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alphatensor bril benchmark, tested against numpy
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Bennett Wineholt
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Sep 8, 2023
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| # test alpha tensor 4x4 against numpy matmul for correctness | ||
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| import numpy as np | ||
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| 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) | ||
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| def at4x4(A,B): | ||
| '''Alphatensor Multiply 4-by-4 matrix A with 4-by-4 matrix B, return result C''' | ||
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| 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 | ||
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| if __name__ == "__main__": | ||
| main() | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,236 @@ | ||
| # test alpha tensor 4x4 against numpy matmul for correctness | ||
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| import numpy as np | ||
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| 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) | ||
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| def at4x4(A,B): | ||
| '''Alphatensor Multiply 4-by-4 matrix A with 4-by-4 matrix B, return result C''' | ||
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| 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 | ||
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| if __name__ == "__main__": | ||
| main() | ||
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