Python Q.fullrankの例

コード例 #1

ファイル: test_matrices.py プロジェクト: KonstantinTogoi/sympy

def test_invertible():
    assert ask(Q.invertible(X), Q.invertible(X))
    assert ask(Q.invertible(Y)) is False
    assert ask(Q.invertible(X*Y), Q.invertible(X)) is False
    assert ask(Q.invertible(X*Z), Q.invertible(X)) is None
    assert ask(Q.invertible(X*Z), Q.invertible(X) & Q.invertible(Z)) is True
    assert ask(Q.invertible(X.T)) is None
    assert ask(Q.invertible(X.T), Q.invertible(X)) is True
    assert ask(Q.invertible(X.I)) is True
    assert ask(Q.invertible(Identity(3))) is True
    assert ask(Q.invertible(ZeroMatrix(3, 3))) is False
    assert ask(Q.invertible(X), Q.fullrank(X) & Q.square(X))

コード例 #2

ファイル: test_matrices.py プロジェクト: Daaofer/sympyTest

def test_invertible():
    assert ask(Q.invertible(X), Q.invertible(X))
    assert ask(Q.invertible(Y)) is False
    assert ask(Q.invertible(X*Y), Q.invertible(X)) is False
    assert ask(Q.invertible(X*Z), Q.invertible(X)) is None
    assert ask(Q.invertible(X*Z), Q.invertible(X) & Q.invertible(Z)) is True
    assert ask(Q.invertible(X.T)) is None
    assert ask(Q.invertible(X.T), Q.invertible(X)) is True
    assert ask(Q.invertible(X.I)) is True
    assert ask(Q.invertible(Identity(3))) is True
    assert ask(Q.invertible(ZeroMatrix(3, 3))) is False
    assert ask(Q.invertible(X), Q.fullrank(X) & Q.square(X))

コード例 #3

ファイル: test_matrices.py プロジェクト: vchekan/sympy

def test_positive_definite():
    assert ask(Q.positive_definite(X), Q.positive_definite(X))
    assert ask(Q.positive_definite(X.T), Q.positive_definite(X)) is True
    assert ask(Q.positive_definite(X.I), Q.positive_definite(X)) is True
    assert ask(Q.positive_definite(Y)) is False
    assert ask(Q.positive_definite(X)) is None
    assert ask(Q.positive_definite(X * Z * X),
               Q.positive_definite(X) & Q.positive_definite(Z)) is True
    assert ask(Q.positive_definite(X), Q.orthogonal(X))
    assert ask(Q.positive_definite(Y.T * X * Y),
               Q.positive_definite(X) & Q.fullrank(Y)) is True
    assert not ask(Q.positive_definite(Y.T * X * Y), Q.positive_definite(X))
    assert ask(Q.positive_definite(Identity(3))) is True
    assert ask(Q.positive_definite(ZeroMatrix(3, 3))) is False
    assert ask(Q.positive_definite(X + Z),
               Q.positive_definite(X) & Q.positive_definite(Z)) is True
    assert not ask(Q.positive_definite(-X), Q.positive_definite(X))

コード例 #4

ファイル: test_matrices.py プロジェクト: Tyf0n/sympy

def test_positive_definite():
    assert ask(Q.positive_definite(X), Q.positive_definite(X))
    assert ask(Q.positive_definite(X.T), Q.positive_definite(X)) is True
    assert ask(Q.positive_definite(X.I), Q.positive_definite(X)) is True
    assert ask(Q.positive_definite(Y)) is False
    assert ask(Q.positive_definite(X)) is None
    assert ask(Q.positive_definite(X*Z*X),
            Q.positive_definite(X) & Q.positive_definite(Z)) is True
    assert ask(Q.positive_definite(X), Q.orthogonal(X))
    assert ask(Q.positive_definite(Y.T*X*Y),
            Q.positive_definite(X) & Q.fullrank(Y)) is True
    assert not ask(Q.positive_definite(Y.T*X*Y), Q.positive_definite(X))
    assert ask(Q.positive_definite(Identity(3))) is True
    assert ask(Q.positive_definite(ZeroMatrix(3, 3))) is False
    assert ask(Q.positive_definite(X + Z), Q.positive_definite(X) &
            Q.positive_definite(Z)) is True
    assert not ask(Q.positive_definite(-X), Q.positive_definite(X))

コード例 #5

ファイル: test_matrices.py プロジェクト: Daaofer/sympyTest

def test_fullrank():
    assert ask(Q.fullrank(X), Q.fullrank(X))
    assert ask(Q.fullrank(X**2), Q.fullrank(X))
    assert ask(Q.fullrank(X.T), Q.fullrank(X)) is True
    assert ask(Q.fullrank(X)) is None
    assert ask(Q.fullrank(Y)) is None
    assert ask(Q.fullrank(X*Z), Q.fullrank(X) & Q.fullrank(Z)) is True
    assert ask(Q.fullrank(Identity(3))) is True
    assert ask(Q.fullrank(ZeroMatrix(3, 3))) is False
    assert ask(Q.invertible(X), ~Q.fullrank(X)) == False

コード例 #6

ファイル: test_matrices.py プロジェクト: Daaofer/sympyTest

def test_invertible_fullrank():
    assert ask(Q.invertible(X), Q.fullrank(X)) is True

コード例 #7

ファイル: test_matrices.py プロジェクト: KonstantinTogoi/sympy

def test_fullrank():
    assert ask(Q.fullrank(X), Q.fullrank(X))
    assert ask(Q.fullrank(X.T), Q.fullrank(X)) is True
    assert ask(Q.fullrank(X)) is None
    assert ask(Q.fullrank(Y)) is None
    assert ask(Q.fullrank(X*Z), Q.fullrank(X) & Q.fullrank(Z)) is True
    assert ask(Q.fullrank(Identity(3))) is True
    assert ask(Q.fullrank(ZeroMatrix(3, 3))) is False
    assert ask(Q.invertible(X), ~Q.fullrank(X)) == False

コード例 #8

ファイル: test_matrices.py プロジェクト: KonstantinTogoi/sympy

def test_invertible_fullrank():
    assert ask(Q.invertible(X), Q.fullrank(X))

コード例 #9

ファイル: linregress.py プロジェクト: mrocklin/computations

""" Linear Regression """

from sympy import MatrixSymbol, Q, ZeroMatrix, assuming
from sympy import Symbol
n = Symbol('n')
m = Symbol('m')
X = MatrixSymbol('X', n, m)
y = MatrixSymbol('y', n, 1)
beta = (X.T*X).I * X.T*y

from computations.matrices.blas import SYRK, GEMM
from computations.matrices.lapack import POSV
c = (POSV(X.T*X, X.T*y)
   + SYRK(1.0, X.T, 0.0, ZeroMatrix(m, m))
   + GEMM(1.0, X.T, y, 0.0, ZeroMatrix(n, 1)))

assumptions = Q.fullrank(X), Q.real_elements(X), Q.real_elements(y)

コード例 #10

ファイル: kalman.py プロジェクト: thewtex/dask-blog

from sympy.matrices.expressions import MatrixSymbol
from sympy import Symbol, Q

n, k = 1000, 500  #Symbol('n'), Symbol('k')
mu = MatrixSymbol('mu', n, 1)
Sigma = MatrixSymbol('Sigma', n, n)
H = MatrixSymbol('H', k, n)
R = MatrixSymbol('R', k, k)
data = MatrixSymbol('data', k, 1)

newmu = mu + Sigma * H.T * (R + H * Sigma * H.T).I * (H * mu - data)
newSigma = Sigma - Sigma * H.T * (R + H * Sigma * H.T).I * H * Sigma

assumptions = (Q.positive_definite(Sigma), Q.symmetric(Sigma),
               Q.positive_definite(R), Q.symmetric(R), Q.fullrank(H))

inputs = mu, Sigma, H, R, data
outputs = newmu, newSigma

コード例 #11

ファイル: kalman.py プロジェクト: mrocklin/computations

from sympy.matrices.expressions import MatrixSymbol, Transpose
from sympy import Symbol, Q

n, k    = Symbol('n'), Symbol('k')
mu      = MatrixSymbol('mu', n, 1)
Sigma   = MatrixSymbol('Sigma', n, n)
H       = MatrixSymbol('H', k, n)
R       = MatrixSymbol('R', k, k)
data    = MatrixSymbol('data', k, 1)

newmu   = mu + Sigma*H.T * (R + H*Sigma*H.T).I * (H*mu - data)
newSigma= Sigma - Sigma*H.T * (R + H*Sigma*H.T).I * H * Sigma

newSigma =  -1.0*Sigma*H.T*(H*Transpose(H*Sigma) + R).I*H*Sigma + Sigma
newmu =  Sigma*H.T*(H*Transpose(H*Sigma) + R).I*(-1.0*data + H*mu) + mu



assumptions = (Q.positive_definite(Sigma), Q.symmetric(Sigma),
               Q.positive_definite(R), Q.symmetric(R), Q.fullrank(H))

inputs = mu, Sigma, H, R, data
outputs = newmu, newSigma