Stefano Bosisio Steboss89

## floatingpoint.csv

          
            floating point format
             number of bits
             bit for sign
             bits for exponent
             bits for mantissa
             base

            
              f16 (half-precision)
               16
               1
               5
               10
               2

            
              f32 (single-precision)
               32
               1
               8
               23
               2

            
              f64 (double-precision)
               64
               1
               11
               52
               2

## example.py
# Pipeline to retrieve some data on staging
# trustedplatform-pl-stging.italianpromo.fake_dataset
from pathlib import Path
from typing import List

import kfp
import yaml

from trustedplatform_kfpvertex.pipelines.components import bigquery, virtual_machine
from trustedplatform_kfpvertex.pipelines.utils import compile

## T4_comparison.csv

          
            Matrix size
             JAX
             Strassen
             AlphaTensor

            
              8192
                     2.51+/-      0.01
                    2.34+/-      0.01
                    2.24+/-      0.01

            
              10240
                     5.18+/-      0.03
                    4.31+/-      0.01
                    4.12+/-      0.01

            
              12288
                     8.67+/-      0.04
                    8.09+/-      0.02
                    7.94+/-      0.05

            
              14336
                    13.67+/-      0.03
                   11.52+/-      0.01
                   11.16+/-      0.02

            
              16384
                    20.41+/-      0.03
                   21.69+/-      0.03
                   21.03+/-      0.02

            
              18432
                    30.64+/-      0.09
                   25.50+/-      0.01
                   24.96+/-      0.03

## T4_comparison.csv

          
            Matrix size
             JAX
             Strassen
             AlphaTensor

            
              8192
               2.513199887099989+/-0.014528186425767666
              2.344882236099994+/-0.013139273132835319
              2.235233979999987+/-0.0060807684769800165

            
              10240
               5.178147598400005+/-0.0341956234999571
              4.310240157300029+/-0.006896268670154992
              4.115188468500003+/-0.009684188165498608

            
              12288
               8.674847026200018+/-0.042683489691167704
              8.094868272800023+/-0.023601467532573948
              7.936362483399989+/-0.04820043866223

            
              14336
               13.67069818479997+/-0.026384762961236184
              11.523782438399985+/-0.011888051059463828
              11.158847375799905+/-0.023378686004509534

            
              16384
               20.408328052200023+/-0.029682819426008433
              21.686704270200018+/-0.03336953765400482
              21.02908948869999+/-0.023961257266623504

            
              18432
               30.6381309062+/-0.09175637807267167
              25.495546809300027+/-0.008717825537352966
              24.961940088700022+/-0.03458530070354073

## jax_concatenate_matrix.py
c = f(a, c)
# remember to block until ready
c[0][0].block_until_ready()
# convert back to original matrix size
c_arr = np.hstack(np.concatenate(np.array(c), axis=1)).reshape(SIZE,SIZE)

## jax_strassen.py
def f(a: BlockMatrix, b: BlockMatrix) -> BlockMatrix:
    """Multiplies block matrices `a` and `b`."""
    n = len(a)
    result = [[None] * n for _ in range(n)]
    for alpha in range(rank):
      left = None
      for i in range(n):
        for j in range(n):
          if factors[0][i, j, alpha] != 0:
            curr = factors[0][i, j, alpha] * a[i][j]

## strassen_recursive.py
def strassen(A, B):
    """
    Parameters
    ----------
    A: np.array: block matrix A
    B: np.array: block matrix B

    Return
    ------
    C: np.array: product matrix C

## strassen_improvements.csv

          
            Year
             ω
             Author

            
              1969
               2.81
               Strassen [8]

            
              1978
               2.79
               Pan [15]

            
              1979
               2.78
               Bini [3]

            
              1981
               2.55
               Schonage [16]

            
              1987
               2.38
               Coppersmith Winograd [5]

            
              2013
               2.37
               Stothers Munro [17]

            
              2014
               2.36
               Le Gall [12]

            
              2021
               2.36
               Vassilevska Alman [11]

## strassen_improvements.csv

          
            Yes
             O(n^\omega)
             Author

            
              1969
               2.81
               Strassen [8]

            
              1978
               2.79
               Pan [15]

            
              1979
               2.78
               Bini [3]

            
              1981
               2.55
               Schonage [16]

            
              1987
               2.38
               Coppersmith Winograd [5]

            
              2013
               2.37
               Stothers Munro [17]

            
              2014
               2.36
               Le Gall [12]

            
              2021
               2.36
               Vassilevska Alman [11]

## strassen.latex
I = (A_{11} + A_{22})(B_{11} + B_{22})
floating point format	number of bits	bit for sign	bits for exponent	bits for mantissa	base
f16 (half-precision)	16	1	5	10	2
f32 (single-precision)	32	1	8	23	2
f64 (double-precision)	64	1	11	52	2
	# Pipeline to retrieve some data on staging
	# trustedplatform-pl-stging.italianpromo.fake_dataset
	from pathlib import Path
	from typing import List

	import kfp
	import yaml

	from trustedplatform_kfpvertex.pipelines.components import bigquery, virtual_machine
	from trustedplatform_kfpvertex.pipelines.utils import compile
Matrix size	JAX	Strassen	AlphaTensor
8192	2.51+/- 0.01	2.34+/- 0.01	2.24+/- 0.01
10240	5.18+/- 0.03	4.31+/- 0.01	4.12+/- 0.01
12288	8.67+/- 0.04	8.09+/- 0.02	7.94+/- 0.05
14336	13.67+/- 0.03	11.52+/- 0.01	11.16+/- 0.02
16384	20.41+/- 0.03	21.69+/- 0.03	21.03+/- 0.02
18432	30.64+/- 0.09	25.50+/- 0.01	24.96+/- 0.03
	c = f(a, c)
	# remember to block until ready
	c[0][0].block_until_ready()
	# convert back to original matrix size
	c_arr = np.hstack(np.concatenate(np.array(c), axis=1)).reshape(SIZE,SIZE)
	def f(a: BlockMatrix, b: BlockMatrix) -> BlockMatrix:
	"""Multiplies block matrices `a` and `b`."""
	n = len(a)
	result = [[None] * n for _ in range(n)]
	for alpha in range(rank):
	left = None
	for i in range(n):
	for j in range(n):
	if factors[0][i, j, alpha] != 0:
	curr = factors[0][i, j, alpha] * a[i][j]
	def strassen(A, B):
	"""
	Parameters
	----------
	A: np.array: block matrix A
	B: np.array: block matrix B

	Return
	------
	C: np.array: product matrix C
Year	ω	Author
1969	2.81	Strassen [8]
1978	2.79	Pan [15]
1979	2.78	Bini [3]
1981	2.55	Schonage [16]
1987	2.38	Coppersmith Winograd [5]
2013	2.37	Stothers Munro [17]
2014	2.36	Le Gall [12]
2021	2.36	Vassilevska Alman [11]
Yes	O(n^\omega)	Author
1969	2.81	Strassen [8]
1978	2.79	Pan [15]
1979	2.78	Bini [3]
1981	2.55	Schonage [16]
1987	2.38	Coppersmith Winograd [5]
2013	2.37	Stothers Munro [17]
2014	2.36	Le Gall [12]
2021	2.36	Vassilevska Alman [11]