||||
def A: [[1, 2], [3, 4]];
|
||||
def B: [[5, 6], [7, 8]];
|
||||
def C: [[1, 1, 1, 1],
|
||||
[2, 4, 8, 16],
|
||||
[3, 9, 27, 81],
|
||||
[4, 16, 64, 256]];
|
||||
def D: [[4, -3, 4/3, -1/4],
|
||||
[-13/3, 19/4, -7/3, 11/24],
|
||||
[3/2, -2, 7/6, -1/4],
|
||||
[-1/6, 1/4, -1/6, 1/24]];
|
||||
def E: [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]];
|
||||
def F: [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [ 0, 0, 0, 1]];
|
||||
|
||||
def r: (2|sqrt)/2;
|
||||
def R: [[r, r], [-r, r]];
|
||||
|
||||
"A*B == Strassen(A;B): \((multiply(A; B) == Strassen(A; B)))",
|
||||
|
||||
"Frobenius norm for C*D - Strassen(C;D): \(vector_subtract(multiply(C; D); Strassen(C; D)) | frobenius)",
|
||||
|
||||
"E*F == Strassen(E;F): \(multiply(E; F) == Strassen( E; F))",
|
||||
|
||||
"R*R == Strassen(R;R): \(multiply(R ; R) == Strassen(R; R))"
|
||||
Loading…
Add table
Add a link
Reference in a new issue