Python numpy 模块，triu_indices_from() 实例源码

def get_adjacency_matrix(out_dir, sid, expt_id):
    "Returns the adjacency matrix"

    vec_path = pjoin(out_dir, sid, '{}_graynet.csv'.format(expt_id))
    edge_vec = np.genfromtxt(vec_path)

    matrix_size = np.int64( (1.0 + np.sqrt(1.0+8.0*len(edge_vec)))/2.0 )
    edge_mat = np.zeros([matrix_size, matrix_size])

    # making this symmetric as required by nilearn's plot_connectome (stupid)
    # upper tri; diag +1; # lower tri; diag -1
    upper_tri = np.triu_indices_from(edge_mat, +1)
    lower_tri = np.tril_indices_from(edge_mat, -1)
    edge_mat[upper_tri] = edge_vec
    edge_mat[lower_tri] = edge_mat.T[lower_tri]

    return edge_mat

def from_sym_2_tri(symm):
    """convert a 2D symmetric matrix to an upper
       triangular matrix in 1D format

    Parameters
    ----------

    symm : 2D array
          Symmetric matrix


    Returns
    -------

    tri: 1D array
          Contains elements of upper triangular matrix
    """

    inds = np.triu_indices_from(symm)
    tri = symm[inds]
    return tri

def tangent_space(covmats, Cref):
    """Project a set of covariance matrices in the tangent space according to the given reference point Cref

    :param covmats: Covariance matrices set, Ntrials X Nchannels X Nchannels
    :param Cref: The reference covariance matrix
    :returns: the Tangent space , a matrix of Ntrials X (Nchannels*(Nchannels+1)/2)

    """
    Nt, Ne, Ne = covmats.shape
    Cm12 = invsqrtm(Cref)
    idx = numpy.triu_indices_from(Cref)
    T = numpy.empty((Nt, Ne * (Ne + 1) / 2))
    coeffs = (
        numpy.sqrt(2) *
        numpy.triu(
            numpy.ones(
                (Ne,
                 Ne)),
            1) +
        numpy.eye(Ne))[idx]
    for index in range(Nt):
        tmp = numpy.dot(numpy.dot(Cm12, covmats[index, :, :]), Cm12)
        tmp = logm(tmp)
        T[index, :] = numpy.multiply(coeffs, tmp[idx])
    return T

def untangent_space(T, Cref):
    """Project a set of Tangent space vectors in the manifold according to the given reference point Cref

    :param T: the Tangent space , a matrix of Ntrials X (Nchannels*(Nchannels+1)/2)
    :param Cref: The reference covariance matrix
    :returns: A set of Covariance matrix, Ntrials X Nchannels X Nchannels

    """
    Nt, Nd = T.shape
    Ne = int((numpy.sqrt(1 + 8 * Nd) - 1) / 2)
    C12 = sqrtm(Cref)

    idx = numpy.triu_indices_from(Cref)
    covmats = numpy.empty((Nt, Ne, Ne))
    covmats[:, idx[0], idx[1]] = T
    for i in range(Nt):
        covmats[i] = numpy.diag(numpy.diag(covmats[i])) + numpy.triu(
            covmats[i], 1) / numpy.sqrt(2) + numpy.triu(covmats[i], 1).T / numpy.sqrt(2)
        covmats[i] = expm(covmats[i])
        covmats[i] = numpy.dot(numpy.dot(C12, covmats[i]), C12)

    return covmats

def correlation(data,title=''):

    corr = data.corr(method='spearman')
    mask = np.zeros_like(corr)
    mask[np.triu_indices_from(mask)] = True

    sns.set(style="white")
    sns.set_context("notebook", font_scale=2, rc={"lines.linewidth": 0.3})

    rcParams['figure.figsize'] = 25, 12
    rcParams['font.family'] = 'Verdana'
    rcParams['figure.dpi'] = 300

    g = sns.heatmap(corr, mask=mask, linewidths=1, cmap="RdYlGn", annot=False)
    g.set_xticklabels(data,rotation=25,ha="right");
    plt.tick_params(axis='both', which='major', pad=15);

def get_net_vectors(subject_list, kind, atlas_name="aal"):
    """
        subject_list : the subject short IDs list
        kind         : the kind of connectivity to be used, e.g. lasso, partial correlation, correlation
        atlas_name   : name of the atlas used

    returns:
        matrix       : matrix of connectivity vectors (num_subjects x num_connections)
    """

    # This is an alternative implementation
    networks = load_all_networks(subject_list, kind, atlas_name=atlas_name)
    # Get Fisher transformed matrices
    norm_networks = [np.arctanh(mat) for mat in networks]
    # Get upper diagonal indices
    idx = np.triu_indices_from(norm_networks[0], 1)
    # Get vectorised matrices
    vec_networks = [mat[idx] for mat in norm_networks]
    # Each subject should be a row of the matrix
    matrix = np.vstack(vec_networks)

    return matrix

def tangent_space(covmats, Cref):
    """Project a set of covariance matrices in the tangent space according to the given reference point Cref

    :param covmats: Covariance matrices set, Ntrials X Nchannels X Nchannels
    :param Cref: The reference covariance matrix
    :returns: the Tangent space , a matrix of Ntrials X (Nchannels*(Nchannels+1)/2)

    """
    Nt, Ne, Ne = covmats.shape
    Cm12 = invsqrtm(Cref)
    idx = numpy.triu_indices_from(Cref)
    T = numpy.empty((Nt, Ne * (Ne + 1) / 2))
    coeffs = (
        numpy.sqrt(2) *
        numpy.triu(
            numpy.ones(
                (Ne,
                 Ne)),
            1) +
        numpy.eye(Ne))[idx]
    for index in range(Nt):
        tmp = numpy.dot(numpy.dot(Cm12, covmats[index, :, :]), Cm12)
        tmp = logm(tmp)
        T[index, :] = numpy.multiply(coeffs, tmp[idx])
    return T

def untangent_space(T, Cref):
    """Project a set of Tangent space vectors in the manifold according to the given reference point Cref

    :param T: the Tangent space , a matrix of Ntrials X (Nchannels*(Nchannels+1)/2)
    :param Cref: The reference covariance matrix
    :returns: A set of Covariance matrix, Ntrials X Nchannels X Nchannels

    """
    Nt, Nd = T.shape
    Ne = int((numpy.sqrt(1 + 8 * Nd) - 1) / 2)
    C12 = sqrtm(Cref)

    idx = numpy.triu_indices_from(Cref)
    covmats = numpy.empty((Nt, Ne, Ne))
    covmats[:, idx[0], idx[1]] = T
    for i in range(Nt):
        covmats[i] = numpy.diag(numpy.diag(covmats[i])) + numpy.triu(
            covmats[i], 1) / numpy.sqrt(2) + numpy.triu(covmats[i], 1).T / numpy.sqrt(2)
        covmats[i] = expm(covmats[i])
        covmats[i] = numpy.dot(numpy.dot(C12, covmats[i]), C12)

    return covmats

def sns_triangle(matrix, plt_title, only_class=None):

    sns.set(style="white")
    # Generate a mask for the upper triangle
    mask = np.zeros_like(matrix, dtype=np.bool)
    mask[np.triu_indices_from(mask)] = True

    # Set up the matplotlib figure
    f, ax = subplots(figsize=(11, 9))

    # Generate a custom diverging colormap
    cmap = sns.diverging_palette(220, 10, as_cmap=True)

    # Draw the heatmap with the mask and correct aspect ratio
    sns.heatmap(matrix.as_matrix(), mask=mask, cmap=cmap, vmax=.3,
                square=True, xticklabels=5, yticklabels=5,
                linewidths=.5, cbar_kws={"shrink": .5}, ax=ax)
    title(plt_title)
    xlabel('Preprocessed Features')
    ylabel('Preprocessed Features')
    if only_class is None:
        only_class = ''
    savefig('images/triangle'+only_class+'.png')

def _compute_indices_of_one_pair_of_mergeable_groups(distance_matrix, min_dist_between_items_in_different_groups):
    """
    This function semantically operates on a collection of grouped items.
    It returns a pair of indices corresponding to a pair of groups which are close enough to merge.

    Args:
        distance_matrix (np.ndarray): the matrix containing distances between all groups
        min_dist_between_items_in_different_groups (float): the algorithm will only suggest a pair of groups to be
                                                            merged if they each contain an item which is within this
                                                            value of the other.

    Returns:
        a pair of indices corresponding to a mergeable pair of groups
    """
    # Get all indices (i,j) with i<j, in a 2-element tuple (all rows indices, all column indices).
    inds = np.triu_indices_from(distance_matrix, 1)  # type: tuple
    # Get a boolean vector which indexes both elements of inds and tells whether the pair of groups should be merged
    groups_could_be_merged = distance_matrix[inds] < min_dist_between_items_in_different_groups
    # Get the subset of indices for groups we can merge
    inds_of_mergeable_groups = [inds[i][groups_could_be_merged] for i in range(len(inds))]
    # Return the first pair of indices, if any were found
    indices_matrix = np.transpose(inds_of_mergeable_groups)
    return indices_matrix[0] if len(indices_matrix) > 0 else None

def plot_corr_heatmap(corr, labels, heading):

    sns.set(style="white")

    # Generate a mask for the upper triangle
    mask = np.zeros_like(corr, dtype=np.bool)
    mask[np.triu_indices_from(mask)] = True

    # Set up the matplotlib figure
    f, ax = plt.subplots(figsize=(8, 8))

    # Generate a custom diverging colormap
    cmap = sns.diverging_palette(220, 10, as_cmap=True)

    # Draw the heatmap with the mask and correct aspect ratio
    sns.heatmap(corr, mask=mask, cmap=cmap, vmax=.3,
                square=True, xticklabels=labels, yticklabels=labels,
                linewidths=.5, ax=ax, cbar_kws={"shrink": .5}, annot=True)
    ax.set_title(heading)
    plt.show()

def lowertosymmetric(a, copy=False):
    a = np.copy(a) if copy else a
    idxs = np.triu_indices_from(a)
    a[idxs] = a[(idxs[1], idxs[0])]

def uppertosymmetric(a, copy=False):
    a = np.copy(a) if copy else a
    idxs = np.triu_indices_from(a)
    a[(idxs[1], idxs[0])] = a[idxs]

def __init__(self, parent, data, labels, width=6, height=6, dpi=100):
        figure = Figure(figsize=(width, height), dpi=dpi, tight_layout=True)
        axes = figure.add_subplot(111)

        super(CorrelationPlot, self).__init__(figure)
        self.setParent(parent)

        sns.set(style="darkgrid")

        corr = data
        # cmap = sns.diverging_palette(220, 10, as_cmap=True)
        # corrplot(data, names=labels, annot=True, sig_stars=False,
        #      diag_names=True, cmap=cmap, ax=axes, cbar=True)

        df = pd.DataFrame(data=data, columns=labels)
        corr = df.corr()
        # Generate a mask for the upper triangle
        mask = np.zeros_like(corr, dtype=np.bool)
        mask[np.triu_indices_from(mask)] = True
        # Draw the heatmap with the mask and correct aspect ratio
        vmax = np.abs(corr.values[~mask]).max()
        # vmax = np.abs(corr).max()
        sns.heatmap(corr, mask=mask, cmap=plt.cm.PuOr, vmin=-vmax, vmax=vmax,
                    square=True, linecolor="lightgray", linewidths=1, ax=axes)
        for i in range(len(corr)):
            axes.text(i + 0.5, i + 0.5, corr.columns[i],
                      ha="center", va="center", rotation=0)
            for j in range(i + 1, len(corr)):
                s = "{:.3f}".format(corr.values[i, j])
                axes.text(j + 0.5, i + 0.5, s,
                          ha="center", va="center")
        axes.axis("off")
        # If uncommented, fills widget
        self.setSizePolicy(QtWidgets.QSizePolicy.Expanding, QtWidgets.QSizePolicy.Expanding)
        self.updateGeometry()
        self.setMinimumSize(self.size())

def get_triu_handle_inf_nan(weights_matrix):
    "Issue a warning when NaNs or Inf are found."

    if weights_matrix is None:
        raise ValueError('Computation failed.')

    upper_tri_vec = weights_matrix[np.triu_indices_from(weights_matrix, 1)]

    warn_nan(upper_tri_vec)

    return upper_tri_vec

def plot_corrmat(in_csv, out_file=None):
    import seaborn as sn
    sn.set(style="whitegrid")

    dataframe = pd.read_csv(in_csv, index_col=False, na_values='n/a', na_filter=False)
    colnames = dataframe.columns.ravel().tolist()

    for col in ['subject_id', 'site', 'modality']:
        try:
            colnames.remove(col)
        except ValueError:
            pass

    # Correlation matrix
    corr = dataframe[colnames].corr()
    corr = corr.dropna((0,1), 'all')

    # Generate a mask for the upper triangle
    mask = np.zeros_like(corr, dtype=np.bool)
    mask[np.triu_indices_from(mask)] = True

    # Generate a custom diverging colormap
    cmap = sn.diverging_palette(220, 10, as_cmap=True)

    # Draw the heatmap with the mask and correct aspect ratio
    corrplot = sn.clustermap(corr, cmap=cmap, center=0., method='average', square=True, linewidths=.5)
    plt.setp(corrplot.ax_heatmap.yaxis.get_ticklabels(), rotation='horizontal')
    # , mask=mask, square=True, linewidths=.5, cbar_kws={"shrink": .5})

    if out_file is None:
        out_file = 'corr_matrix.svg'

    fname, ext = op.splitext(out_file)
    if ext[1:] not in ['pdf', 'svg', 'png']:
        ext = '.svg'
        out_file = fname + '.svg'

    corrplot.savefig(out_file, format=ext[1:], bbox_inches='tight', pad_inches=0, dpi=100)
    return corrplot

def heatmap(data, half=True, scale=1, vmin=-0.8, vmax=0.8, cmap='RdBu_r', **kwargs):
        """

        :param dataframe:
        :param half:
        :param scale:
        :param vmin:
        :param vmax:
        :param cmap:
        :param kwargs:
        :return:
        """
        figsize = (6 * scale, 4 * scale)
        for arg in kwargs.keys():
            if arg is 'figsize':
                figsize = kwargs[arg]
        if half:
            mask = np.zeros_like(data)
            mask[np.triu_indices_from(mask)] = True
        else:
            mask = None
        fig = plt.figure(figsize=figsize, dpi=300)
        fig.set_facecolor('white')
        axes = fig.add_subplot(111)

        with sns.plotting_context("notebook", font_scale=1):
            ax = sns.heatmap(data, mask=mask, vmin=vmin, vmax=vmax,
                             cmap=cmap, square=True, ax=axes)
            # ax.set_xticklabels(ax.xaxis.get_majorticklabels(), rotation=45)
            ax.tick_params(labelsize=3.5, length=0)
            # ax.set_yticklabels(ax.yaxis.get_majorticklabels(), rotation=45)
            cbar = ax.collections[0].colorbar
            cbar.set_ticks([vmin, 0, vmax])
            # cbar.set_ticklabels(['low', '20%', '75%', '100%'])

def scatterplot_matrix(data, attNames, **kwargs):
    rows, atts = data.shape
    fig, axes = plt.subplots(nrows = atts, ncols =atts, figsize=(30,30))
    fig.subplots_adjust(hspace = 0.05 , wspace = 0.05)

    for ax in axes.flat:
        ax.xaxis.set_visible(False)
        ax.yaxis.set_visible(False)

        if ax.is_first_col():
            ax.yaxis.set_ticks_position('left')
        if ax.is_last_col():
            ax.yaxis.set_ticks_position('right')
        if ax.is_first_row():
            ax.xaxis.set_ticks_position('top')
        if ax.is_last_row():
            ax.xaxis.set_ticks_position('bottom')

    for i, j in zip(*np.triu_indices_from(axes, k=1)):
        for x, y in [(i,j), (j,i)]:
            axes[x,y].plot(data[y], data[x], **kwargs)

    # Label the diagonal subplots...
    for i, label in enumerate(attNames):
        axes[i,i].annotate(label, (0.5, 0.5), xycoords='axes fraction',
                ha='center', va='center')

    for i, j in zip(range(atts), itertools.cycle((-1, 0))):
        axes[j,i].xaxis.set_visible(True)
        axes[i,j].yaxis.set_visible(True)

    return fig

def draw(self, **kwargs):
        """
        Draws the heatmap of the ranking matrix of variables.
        """
        # Set the axes aspect to be equal
        self.ax.set_aspect("equal")

        # Generate a mask for the upper triangle
        mask = np.zeros_like(self.ranks_, dtype=np.bool)
        mask[np.triu_indices_from(mask)] = True

        # Draw the heatmap
        # TODO: Move mesh to a property so the colorbar can be finalized
        data = np.ma.masked_where(mask, self.ranks_)
        mesh = self.ax.pcolormesh(data, cmap=self.colormap, vmin=-1, vmax=1)

        # Set the Axis limits
        self.ax.set(
            xlim=(0, data.shape[1]), ylim=(0, data.shape[0])
        )

        # Add the colorbar
        cb = self.ax.figure.colorbar(mesh, None, self.ax)
        cb.outline.set_linewidth(0)

        # Reverse the rows to get the lower left triangle
        self.ax.invert_yaxis()

        # Add ticks and tick labels
        self.ax.set_xticks(np.arange(len(self.ranks_)) + 0.5)
        self.ax.set_yticks(np.arange(len(self.ranks_)) + 0.5)
        if self.show_feature_names_:
            self.ax.set_xticklabels(self.features_, rotation=90)
            self.ax.set_yticklabels(self.features_)
        else:
            self.ax.set_xticklabels([])
            self.ax.set_yticklabels([])

def mds_variance_explained(corrmat, mds_coords):
    """Determine how much variance is explained by projection onto MDS coords."""
    orig_dist = (1 - corrmat)[np.triu_indices_from(corrmat, 1)]
    mds_dist = distance.pdist(mds_coords)
    r, _ = stats.pearsonr(orig_dist, mds_dist)
    return r ** 2

def plot_scatters(subjects, axes):

    ftemp = "correlation_analysis/{}_{}_ifs.pkz"
    for subj, ax in zip(subjects, axes):

        sticks = moss.load_pkl(ftemp.format(subj, "sticks")).corrmat
        rest = moss.load_pkl(ftemp.format(subj, "rest")).corrmat

        triu = np.triu_indices_from(rest, 1)

        ax.scatter(sticks[triu], rest[triu], s=3, linewidth=.2,
                   color=".6", edgecolor="w",
                   rasterized=True)

        ax.plot([-.2, .8], [-.2, .8], lw=1, dashes=(5, 2), color=".3")

    plt.setp(axes,
             xlim=(-.25, .8), ylim=(-.25, .8),
             xticks=np.linspace(-.2, .8, 6),
             yticks=np.linspace(-.2, .8, 6),
             aspect="equal")
    plt.setp(axes[1:], yticklabels=[])
    for ax in axes:
        sns.despine(ax=ax, trim=True)
        plt.setp(ax.get_xticklabels(), size=6)
        plt.setp(ax.get_yticklabels(), size=6)

def plot_kdes(subjects, axes):

    ftemp = "correlation_analysis/{}_{}_ifs.pkz"
    for subj, ax in zip(subjects, axes):

        sticks = moss.load_pkl(ftemp.format(subj, "sticks")).corrmat
        rest = moss.load_pkl(ftemp.format(subj, "rest")).corrmat

        triu = np.triu_indices_from(rest, 1)

        sns.kdeplot(sticks[triu], color=".15",
                    label="residual", ax=ax)
        sns.kdeplot(rest[triu], color=".45", dashes=[4, 1],
                    label="resting", ax=ax)

    plt.setp(axes,
             xlim=(-.25, .8), ylim=(0, 17),
             xticks=np.linspace(-.2, .8, 6),
             yticks=[])

    for ax in axes:
        sns.despine(ax=ax, left=True, trim=True)
        plt.setp(ax.get_xticklabels(), size=6)
        plt.setp(ax.get_yticklabels(), size=6)

    axes[0].legend(bbox_to_anchor=(1.2, .8))
    for ax in axes[1:]:
        ax.legend_ = None

def upper_tri_vec(matrix):
    "Returns the vectorized values of upper triangular part of a matrix"

    triu_idx = np.triu_indices_from(matrix, 1)
    return matrix[triu_idx]

def triang2mtx(xs: Vector, dim: int) -> Matrix:
    """
    Transform a symmetric matrix represented as a flatten upper triangular
    matrix to the correspoding 2-dimensional array.
    """
    # New array
    mtx = np.zeros((dim, dim))
    # indexes of the upper triangular
    inds = np.triu_indices_from(mtx)
    # Fill the upper triangular of the new array
    mtx[inds] = xs
    # Fill the lower triangular
    mtx[(inds[1], inds[0])] = xs

    return mtx

def mask_upper_triangle(data):
    mask = np.zeros_like(data)
    mask[np.triu_indices_from(mask)] = True
    data = np.ma.array(data, mask=mask)
    return data

def read_triangular(filepath):
    """Open Pi matrix output from SLICE.

    All matrix opening functions return first the
    genomic windows corresponding to the axes of the
    proximity matrix, then the proximity matrix itself.
    Since SLICE output matrices do not embed the genomic
    locations of the windows, the first return value is
    None.

    :param str filepath: Path to the SLICE output file
    :returns: (None, SLICE Pi matrix)
    """

    with open(filepath) as in_data:
        arr = [[float(i) for i in line.split()] for line in in_data]
    size = len(arr[-1])
    proximity_matrix = np.zeros((size, size))
    lower_i = np.tril_indices_from(proximity_matrix)
    upper_i = np.triu_indices_from(proximity_matrix)
    proximity_matrix[:] = np.NAN
    proximity_matrix[lower_i] = list(itertools.chain(*arr))
    proximity_matrix[upper_i] = proximity_matrix.T[upper_i]
    proximity_matrix[proximity_matrix > 1.] = np.NAN

    return None, proximity_matrix

def sample_invwishart(S,nu):
    # TODO make a version that returns the cholesky
    # TODO allow passing in chol/cholinv of matrix parameter lmbda
    # TODO lowmem! memoize! dchud (eigen?)
    n = S.shape[0]
    chol = np.linalg.cholesky(S)

    if (nu <= 81+n) and (nu == np.round(nu)):
        x = np.random.randn(nu,n)
    else:
        x = np.diag(np.sqrt(np.atleast_1d(stats.chi2.rvs(nu-np.arange(n)))))
        x[np.triu_indices_from(x,1)] = np.random.randn(n*(n-1)//2)
    R = np.linalg.qr(x,'r')
    T = scipy.linalg.solve_triangular(R.T,chol.T,lower=True).T
    return np.dot(T,T.T)

def sample_invwishart(S,nu):
    # TODO make a version that returns the cholesky
    # TODO allow passing in chol/cholinv of matrix parameter lmbda
    # TODO lowmem! memoize! dchud (eigen?)
    n = S.shape[0]
    chol = np.linalg.cholesky(S)

    if (nu <= 81+n) and (nu == np.round(nu)):
        x = np.random.randn(nu,n)
    else:
        x = np.diag(np.sqrt(np.atleast_1d(stats.chi2.rvs(nu-np.arange(n)))))
        x[np.triu_indices_from(x,1)] = np.random.randn(n*(n-1)/2)
    R = np.linalg.qr(x,'r')
    T = scipy.linalg.solve_triangular(R.T,chol.T,lower=True).T
    return np.dot(T,T.T)

def plot_2_corr_heatmaps(corr1, corr2, labels, title1, title2):
    fig=plt.figure(figsize=(9, 8))
    gs = gridspec.GridSpec(1, 2)
    ax1 = fig.add_subplot(gs[0, 0])
    ax2 = fig.add_subplot(gs[0, 1])

    sns.set(style="white")

    # Generate a mask for the upper triangle
    mask = np.zeros_like(corr1, dtype=np.bool)
    mask[np.triu_indices_from(mask)] = True

    # Generate a custom diverging colormap
    cmap = sns.diverging_palette(220, 10, as_cmap=True)

    # Draw the heatmap with the mask and correct aspect ratio
    sns.heatmap(corr1, mask=mask, cmap=cmap, vmax=.3,
                square=True, xticklabels=labels, yticklabels=labels,
                linewidths=.5, ax=ax1, cbar_kws={"shrink": .3}, annot=True)
    ax1.set_title(title1)
    sns.heatmap(corr2, mask=mask, cmap=cmap, vmax=.3,
                square=True, xticklabels=labels, yticklabels=labels,
                linewidths=.5, ax=ax2, cbar_kws={"shrink": .3}, annot=True)
    ax2.set_title(title2)
    fig.tight_layout()
    plt.show()

###############################################################################
# Attribution
###############################################################################