Python cudamat.dot方法代碼示例

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def dot(a1, a2):
 # internally: for matrix-matrix multiplies only; vectors are treated like special cases.
 a1 = as_garray(a1); a2 = as_garray(a2)
 if a1.ndim==0 or a2.ndim==0: return a1*a2
 if a1.ndim==a2.ndim==1:
  if a1 is a2: return sum(a1**2)
  else: return dot(a1.reshape(1, a1.size), a2.reshape(a2.size, 1)).item()
 if a1.ndim==2 and a2.ndim==1: return dot(a1, a2.reshape(a2.size, 1)).ravel() # treat a2 like a column vector
 if a1.ndim==1 and a2.ndim==2: return dot(a1._add_axes(2), a2)[0]   # treat a1 like a row vector
 if a1.shape[-1] != a2.shape[-2]: raise ValueError('arrays not aligned for dot product. a dot product was requested of arrays with shapes %s and %s' % (a1.shape, a2.shape))
 if a1.ndim==a2.ndim==2:
  retShape = (a1.shape[0], a2.shape[1])
  if a1.shape[1]==0: return zeros(retShape) # cudamat bug workaround
  ret = empty(retShape)
  if ret.size!=0: _cudamat.dot(a2._base_as_2d(), a1._base_as_2d(), ret._base_as_2d())
  return ret
 if a1.ndim >= 2 and a2.ndim >= 2:
  # this is not necessarily fast, because if a2.ndim>=3 then it involves a transpose
  a12 = ( a1.reshape_2d(-1) if a1.ndim!=2 else a1)
  a22 = ( a2.transpose((a2.ndim-2,) + tuple(xrange(a2.ndim-2)) + (a2.ndim-1,)).reshape_2d(1)
          if a2.ndim!=2 else
          a2)
  retShape = _deleteT2(a1.shape, -1) + _deleteT2(a2.shape, -2)
  return dot(a12, a22).reshape(retShape)
 raise NotImplementedError('dot with arguments of shapes %s and %s' % (a1.shape, a2.shape)) 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def _sig(self, x, u):
        """Multiple the matrix u by the covariance matrix of x. We are interested in situations where
        n_variables >> n_samples, so we do this without explicitly constructing the covariance matrix."""
        if self.gpu:
            y = cm.empty((self.n_samples, self.m))
            uc = cm.CUDAMatrix(u)
            cm.dot(x, uc.T, target=y)
            del uc
            tmp = cm.empty((self.nv, self.m))
            cm.dot(x.T, y, target=tmp)
            tmp_dot = tmp.asarray()
            del y
            del tmp
        else:
            y = x.dot(u.T)
            tmp_dot = x.T.dot(y)
        prod = (1 - self.eps**2) * tmp_dot.T / self.n_samples + self.eps**2 * u  # nv by m,  <X_i Y_j> / std Y_j
        return prod 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def outer(vec1, vec2): return dot(vec1.ravel()[:, newaxis], vec2.ravel()[newaxis, :]) 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def tensordot(a, b, axes=2):
 if type(axes) in _numberTypes: return dot(a.reshape_2d(a.ndim-axes), b.reshape_2d(axes)).reshape(a.shape[:a.ndim-axes] + b.shape[axes:])
 assert len(axes)==2 and len(axes[0])==len(axes[1]), 'the axes parameter to gnumpy.tensordot looks bad'
 aRemove, bRemove = (tuple(axes[0]), tuple(axes[1]))
 return tensordot(a.transpose(filter(lambda x: x not in aRemove, tuple(xrange(a.ndim))) + aRemove),
                  b.transpose(bRemove + filter(lambda x: x not in bRemove, tuple(xrange(b.ndim)))),
                  len(aRemove))

 
 
# ------------------------------------------------------------------------------- reductors 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def _covar_mstep_diag(gmm, X, posteriors, weighted_X_sum, inv_weights,
                      min_covar, temp_gpu_mem):
    '''Performing the covariance M step for diagonal cases'''

    X2 = temp_gpu_mem['temp_NxD']
    X.mult(X, target=X2)  # X2 = X*X

    # avg_X2 = np.dot(posteriors.T, X2) * inv_weights # ([KxN]*[NxD]) * [Kx1]
    avg_X2 = temp_gpu_mem['temp_KxD']
    cm.dot(posteriors.T, X2, target=avg_X2)  # [KxN]x[NxD] -> [KxD]
    avg_X2.mult_by_col(inv_weights)

    # avg_means2 = gmm.means_ ** 2
    temp_KxD_2 = temp_gpu_mem['temp_KxD_2']
    gmm.means.mult(gmm.means, target=temp_KxD_2)
    # avg_X2 += avg_means2
    avg_X2.add(temp_KxD_2)

    # avg_X_means = gmm.means_ * weighted_X_sum * inv_weights
    # [KxD]*[KxD]*[Kx1] -> [KxD]
    gmm.means.mult(weighted_X_sum, target=temp_KxD_2)
    temp_KxD_2.mult_by_col(inv_weights)
    # avg_X2 -= 2*avg_X_means
    # import pdb; pdb.set_trace()
    avg_X2.add_mult(temp_KxD_2, alpha=-2.0)

    # avg_X2 += min_covar
    avg_X2.add(min_covar)

    # return avg_X2 - 2 * avg_X_means + avg_means2 + min_covar
    # [KxD] - 2*[KxD] + [KxD] + [1]
    return avg_X2 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def _norm(self, x, ws):
        """Calculate uj so that we can normalize it."""
        if self.gpu:
            y = cm.empty((self.n_samples, self.m))
            wc = cm.CUDAMatrix(ws)
            cm.dot(x, wc.T, target=y)  # + noise, but it is included analytically
            y_local = y.asarray()
            del y
            del wc
            tmp_sum = np.einsum('lj,lj->j', y_local, y_local)  # TODO: Should be able to do on gpu...
        else:
            y = x.dot(ws.T)  # + noise / std Y_j^2, but it is included analytically
            tmp_sum = np.einsum('lj,lj->j', y, y)
        return np.sqrt((1 - self.eps**2) * tmp_sum / self.n_samples + self.eps**2 * np.sum(ws**2, axis=1)) 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def _calculate_moments_syn(self, x, ws, quick=False):
        """Calculate moments based on the weights and samples. We also calculate and save MI, TC, additivity, and
        the value of the objective. Note it is assumed that <X_i^2> = 1! """
        m = {}  # Dictionary of moments
        if self.gpu:
            y = cm.empty((self.n_samples, self.m))
            wc = cm.CUDAMatrix(ws)
            cm.dot(x, wc.T, target=y)  # + noise, but it is included analytically
            del wc
        else:
            y = x.dot(ws.T)  # + noise, but it is included analytically
        if self.gpu:
            tmp_dot = cm.empty((self.nv, self.m))
            cm.dot(x.T, y, target=tmp_dot)
            m["X_i Y_j"] = tmp_dot.asarray() / self.n_samples  # nv by m,  <X_i Y_j>
            del y
            del tmp_dot
        else:
            m["X_i Y_j"] = x.T.dot(y) / self.n_samples
        m["cy"] = ws.dot(m["X_i Y_j"]) + self.yscale ** 2 * np.eye(self.m)  # cov(y.T), m by m
        m["Y_j^2"] = np.diag(m["cy"]).copy()
        m["ry"] = m["cy"] / (np.sqrt(m["Y_j^2"]) * np.sqrt(m["Y_j^2"][:, np.newaxis]))
        m["rho"] = (m["X_i Y_j"] / np.sqrt(m["Y_j^2"])).T
        m["invrho"] = 1. / (1. - m["rho"]**2)
        m["rhoinvrho"] = m["rho"] * m["invrho"]
        m["Qij"] = np.dot(m['ry'], m["rhoinvrho"])
        m["Qi"] = np.einsum('ki,ki->i', m["rhoinvrho"], m["Qij"])
        m["Si"] = np.sum(m["rho"] * m["rhoinvrho"], axis=0)

        m["MI"] = - 0.5 * np.log1p(-m["rho"]**2)
        m["X_i Z_j"] = np.linalg.solve(m["cy"], m["X_i Y_j"].T).T
        m["X_i^2 | Y"] = (1. - np.einsum('ij,ij->i', m["X_i Z_j"], m["X_i Y_j"])).clip(1e-6)
        mi_yj_x = 0.5 * np.log(m["Y_j^2"]) - 0.5 * np.log(self.yscale ** 2)
        mi_xi_y = - 0.5 * np.log(m["X_i^2 | Y"])
        m["TCs"] = m["MI"].sum(axis=1) - mi_yj_x
        m["additivity"] = (m["MI"].sum(axis=0) - mi_xi_y).sum()
        m["TC"] = np.sum(mi_xi_y) - np.sum(mi_yj_x)
        return m 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def transform(self, x, details=False):
        """Transform an array of inputs, x, into an array of k latent factors, Y.
            Optionally, you can get the remainder information and/or stop at a specified level."""
        x = self.preprocess(x)
        ns, nv = x.shape
        assert self.nv == nv, "Incorrect number of variables in input, %d instead of %d" % (nv, self.nv)
        if details:
            moments = self._calculate_moments(x, self.ws)
            return x.dot(self.ws.T), moments
        return x.dot(self.ws.T) 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def predict(self, y):
        return self.invert(np.dot(self.moments["X_i Z_j"], y.T).T) 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def get_covariance(self):
        # This uses E(Xi|Y) formula for non-synergistic relationships
        m = self.moments
        if self.discourage_overlap:
            z = m['rhoinvrho'] / (1 + m['Si'])
            cov = np.dot(z.T, z)
            cov /= (1. - self.eps**2)
            np.fill_diagonal(cov, 1)
            return self.theta[1][:, np.newaxis] * self.theta[1] * cov
        else:
            cov = np.einsum('ij,kj->ik', m["X_i Z_j"], m["X_i Y_j"])
            np.fill_diagonal(cov, 1)
            return self.theta[1][:, np.newaxis] * self.theta[1] * cov 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def pinvh(a, cond=None, rcond=None, lower=True):
    '''Compute the (Moore-Penrose) pseudo-inverse of a hermetian matrix.

    Calculate a generalized inverse of a symmetric matrix using its
    eigenvalue decomposition and including all 'large' eigenvalues.

    Parameters
    ----------
    a : array, shape (N, N)
        Real symmetric or complex hermetian matrix to be pseudo-inverted
    cond, rcond : float or None
        Cutoff for 'small' eigenvalues.
        Singular values smaller than rcond * largest_eigenvalue are considered
        zero.

        If None or -1, suitable machine precision is used.
    lower : boolean
        Whether the pertinent array data is taken from the lower or upper
        triangle of a. (Default: lower)

    Returns
    -------
    B : array, shape (N, N)

    Raises
    ------
    LinAlgError
        If eigenvalue does not converge

    Examples
    --------
    >>> import numpy as np
    >>> a = np.random.randn(9, 6)
    >>> a = np.dot(a, a.T)
    >>> B = pinvh(a)
    >>> np.allclose(a, np.dot(a, np.dot(B, a)))
    True
    >>> np.allclose(B, np.dot(B, np.dot(a, B)))
    True

    '''
    a = np.asarray_chkfinite(a)
    s, u = linalg.eigh(a, lower=lower)

    if rcond is not None:
        cond = rcond
    if cond in [None, -1]:
        t = u.dtype.char.lower()
        factor = {'f': 1E3, 'd': 1E6}
        cond = factor[t] * np.finfo(t).eps

    # unlike svd case, eigh can lead to negative eigenvalues
    above_cutoff = (abs(s) > cond * np.max(abs(s)))
    psigma_diag = np.zeros_like(s)
    psigma_diag[above_cutoff] = 1.0 / s[above_cutoff]

    return np.dot(u * psigma_diag, np.conjugate(u).T) 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def _do_mstep(
            self, X, posteriors,
            update_params, min_covar=0,
            temp_gpu_mem=None):
        ''' Perform the Mstep of the EM algorithm and return the class weights.
        '''

        N = X.shape[0]
        K, D = self.n_components, self.n_dimensions

        X = return_CUDAMatrix(X)

        if temp_gpu_mem is None:
            temp_gpu_mem = TempGPUMem()
        temp_gpu_mem.alloc(N, K, D)

        weights = temp_gpu_mem['temp_Kx1']

        weights.reshape((1, K))
        posteriors.sum(axis=0, target=weights)
        weights.reshape((K, 1))

        weighted_X_sum = temp_gpu_mem['weighted_X_sum_KxD']
        cm.dot(posteriors.T, X, target=weighted_X_sum)  # [KxN]x[NxD] -> [KxD]
        # inv_weights = 1.0 / (weights[:, np.newaxis] + 10 * EPS)
        inv_weights = temp_gpu_mem['inv_weights_Kx1']
        denom = temp_gpu_mem['temp_Kx1_2']
        weights.add(10*EPS, target=denom)
        inv_weights.assign(1.0)
        inv_weights.divide(denom)

        if 'w' in update_params:
            # self.weights = (weights / (weights.sum() + 10 * EPS) + EPS)
            weights.div_by_row(
                weights.sum(axis=0).add(10*EPS),
                target=self.weights)
            weights.add(EPS)
        if 'm' in update_params:
            # self.means = weighted_X_sum * inv_weights
            # [KxD].*[Kx1]
            weighted_X_sum.mult_by_col(inv_weights, target=self.means)
        if 'c' in update_params:
            covar_mstep_func = _covar_mstep_funcs[self.covariance_type]
            temp_result = covar_mstep_func(
                self, X, posteriors, weighted_X_sum, inv_weights,
                min_covar, temp_gpu_mem)
            self.covars.assign(temp_result)

        return weights 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def _log_multivariate_normal_density_diag(X, means, covars, temp_gpu_mem):
    '''Compute Gaussian log-density at X for a diagonal model'''

    N, D = X.shape
    K = means.shape[0]

    lpr_NxK = temp_gpu_mem['posteriors_NxK']
    inv_covars_KxD = temp_gpu_mem['temp_KxD_2']
    temp_NxD = temp_gpu_mem['temp_NxD']
    temp_KxD = temp_gpu_mem['temp_KxD']
    temp_Kx1 = temp_gpu_mem['temp_Kx1']

    # compute inverse variances
    inv_covars_KxD.assign(1.0)
    inv_covars_KxD.divide(covars)

    # lpr = D * np.log(2*np.pi)
    lpr_NxK.assign(D * np.log(2*np.pi))

    # temp_Kx1 =  np.sum(np.log(covars), 1)
    cm.log(covars, target=temp_KxD)
    temp_KxD.sum(axis=1, target=temp_Kx1)

    # temp_Kx1 += np.sum((means**2)/covars, 1)
    means.mult(means, target=temp_KxD)
    temp_KxD.mult(inv_covars_KxD)
    temp_Kx1.add_sums(temp_KxD, axis=1)

    # lpr += temp_Kx1
    temp_Kx1.reshape((1, K))  # transpose
    lpr_NxK.add_row_vec(temp_Kx1)
    temp_Kx1.reshape((K, 1))  # return to original shape

    # lpr += -2*np.dot(X, (means / covars).T)
    temp_KxD.assign(means)
    temp_KxD.mult(inv_covars_KxD)
    lpr_NxK.add_dot(X, temp_KxD.T, mult=-2.)

    # lpr += np.dot(X**2, (1.0 / covars).T)
    temp_NxD.assign(X)
    temp_NxD.mult(temp_NxD)
    lpr_NxK.add_dot(temp_NxD, inv_covars_KxD.T)

    # lpr *= -0.5
    lpr_NxK.mult(-0.5)

    # lpr_NxK still in use

    # lpr = -0.5 * (D * np.log(2 * np.pi) + np.sum(np.log(covars), 1)
    #              + np.sum((means ** 2) / covars, 1)
    #              - 2 * np.dot(X, (means / covars).T)
    #              + np.dot(X ** 2, (1.0 / covars).T))

    return lpr_NxK 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def costAndGrad(self,data,labels):
        
        batchSize = data.shape[1]
        self.setViews(batchSize)
        
        # forward prop
        self.hActs[0].assign(cm.CUDAMatrix(data))

        i = 1
        for w,b in self.stack:
            cm.dot(w,self.hActs[i-1],self.hActs[i])
            self.hActs[i].add_col_vec(b)
            if i <= len(self.layerSizes):
                # hard relu
                self.hActs[i].maximum(0.0)
            i += 1

        # Subtract max activation
        self.hActs[-1].max(axis=0,target=self.rowVec)
        self.hActs[-1].add_row_mult(self.rowVec,-1.0,target=self.probs)

        # Softmax
        cm.exp(self.probs)
        self.probs.sum(axis=0,target=self.rowVec)
        cm.pow(self.rowVec,-1.0,target=self.rowVec)
        self.probs.mult_by_row(self.rowVec)

        self.probs.copy_to_host()
        cost, deltas, skip = ctc.ctc_loss(self.probs.numpy_array.astype(np.float64),
                labels,blank=0)
        self.deltasC.assign(cm.CUDAMatrix(deltas))

        if skip:
            return cost,self.grad,skip

        # back prop
        nl = len(self.layerSizes)
        i = nl 
        deltasIn,deltasOut = self.deltasC,self.deltasOut
        for w,b in reversed(self.stack):
            # compute gradient
            cm.dot(deltasIn,self.hActs[i].T,target=self.grad[i][0])
            deltasIn.sum(axis=1,target=self.grad[i][1])

            # compute next layer deltas
            if i > 0:
                self.hActs[i].sign(target=self.tmpGrad)
                cm.dot(w.T,deltasIn,target=deltasOut)
                deltasOut.mult(self.tmpGrad)

            if i == nl:
                deltasIn = self.deltasIn

            deltasIn,deltasOut = deltasOut,deltasIn
            i -= 1

        return cost,self.grad,skip 

# 需要導入模塊: import cudamat [as 別名]
# 或者: from cudamat import dot [as 別名]
def _calculate_moments_ns(self, x, ws, quick=False):
        """Calculate moments based on the weights and samples. We also calculate and save MI, TC, additivity, and
        the value of the objective. Note it is assumed that <X_i^2> = 1! """
        m = {}  # Dictionary of moments
        if self.gpu:
            y = cm.empty((self.n_samples, self.m))
            wc = cm.CUDAMatrix(ws)
            cm.dot(x, wc.T, target=y)  # + noise, but it is included analytically
            del wc
            tmp_sum = np.einsum('lj,lj->j', y.asarray(), y.asarray())  # TODO: Should be able to do on gpu...
        else:
            y = x.dot(ws.T)
            tmp_sum = np.einsum('lj,lj->j', y, y)
        m["uj"] = (1 - self.eps**2) * tmp_sum / self.n_samples + self.eps**2 * np.sum(ws**2, axis=1)
        if quick and np.max(m["uj"]) >= 1.:
            return False
        if self.gpu:
            tmp = cm.empty((self.nv, self.m))
            cm.dot(x.T, y, target=tmp)
            tmp_dot = tmp.asarray()
            del tmp
            del y
        else:
            tmp_dot = x.T.dot(y)
        m["rho"] = (1 - self.eps**2) * tmp_dot.T / self.n_samples + self.eps**2 * ws  # m by nv
        m["ry"] = ws.dot(m["rho"].T)  # normalized covariance of Y
        m["Y_j^2"] = self.yscale ** 2 / (1. - m["uj"])
        np.fill_diagonal(m["ry"], 1)
        m["invrho"] = 1. / (1. - m["rho"]**2)
        m["rhoinvrho"] = m["rho"] * m["invrho"]
        m["Qij"] = np.dot(m['ry'], m["rhoinvrho"])
        # m["Qi"] = np.einsum('ki,ki->i', m["rhoinvrho"], m["Qij"])
        m["Si"] = np.sum(m["rho"] * m["rhoinvrho"], axis=0)
        m["Qi-Si^2"] = np.einsum('ki,ki->i', m["rhoinvrho"], m["Qij"] - m["Si"] * m["rho"])

        # This is the objective, a lower bound for TC
        m["TC"] = np.sum(np.log(1 + m["Si"])) \
                     - 0.5 * np.sum(np.log(1 + m["Qi-Si^2"])) \
                     + 0.5 * np.sum(np.log(1 - m["uj"]))
                    # - m["Si"]**2 + m["Qi"]))

        if not quick:
            m["MI"] = - 0.5 * np.log1p(-m["rho"]**2)
            m["X_i Y_j"] = m["rho"].T * np.sqrt(m["Y_j^2"])
            m["X_i Z_j"] = np.linalg.solve(m["ry"], m["rho"]).T
            m["X_i^2 | Y"] = (1. - np.einsum('ij,ji->i', m["X_i Z_j"], m["rho"])).clip(1e-6)
            m['I(Y_j ; X)'] = 0.5 * np.log(m["Y_j^2"]) - 0.5 * np.log(self.yscale ** 2)
            m['I(X_i ; Y)'] = - 0.5 * np.log(m["X_i^2 | Y"])
            m["TCs"] = m["MI"].sum(axis=1) - m['I(Y_j ; X)']
            m["TC_no_overlap"] = m["MI"].max(axis=0).sum() - m['I(Y_j ; X)'].sum()  # A direct calculation of TC where each variable is in exactly one group.
            m["TC_direct"] = m['I(X_i ; Y)'].sum() - m['I(Y_j ; X)']  # A direct calculation of TC. Should be upper bound for "TC", "TC_no_overlap"
            m["additivity"] = (m["MI"].sum(axis=0) - m['I(X_i ; Y)']).sum()
        return m