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Alphatensor4x4 and Matmul4x4 bril benchmarks tested against numpy #291

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Alphatensor4x4 and Matmul4x4 bril benchmarks tested against numpy #291

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cd30f59
matmul2x2, but a general matmul exists
Aug 31, 2023
9dac88c
added to benchmark list
Sep 1, 2023
fd91376
python generator for multiple 2x2 bril multiplications, tested with t…
Sep 1, 2023
785e829
bril matmul 4x4 with more matrices, tested
Sep 1, 2023
7c2ad91
alphatensor bril benchmark, tested against numpy
Sep 8, 2023
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106 changes: 106 additions & 0 deletions benchmarks/float/atmulti4x4/at_np_test.py
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# test alpha tensor 4x4 against numpy matmul for correctness

import numpy as np

def main():
# [A,B]
matrices = [
[[8, 3, 2, 4],[2, 7, 4, 5],[0, 1, 2, 3],[0, 1, 2, 3]],
[[1, 2, 3, 4],[5, 6, 7, 8],[9, 10, 11, 12],[13, 14, 15, 16]],
]
A = np.array(matrices[0])
B = np.array(matrices[1])
res_np = np.matmul(A,B)
res_at = at4x4(A,B)
if np.array_equal(res_np, res_at):
print("Arrays equal")
print(res_np)
else:
print("Arrays are not equal")
print("np")
print(res_np)
print("at")
print(res_at)



def at4x4(A,B):
'''Alphatensor Multiply 4-by-4 matrix A with 4-by-4 matrix B, return result C'''

a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41, a42, a43, a44 = A.ravel()
b11, b12, b13, b14, b21, b22, b23, b24, b31, b32, b33, b34, b41, b42, b43, b44 = B.ravel()
h1 = (a11 + a31) * (b11 + b31)
h2 = (a11 - a13 + a31) * (b11 - b13 + b31)
h3 = - a13 * (b11 - b13 + b31 - b33)
h4 = - a33 * - b33
h5 = - a31 * - b13
h6 = (a11 - a13 + a31 - a33) * - b31
h7 = (- a21 + a22 - a23 - a24) * (- b21 + b22 - b23 - b24)
h8 = (- a21 + a22 - a23 - a24 - a41 + a42) * (- b21 + b22 - b23 - b24 - b41 + b42)
h9 = (a11 - a13) * (b11 - b13)
h10 = (- a21 + a22 - a41 + a42) * (- b21 + b22 - b41 + b42)
h11 = (a41 - a42) * (- b23 - b24)
h12 = (- a21 + a22 - a23 - a24 - a41 + a42 - a43 - a44) * (b41 - b42)
h13 = (- a23 - a24) * (- b21 + b22 - b23 - b24 - b41 + b42 - b43 - b44)
h14 = (a11 - a12 + a21 - a22) * (- b12 - b14)
h15 = (- a12 - a14) * - b21
h16 = (a12 + a14 - a21 + a22 + a23 + a24) * (b12 + b14 - b21 + b22 + b23 + b24)
h17 = (a12 + a14 - a21 + a22 + a23 + a24 + a32 + a41 - a42) * (b12 + b14 - b21 + b22 + b23 + b24 + b32 + b41 - b42)
h18 = (a12 - a21 + a22 + a32 + a41 - a42) * (b12 - b21 + b22 + b32 + b41 - b42)
h19 = (a14 + a23 + a24) * (b12 + b14 - b21 + b22 + b23 + b24 + b32 + b34 + b41 - b42 - b43 - b44)
h20 = (a12 + a14 - a21 + a22 + a23 + a24 + a32 + a34 + a41 - a42 - a43 - a44) * (b32 + b41 - b42)
h21 = (a32 + a41 - a42) * (b14 + b23 + b24)
h22 = (a12 + a14 + a22 + a24) * (b12 + b14 + b22 + b24)
h23 = (a12 + a14 + a22 + a24 + a32 - a42) * (b12 + b14 + b22 + b24 + b32 - b42)
h24 = (a14 + a24) * (b12 + b14 + b22 + b24 + b32 + b34 - b42 - b44)
h25 = (a12 + a14 + a22 + a24 + a32 + a34 - a42 - a44) * (b32 - b42)
h26 = (a32 - a42) * (b14 + b24)
h27 = (a34 - a44) * (b34 - b44)
h28 = (a34 - a43 - a44) * (b34 - b43 - b44)
h29 = (a14 + a34) * - b43
h30 = (a13 + a14 + a23 + a24 + a33 + a34 - a43 - a44) * (b14 + b34)
h31 = (a11 - a12 - a13 - a14 + a21 - a22 - a23 - a24 + a31 - a32 - a33 - a34 - a41 + a42 + a43 + a44) * b14
h32 = - a43 * (b13 + b14 + b23 + b24 + b33 + b34 - b43 - b44)
h33 = a14 * (- b21 + b41)
h34 = (a14 - a32) * (- b21 + b41 - b43)
h35 = (a13 + a14 + a23 + a24 - a31 + a32 + a33 + a34 + a41 - a42 - a43 - a44) * (b14 - b32)
h36 = (- a31 + a32 + a33 + a34 + a41 - a42 - a43 - a44) * b32
h37 = (- a12 - a32) * - b23
h38 = (a32 + a34) * (b41 - b43)
h39 = (- a13 - a14 - a23 - a24) * (b32 + b34)
h40 = a32 * (- b21 + b23 + b41 - b43)
h41 = - a21 * (b11 - b12 + b21 - b22)
h42 = (- a21 + a41) * (b11 - b12 - b13 - b14 + b21 - b22 - b23 - b24 + b31 - b32 - b33 - b34 - b41 + b42 + b43 + b44)
h43 = (- a21 + a41 - a43) * (b13 + b14 + b23 + b24 - b31 + b32 + b33 + b34 + b41 - b42 - b43 - b44)
h44 = (a12 + a22 + a32 - a42) * (b12 + b22 + b32 - b42)
h45 = (- a21 + a23 + a41 - a43) * (- b31 + b32 + b33 + b34 + b41 - b42 - b43 - b44)
h46 = (- a31 + a32 + a41 - a42) * (- b12 - b32)
h47 = (a41 - a43) * (- b13 - b14 - b23 - b24)
h48 = (- a43 - a44) * (- b43 - b44)
h49 = - a23 * (- b31 + b32 + b41 - b42)
c11 = h1 - h2 - h5 + h9 + h15 + h33
c12 = - h15 - h16 + h17 - h18 - h21 + h22 - h23 + h26 - h33 - h41 + h44 + h49
c13 = h2 + h5 + h6 - h9 - h29 - h33 + h34 + h38
c14 = - h16 + h17 - h20 - h21 + h22 - h23 + h25 + h26 - h29 - h32 - h33 + h34 + h38 - h41 + h42 + h43
c21 = - h7 + h8 - h10 + h11 - h14 + h15 + h16 - h17 + h18 + h21 - h31 + h33 - h35 - h36
c22 = h7 - h8 + h10 - h11 - h15 - h16 + h17 - h18 - h21 + h22 - h23 + h26 - h33 + h44
c23 = - h7 + h8 + h11 + h12 - h16 + h17 - h20 - h21 - h29 - h33 + h34 + h36 + h38 + h46
c24 = - h7 + h8 + h11 + h12 - h16 + h17 - h20 - h21 + h22 - h23 + h25 + h26 - h29 - h33 + h34 + h38
c31 = h1 - h2 + h3 - h5 + h33 - h34 + h37 - h40
c32 = h17 - h18 - h19 - h21 - h23 + h24 + h26 - h33 + h34 - h37 + h40 - h43 + h44 + h45 - h47 + h49
c33 = h4 + h5 - h29 - h33 + h34 + h40
c34 = - h21 + h26 - h27 + h28 - h29 - h32 - h33 + h34 + h40 - h47
c41 = h8 - h10 + h11 - h13 + h17 - h18 - h19 - h21 + h31 - h33 + h34 + h35 + h36 - h37 - h39 + h40
c42 = - h8 + h10 - h11 + h13 - h17 + h18 + h19 + h21 + h23 - h24 - h26 + h33 - h34 + h37 - h40 - h44
c43 = h11 + h21 - h28 + h29 + h30 + h33 - h34 - h35 - h36 + h39 - h40 + h48
c44 = h11 + h21 - h26 + h27 - h28 + h29 + h33 - h34 - h40 + h48
C = np.array([c11, c12, c13, c14, c21, c22, c23, c24, c31, c32, c33, c34, c41, c42, c43, c44]).reshape(4, 4).T
return C




if __name__ == "__main__":
main()


236 changes: 236 additions & 0 deletions benchmarks/float/atmulti4x4/at_partial_print.py
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Original file line number Diff line number Diff line change
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# test alpha tensor 4x4 against numpy matmul for correctness

import numpy as np

def main():
# [A,B]
matrices = [
[[8, 3, 2, 4],[2, 7, 4, 5],[0, 1, 2, 3],[0, 1, 2, 3]],
[[1, 2, 3, 4],[5, 6, 7, 8],[9, 10, 11, 12],[13, 14, 15, 16]],
]
A = np.array(matrices[0])
B = np.array(matrices[1])
#res_np = np.matmul(A,B)
res_at = at4x4(A,B)
#if np.array_equal(res_np, res_at):
# print("Arrays equal")
# print(res_np)
#else:
# print("Arrays are not equal")
# print("np")
# print(res_np)
# print("at")
# print(res_at)



def at4x4(A,B):
'''Alphatensor Multiply 4-by-4 matrix A with 4-by-4 matrix B, return result C'''

a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41, a42, a43, a44 = A.ravel()
b11, b12, b13, b14, b21, b22, b23, b24, b31, b32, b33, b34, b41, b42, b43, b44 = B.ravel()
h1 = (a11 + a31) * (b11 + b31)
print("h1")
print(h1)
h2 = (a11 - a13 + a31) * (b11 - b13 + b31)
print("h2")
print(h2)
h3 = - a13 * (b11 - b13 + b31 - b33)
print("h3")
print(h3)
h4 = - a33 * - b33
print("h4")
print(h4)
h5 = - a31 * - b13
print("h5")
print(h5)
h6 = (a11 - a13 + a31 - a33) * - b31
print("h6")
print(h6)
h7 = (- a21 + a22 - a23 - a24) * (- b21 + b22 - b23 - b24)
print("h7")
print(h7)
h8 = (- a21 + a22 - a23 - a24 - a41 + a42) * (- b21 + b22 - b23 - b24 - b41 + b42)
print("h8")
print(h8)
h9 = (a11 - a13) * (b11 - b13)
print("h9")
print(h9)
h10 = (- a21 + a22 - a41 + a42) * (- b21 + b22 - b41 + b42)
print("h10")
print(h10)
h11 = (a41 - a42) * (- b23 - b24)
print("h11")
print(h11)
h12 = (- a21 + a22 - a23 - a24 - a41 + a42 - a43 - a44) * (b41 - b42)
print("h12")
print(h12)
h13 = (- a23 - a24) * (- b21 + b22 - b23 - b24 - b41 + b42 - b43 - b44)
print("h13")
print(h13)
h14 = (a11 - a12 + a21 - a22) * (- b12 - b14)
print("h14")
print(h14)
h15 = (- a12 - a14) * - b21
print("h15")
print(h15)
h16 = (a12 + a14 - a21 + a22 + a23 + a24) * (b12 + b14 - b21 + b22 + b23 + b24)
print("h16")
print(h16)
h17 = (a12 + a14 - a21 + a22 + a23 + a24 + a32 + a41 - a42) * (b12 + b14 - b21 + b22 + b23 + b24 + b32 + b41 - b42)
print("h17")
print(h17)
h18 = (a12 - a21 + a22 + a32 + a41 - a42) * (b12 - b21 + b22 + b32 + b41 - b42)
print("h18")
print(h18)
h19 = (a14 + a23 + a24) * (b12 + b14 - b21 + b22 + b23 + b24 + b32 + b34 + b41 - b42 - b43 - b44)
print("h19")
print(h19)
h20 = (a12 + a14 - a21 + a22 + a23 + a24 + a32 + a34 + a41 - a42 - a43 - a44) * (b32 + b41 - b42)
print("h20")
print(h20)
h21 = (a32 + a41 - a42) * (b14 + b23 + b24)
print("h21")
print(h21)
h22 = (a12 + a14 + a22 + a24) * (b12 + b14 + b22 + b24)
print("h22")
print(h22)
h23 = (a12 + a14 + a22 + a24 + a32 - a42) * (b12 + b14 + b22 + b24 + b32 - b42)
print("h23")
print(h23)
h24 = (a14 + a24) * (b12 + b14 + b22 + b24 + b32 + b34 - b42 - b44)
print("h24")
print(h24)
h25 = (a12 + a14 + a22 + a24 + a32 + a34 - a42 - a44) * (b32 - b42)
print("h25")
print(h25)
h26 = (a32 - a42) * (b14 + b24)
print("h26")
print(h26)
h27 = (a34 - a44) * (b34 - b44)
print("h27")
print(h27)
h28 = (a34 - a43 - a44) * (b34 - b43 - b44)
print("h28")
print(h28)
h29 = (a14 + a34) * - b43
print("h29")
print(h29)
h30 = (a13 + a14 + a23 + a24 + a33 + a34 - a43 - a44) * (b14 + b34)
print("h30")
print(h30)
h31 = (a11 - a12 - a13 - a14 + a21 - a22 - a23 - a24 + a31 - a32 - a33 - a34 - a41 + a42 + a43 + a44) * b14
print("h31")
print(h31)
h32 = - a43 * (b13 + b14 + b23 + b24 + b33 + b34 - b43 - b44)
print("h32")
print(h32)
h33 = a14 * (- b21 + b41)
print("h33")
print(h33)
h34 = (a14 - a32) * (- b21 + b41 - b43)
print("h34")
print(h34)
h35 = (a13 + a14 + a23 + a24 - a31 + a32 + a33 + a34 + a41 - a42 - a43 - a44) * (b14 - b32)
print("h35")
print(h35)
h36 = (- a31 + a32 + a33 + a34 + a41 - a42 - a43 - a44) * b32
print("h36")
print(h36)
h37 = (- a12 - a32) * - b23
print("h37")
print(h37)
h38 = (a32 + a34) * (b41 - b43)
print("h38")
print(h38)
h39 = (- a13 - a14 - a23 - a24) * (b32 + b34)
print("h39")
print(h39)
h40 = a32 * (- b21 + b23 + b41 - b43)
print("h40")
print(h40)
h41 = - a21 * (b11 - b12 + b21 - b22)
print("h41")
print(h41)
h42 = (- a21 + a41) * (b11 - b12 - b13 - b14 + b21 - b22 - b23 - b24 + b31 - b32 - b33 - b34 - b41 + b42 + b43 + b44)
print("h42")
print(h42)
h43 = (- a21 + a41 - a43) * (b13 + b14 + b23 + b24 - b31 + b32 + b33 + b34 + b41 - b42 - b43 - b44)
print("h43")
print(h43)
h44 = (a12 + a22 + a32 - a42) * (b12 + b22 + b32 - b42)
print("h44")
print(h44)
h45 = (- a21 + a23 + a41 - a43) * (- b31 + b32 + b33 + b34 + b41 - b42 - b43 - b44)
print("h45")
print(h45)
h46 = (- a31 + a32 + a41 - a42) * (- b12 - b32)
print("h46")
print(h46)
h47 = (a41 - a43) * (- b13 - b14 - b23 - b24)
print("h47")
print(h47)
h48 = (- a43 - a44) * (- b43 - b44)
print("h48")
print(h48)
h49 = - a23 * (- b31 + b32 + b41 - b42)
print("h49")
print(h49)
c11 = h1 - h2 - h5 + h9 + h15 + h33
print("c11")
print(c11)
c12 = - h15 - h16 + h17 - h18 - h21 + h22 - h23 + h26 - h33 - h41 + h44 + h49
print("c12")
print(c12)
c13 = h2 + h5 + h6 - h9 - h29 - h33 + h34 + h38
print("c13")
print(c13)
c14 = - h16 + h17 - h20 - h21 + h22 - h23 + h25 + h26 - h29 - h32 - h33 + h34 + h38 - h41 + h42 + h43
print("c14")
print(c14)
c21 = - h7 + h8 - h10 + h11 - h14 + h15 + h16 - h17 + h18 + h21 - h31 + h33 - h35 - h36
print("c21")
print(c21)
c22 = h7 - h8 + h10 - h11 - h15 - h16 + h17 - h18 - h21 + h22 - h23 + h26 - h33 + h44
print("c22")
print(c22)
c23 = - h7 + h8 + h11 + h12 - h16 + h17 - h20 - h21 - h29 - h33 + h34 + h36 + h38 + h46
print("c23")
print(c23)
c24 = - h7 + h8 + h11 + h12 - h16 + h17 - h20 - h21 + h22 - h23 + h25 + h26 - h29 - h33 + h34 + h38
print("c24")
print(c24)
c31 = h1 - h2 + h3 - h5 + h33 - h34 + h37 - h40
print("c31")
print(c31)
c32 = h17 - h18 - h19 - h21 - h23 + h24 + h26 - h33 + h34 - h37 + h40 - h43 + h44 + h45 - h47 + h49
print("c32")
print(c32)
c33 = h4 + h5 - h29 - h33 + h34 + h40
print("c33")
print(c33)
c34 = - h21 + h26 - h27 + h28 - h29 - h32 - h33 + h34 + h40 - h47
print("c34")
print(c34)
c41 = h8 - h10 + h11 - h13 + h17 - h18 - h19 - h21 + h31 - h33 + h34 + h35 + h36 - h37 - h39 + h40
print("c41")
print(c41)
c42 = - h8 + h10 - h11 + h13 - h17 + h18 + h19 + h21 + h23 - h24 - h26 + h33 - h34 + h37 - h40 - h44
print("c42")
print(c42)
c43 = h11 + h21 - h28 + h29 + h30 + h33 - h34 - h35 - h36 + h39 - h40 + h48
print("c43")
print(c43)
c44 = h11 + h21 - h26 + h27 - h28 + h29 + h33 - h34 - h40 + h48
print("c44")
print(c44)
C = np.array([c11, c12, c13, c14, c21, c22, c23, c24, c31, c32, c33, c34, c41, c42, c43, c44]).reshape(4, 4).T
return C




if __name__ == "__main__":
main()


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