CODEWITHSUNDEEP
numpymatrixpython-3.7
William Abma
William Abma

Reputation: 495

Numpy dot issue during matrix by vector multiplication

EDIT: Alright, so, I was indeed stupid. I recommend to close this question as it does not bring anything to the table. Basically, I suck at basic thinking and math at 2am...

This is driving me insane. I'm trying to get the product of a matrix with a vector in python.

I have one 9x9 matrix a and one 1x9 vector b.

a = [[-0.03619046050233981, 0.01694804504223569, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.01694804504223569, -0.03619046050233981, 0.01694804504223569, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.01694804504223569, -0.03619046050233981, 0.01694804504223569, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.01694804504223569, -0.03619046050233981, 0.01694804504223569, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.01694804504223569, -0.03619046050233981, 0.01694804504223569, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.01694804504223569, -0.03619046050233981, 0.01694804504223569, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.01694804504223569, -0.03619046050233981, 0.01694804504223569, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01694804504223569, -0.03619046050233981, 0.01694804504223569], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.04756713402738598, -0.06941534088216819]]

a = np.array(a)

b = [2.774218316317263e-09, 1.9240011547847137e-09, 1.3342489213593189e-09, 9.251229045630879e-10, 6.412369741504171e-10, 4.441595895415701e-10, 3.07211064663576e-10, 2.1185176007909776e-10, -4.172326584582343e-11]

b = np.array(b)

print(np.dot(a,b))
>>> array([-6.77921802e-11,  0.00000000e+00,  6.46234854e-27,  0.00000000e+00,
    6.46234854e-27,  3.23117427e-27, -4.84676140e-27, -3.16751358e-12,
    1.29734158e-11])

What I'm expecting:

...
2nd value: 0.01694805 * 2.77421832e-09 -0.03619046 * 1.92400115e-09 + 0.01694805 * 1.33424892e-09
>>> 2.15478530e-17
...

array([-6.77921695e-11,  2.15478530e-17,  1.47710395e-17,  1.02173204e-17,
    7.13131671e-18,  4.91186255e-18,  3.40092760e-18,  2.36168005e-18,
   -7.44835521e-19])

Here is the kicker:

c = array([[-0.03619046,  0.01694805,  0.        ,  0.        ,  0.        ,
     0.        ,  0.        ,  0.        ,  0.        ],
   [ 0.01694805, -0.03619046,  0.01694805,  0.        ,  0.        ,
     0.        ,  0.        ,  0.        ,  0.        ],
   [ 0.        ,  0.01694805, -0.03619046,  0.01694805,  0.        ,
     0.        ,  0.        ,  0.        ,  0.        ],
   [ 0.        ,  0.        ,  0.01694805, -0.03619046,  0.01694805,
     0.        ,  0.        ,  0.        ,  0.        ],
   [ 0.        ,  0.        ,  0.        ,  0.01694805, -0.03619046,
     0.01694805,  0.        ,  0.        ,  0.        ],
   [ 0.        ,  0.        ,  0.        ,  0.        ,  0.01694805,
    -0.03619046,  0.01694805,  0.        ,  0.        ],
   [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
     0.01694805, -0.03619046,  0.01694805,  0.        ],
   [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
     0.        ,  0.01694805, -0.03619046,  0.01694805],
   [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
     0.        ,  0.        ,  0.04756713, -0.06941534]])

np.dot(c,b)
>>> array([-6.77921692e-11,  2.13353146e-17,  1.47955319e-17,  1.02587195e-17,
    7.11069875e-18,  4.92530088e-18,  3.40667400e-18, -3.16751216e-12,
    1.29734149e-11])

As you can see, c is an approximation of a with less significant numbers. Using it gives me my expected results-ish. Am I hitting some numerical artifact ? Or am I making a huge and stupid mistake?

Note that a @ b and np.matmul(a,b) encounter the same issue.

I'm using Python 3.7.0 and Numpy 1.15.0

Upvotes: 0

Views: 42

Answers (1)

Nico Schlömer
Nico Schlömer

Reputation: 58721

It seems like you copy-pasted the numbers wrong.

print(np.dot(a, b))
print(np.dot(a[1], b))
print(
    0.01694804504223569 * 2.774218316317263e-09
    + -0.03619046050233981 * 1.9240011547847137e-09
    + 0.01694804504223569 * 1.3342489213593189e-09
)

[-6.77921802e-11  0.00000000e+00  6.46234854e-27  0.00000000e+00
  6.46234854e-27  3.23117427e-27 -4.84676140e-27 -3.16751358e-12
  1.29734158e-11]
-6.462348535570529e-27
-6.462348535570529e-27

It's a bit weird that the np.dot(a, b)[1] does not exactly equal np.dot(a[1], b), but with this magnitude it's not too surprising.

You could play with accupy's kdot/fdot (a project of mine) to see if those round-off defeating implementations do you any good.

Upvotes: 1

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