<reponame>whoiszyc/andes<gh_stars>1-10
"""
Module for eigenvalue analysis.
"""

import logging
import scipy.io
import numpy as np

from math import ceil, pi

from andes.io.txt import dump_data
from andes.utils.misc import elapsed
from andes.routines.base import BaseRoutine
from andes.variables.report import report_info

from andes.plot import set_latex

from andes.shared import matrix, spmatrix, sparse, plt, mpl
from andes.shared import mul, div, spdiag, gesv


logger = logging.getLogger(__name__)
__cli__ = 'eig'


class EIG(BaseRoutine):
    """
    Eigenvalue analysis routine
    """
    def __init__(self, system, config):
        super().__init__(system=system, config=config)

        self.config.add(plot=0)
        self.config.add_extra("_help", plot="show plot after computation")
        self.config.add_extra("_alt", plot=(0, 1))

        # internal flags and storage
        self.As = None
        self.eigs = None
        self.mu = None
        self.part_fact = None
        self.singular_idx = np.array([], dtype=int)
        self.x_name = []

    def calc_As(self, dense=True):
        r"""
        Return state matrix and store to ``self.As``.

        Notes
        -----
        For systems in the mass-matrix formulation,

        .. math ::

            T \dot{x} = f(x, y) \\
            0 = g(x, y)

        Assume `T` is non-singular, the state matrix is calculated from

        .. math ::

            A_s = T^{-1} (f_x - f_y * g_y^{-1} * g_x)

        Returns
        -------
        kvxopt.matrix
            state matrix
        """
        system = self.system
        self.find_zero_states()
        self.x_name = np.array(system.dae.x_name)

        self.As = self._calc_state_matrix(system.dae.fx, system.dae.fy,
                                          system.dae.gx, system.dae.gy, system.dae.Tf,
                                          dense=dense)

        if len(self.singular_idx) > 0:
            self.Asc = self.As
            self.As = self._calc_state_matrix(*self.reorder_As())
        return self.As

    def _calc_state_matrix(self, fx, fy, gx, gy, Tf, dense=True):
        """
        Kernel function for calculating state matrix.
        """
        gyx = matrix(gx)
        self.solver.linsolve(gy, gyx)

        Tfnz = Tf + np.ones_like(Tf) * np.equal(Tf, 0.0)
        iTf = spdiag((1 / Tfnz).tolist())

        if dense:
            return iTf * (fx - fy * gyx)
        else:
            return sparse(iTf * (fx - fy * gyx))

    def reorder_As(self):
        """
        reorder As by moving rows and cols associated with zero time constants to the end.

        Returns `fx`, `fy`, `gx`, `gy`, `Tf`.
        """
        system = self.system
        rows = np.arange(system.dae.n, dtype=int)
        cols = np.arange(system.dae.n, dtype=int)
        vals = np.ones(system.dae.n, dtype=float)

        swaps = []
        bidx = self.non_zeros
        for ii in range(system.dae.n - self.non_zeros):
            if ii in self.singular_idx:
                while (bidx in self.singular_idx):
                    bidx += 1
                cols[ii] = bidx
                rows[bidx] = ii
                swaps.append((ii, bidx))

        # swap the variable names
        for fr, bk in swaps:
            bk_name = self.x_name[bk]
            self.x_name[fr] = bk_name
        self.x_name = self.x_name[:self.non_zeros]

        # compute the permutation matrix for `As` containing non-states
        perm = spmatrix(matrix(vals), matrix(rows), matrix(cols))
        As_perm = perm * sparse(self.As) * perm
        self.As_perm = As_perm

        nfx = As_perm[:self.non_zeros, :self.non_zeros]
        nfy = As_perm[:self.non_zeros, self.non_zeros:]
        ngx = As_perm[self.non_zeros:, :self.non_zeros]
        ngy = As_perm[self.non_zeros:, self.non_zeros:]
        nTf = np.delete(system.dae.Tf, self.singular_idx)

        return nfx, nfy, ngx, ngy, nTf

    def calc_eigvals(self):
        """
        Solve eigenvalues of the state matrix ``self.As``

        Returns
        -------
        None
        """
        self.eigs = np.linalg.eigvals(self.As)
        return self.eigs

    def calc_part_factor(self, As=None):
        """
        Compute participation factor of states in eigenvalues.

        Returns
        -------

        """
        if As is None:
            As = self.As
        mu, N = np.linalg.eig(As)

        N = matrix(N)
        n = len(mu)
        idx = range(n)

        mu_complex = np.zeros_like(mu, dtype=np.complex)
        W = matrix(spmatrix(1.0, idx, idx, As.size, N.typecode))
        gesv(N, W)

        partfact = mul(abs(W.T), abs(N))

        b = matrix(1.0, (1, n))
        WN = b * partfact
        partfact = partfact.T

        for item in idx:
            mu_real = float(mu[item].real)
            mu_imag = float(mu[item].imag)
            mu_complex[item] = complex(round(mu_real, 5), round(mu_imag, 5))
            partfact[item, :] /= WN[item]

        # participation factor
        self.mu = matrix(mu_complex)
        self.part_fact = matrix(partfact)

        return self.mu, self.part_fact

    def summary(self):
        """
        Print out a summary to ``logger.info``.
        """
        out = list()
        out.append('')
        out.append('-> Eigenvalue Analysis:')
        out_str = '\n'.join(out)
        logger.info(out_str)

    def find_zero_states(self):
        """
        Find the indices of non-states in x.
        """
        system = self.system
        self.singular_idx = np.array([], dtype=int)

        if sum(system.dae.Tf != 0) != len(system.dae.Tf):
            self.singular_idx = np.argwhere(np.equal(system.dae.Tf, 0.0)).ravel().astype(int)
            logger.info("System contains %d zero time constants. ", len(self.singular_idx))
            logger.debug([system.dae.x_name[i] for i in self.singular_idx])

        self.non_zeros = system.dae.n - len(self.singular_idx)

    def run(self, **kwargs):
        """
        Run small-signal stability analysis.
        """

        succeed = False
        system = self.system

        if system.PFlow.converged is False:
            logger.warning('Power flow not solved. Eig analysis will not continue.')
            return succeed

        if system.TDS.initialized is False:
            system.TDS.init()
            system.TDS.itm_step()

        if system.dae.n == 0:
            logger.error('No dynamic model. Eig analysis will not continue.')

        else:
            self.summary()
            t1, s = elapsed()

            self.calc_As()
            self.calc_part_factor()

            _, s = elapsed(t1)
            logger.info('Eigenvalue analysis finished in {:s}.'.format(s))

            if not self.system.files.no_output:
                self.report()
                if system.options.get('state_matrix') is True:
                    self.export_state_matrix()

            if self.config.plot:
                self.plot()

            succeed = True

        if not succeed:
            system.exit_code += 1
        return succeed

    def plot(self, mu=None, fig=None, ax=None, left=-6, right=0.5, ymin=-8, ymax=8, damping=0.05,
             line_width=0.5, dpi=150, show=True, latex=True):
        """
        Plot utility for eigenvalues in the S domain.
        """
        mpl.rc('font', family='Times New Roman', size=12)

        if mu is None:
            mu = self.mu
        mu_real = mu.real()
        mu_imag = mu.imag()
        p_mu_real, p_mu_imag = list(), list()
        z_mu_real, z_mu_imag = list(), list()
        n_mu_real, n_mu_imag = list(), list()

        for re, im in zip(mu_real, mu_imag):
            if re == 0:
                z_mu_real.append(re)
                z_mu_imag.append(im)
            elif re > 0:
                p_mu_real.append(re)
                p_mu_imag.append(im)
            elif re < 0:
                n_mu_real.append(re)
                n_mu_imag.append(im)

        if len(p_mu_real) > 0:
            logger.warning(
                'System is not stable due to %d positive eigenvalues.', len(p_mu_real))
        else:
            logger.info(
                'System is small-signal stable in the initial neighborhood.')

        if latex:
            set_latex()

        if fig is None or ax is None:
            fig, ax = plt.subplots(dpi=dpi)

        ax.scatter(n_mu_real, n_mu_imag, marker='x', s=40, linewidth=0.5, color='black')
        ax.scatter(z_mu_real, z_mu_imag, marker='o', s=40, linewidth=0.5, facecolors='none', edgecolors='black')
        ax.scatter(p_mu_real, p_mu_imag, marker='x', s=40, linewidth=0.5, color='black')
        ax.axhline(linewidth=0.5, color='grey', linestyle='--')
        ax.axvline(linewidth=0.5, color='grey', linestyle='--')

        # plot 5% damping lines
        xin = np.arange(left, 0, 0.01)
        yneg = xin / damping
        ypos = - xin / damping

        ax.plot(xin, yneg, color='grey', linewidth=line_width, linestyle='--')
        ax.plot(xin, ypos, color='grey', linewidth=line_width, linestyle='--')
        ax.set_xlabel('Real')
        ax.set_ylabel('Imaginary')
        ax.set_xlim(left=left, right=right)
        ax.set_ylim(ymin, ymax)

        if show is True:
            plt.show()
        return fig, ax

    def export_state_matrix(self):
        """
        Export state matrix to a ``<CaseName>_As.mat`` file with the variable name ``As``, where
        ``<CaseName>`` is the test case name.

        State variable names are stored in variables ``x_name`` and ``x_tex_name``.

        Returns
        -------
        bool
            True if successful
        """
        system = self.system
        out = {'As': self.As,
               'x_name': np.array(system.dae.x_name, dtype=np.object),
               'x_tex_name': np.array(system.dae.x_tex_name, dtype=np.object),
               }

        scipy.io.savemat(system.files.mat, mdict=out)
        logger.info('State matrix saved to "%s"', system.files.mat)
        return True

    def report(self, x_name=None, **kwargs):
        """
        Save eigenvalue analysis reports.

        Returns
        -------
        None
        """
        if x_name is None:
            x_name = self.x_name

        text, header, rowname, data = list(), list(), list(), list()

        neig = len(self.mu)
        mu_real = self.mu.real()
        mu_imag = self.mu.imag()
        n_positive = sum(1 for x in mu_real if x > 0)
        n_zeros = sum(1 for x in mu_real if x == 0)
        n_negative = sum(1 for x in mu_real if x < 0)

        numeral = []
        for idx, item in enumerate(range(neig)):
            if mu_real[idx] == 0:
                marker = '*'
            elif mu_real[idx] > 0:
                marker = '**'
            else:
                marker = ''
            numeral.append('#' + str(idx + 1) + marker)

        # compute frequency, un-damped frequency and damping
        freq = [0] * neig
        ufreq = [0] * neig
        damping = [0] * neig
        for idx, item in enumerate(self.mu):
            if item.imag == 0:
                freq[idx] = 0
                ufreq[idx] = 0
                damping[idx] = 0
            else:
                ufreq[idx] = abs(item) / 2 / pi
                freq[idx] = abs(item.imag / 2 / pi)
                damping[idx] = -div(item.real, abs(item)) * 100

        # obtain most associated variables
        var_assoc = []
        for prow in range(neig):
            temp_row = self.part_fact[prow, :]
            name_idx = list(temp_row).index(max(temp_row))
            var_assoc.append(x_name[name_idx])

        pf = []
        for prow in range(neig):
            temp_row = []
            for pcol in range(neig):
                temp_row.append(round(self.part_fact[prow, pcol], 5))
            pf.append(temp_row)

        # opening info section
        text.append(report_info(self.system))
        header.append(None)
        rowname.append(None)
        data.append(None)
        text.append('')

        header.append([''])
        rowname.append(['EIGENVALUE ANALYSIS REPORT'])
        data.append('')

        text.append('STATISTICS\n')
        header.append([''])
        rowname.append(['Positives', 'Zeros', 'Negatives'])
        data.append([n_positive, n_zeros, n_negative])

        text.append('EIGENVALUE DATA\n')
        header.append([
            'Most Associated',
            'Real',
            'Imag.',
            'Damped Freq.',
            'Frequency',
            'Damping [%]'])
        rowname.append(numeral)
        data.append(
            [var_assoc,
             list(mu_real),
             list(mu_imag),
             freq,
             ufreq,
             damping])

        n_cols = 7  # columns per block
        n_block = int(ceil(neig / n_cols))

        if n_block <= 100:
            for idx in range(n_block):
                start = n_cols * idx
                end = n_cols * (idx + 1)
                text.append('PARTICIPATION FACTORS [{}/{}]\n'.format(
                    idx + 1, n_block))
                header.append(numeral[start:end])
                rowname.append(x_name)
                data.append(pf[start:end])

        dump_data(text, header, rowname, data, self.system.files.eig)
        logger.info('Report saved to "%s".', self.system.files.eig)

"""
Module for eigenvalue analysis.
"""

import logging
import scipy.io
import numpy as np

from math import ceil, pi

from andes.io.txt import dump_data
from andes.utils.misc import elapsed
from andes.routines.base import BaseRoutine
from andes.variables.report import report_info

from andes.plot import set_latex

from andes.shared import matrix, spmatrix, sparse, plt, mpl
from andes.shared import mul, div, spdiag, gesv


logger = logging.getLogger(__name__)
__cli__ = 'eig'


class EIG(BaseRoutine):
    """
    Eigenvalue analysis routine
    """
    def __init__(self, system, config):
        super().__init__(system=system, config=config)

        self.config.add(plot=0)
        self.config.add_extra("_help", plot="show plot after computation")
        self.config.add_extra("_alt", plot=(0, 1))

        # internal flags and storage
        self.As = None
        self.eigs = None
        self.mu = None
        self.part_fact = None
        self.singular_idx = np.array([], dtype=int)
        self.x_name = []

    def calc_As(self, dense=True):
        r"""
        Return state matrix and store to ``self.As``.

        Notes
        -----
        For systems in the mass-matrix formulation,

        .. math ::

            T \dot{x} = f(x, y) \\
            0 = g(x, y)

        Assume `T` is non-singular, the state matrix is calculated from

        .. math ::

            A_s = T^{-1} (f_x - f_y * g_y^{-1} * g_x)

        Returns
        -------
        kvxopt.matrix
            state matrix
        """
        system = self.system
        self.find_zero_states()
        self.x_name = np.array(system.dae.x_name)

        self.As = self._calc_state_matrix(system.dae.fx, system.dae.fy,
                                          system.dae.gx, system.dae.gy, system.dae.Tf,
                                          dense=dense)

        if len(self.singular_idx) > 0:
            self.Asc = self.As
            self.As = self._calc_state_matrix(*self.reorder_As())
        return self.As

    def _calc_state_matrix(self, fx, fy, gx, gy, Tf, dense=True):
        """
        Kernel function for calculating state matrix.
        """
        gyx = matrix(gx)
        self.solver.linsolve(gy, gyx)

        Tfnz = Tf + np.ones_like(Tf) * np.equal(Tf, 0.0)
        iTf = spdiag((1 / Tfnz).tolist())

        if dense:
            return iTf * (fx - fy * gyx)
        else:
            return sparse(iTf * (fx - fy * gyx))

    def reorder_As(self):
        """
        reorder As by moving rows and cols associated with zero time constants to the end.

        Returns `fx`, `fy`, `gx`, `gy`, `Tf`.
        """
        system = self.system
        rows = np.arange(system.dae.n, dtype=int)
        cols = np.arange(system.dae.n, dtype=int)
        vals = np.ones(system.dae.n, dtype=float)

        swaps = []
        bidx = self.non_zeros
        for ii in range(system.dae.n - self.non_zeros):
            if ii in self.singular_idx:
                while (bidx in self.singular_idx):
                    bidx += 1
                cols[ii] = bidx
                rows[bidx] = ii
                swaps.append((ii, bidx))

        # swap the variable names
        for fr, bk in swaps:
            bk_name = self.x_name[bk]
            self.x_name[fr] = bk_name
        self.x_name = self.x_name[:self.non_zeros]

        # compute the permutation matrix for `As` containing non-states
        perm = spmatrix(matrix(vals), matrix(rows), matrix(cols))
        As_perm = perm * sparse(self.As) * perm
        self.As_perm = As_perm

        nfx = As_perm[:self.non_zeros, :self.non_zeros]
        nfy = As_perm[:self.non_zeros, self.non_zeros:]
        ngx = As_perm[self.non_zeros:, :self.non_zeros]
        ngy = As_perm[self.non_zeros:, self.non_zeros:]
        nTf = np.delete(system.dae.Tf, self.singular_idx)

        return nfx, nfy, ngx, ngy, nTf

    def calc_eigvals(self):
        """
        Solve eigenvalues of the state matrix ``self.As``

        Returns
        -------
        None
        """
        self.eigs = np.linalg.eigvals(self.As)
        return self.eigs

    def calc_part_factor(self, As=None):
        """
        Compute participation factor of states in eigenvalues.

        Returns
        -------

        """
        if As is None:
            As = self.As
        mu, N = np.linalg.eig(As)

        N = matrix(N)
        n = len(mu)
        idx = range(n)

        mu_complex = np.zeros_like(mu, dtype=np.complex)
        W = matrix(spmatrix(1.0, idx, idx, As.size, N.typecode))
        gesv(N, W)

        partfact = mul(abs(W.T), abs(N))

        b = matrix(1.0, (1, n))
        WN = b * partfact
        partfact = partfact.T

        for item in idx:
            mu_real = float(mu[item].real)
            mu_imag = float(mu[item].imag)
            mu_complex[item] = complex(round(mu_real, 5), round(mu_imag, 5))
            partfact[item, :] /= WN[item]

        # participation factor
        self.mu = matrix(mu_complex)
        self.part_fact = matrix(partfact)

        return self.mu, self.part_fact

    def summary(self):
        """
        Print out a summary to ``logger.info``.
        """
        out = list()
        out.append('')
        out.append('-> Eigenvalue Analysis:')
        out_str = '\n'.join(out)
        logger.info(out_str)

    def find_zero_states(self):
        """
        Find the indices of non-states in x.
        """
        system = self.system
        self.singular_idx = np.array([], dtype=int)

        if sum(system.dae.Tf != 0) != len(system.dae.Tf):
            self.singular_idx = np.argwhere(np.equal(system.dae.Tf, 0.0)).ravel().astype(int)
            logger.info("System contains %d zero time constants. ", len(self.singular_idx))
            logger.debug([system.dae.x_name[i] for i in self.singular_idx])

        self.non_zeros = system.dae.n - len(self.singular_idx)

    def run(self, **kwargs):
        """
        Run small-signal stability analysis.
        """

        succeed = False
        system = self.system

        if system.PFlow.converged is False:
            logger.warning('Power flow not solved. Eig analysis will not continue.')
            return succeed

        if system.TDS.initialized is False:
            system.TDS.init()
            system.TDS.itm_step()

        if system.dae.n == 0:
            logger.error('No dynamic model. Eig analysis will not continue.')

        else:
            self.summary()
            t1, s = elapsed()

            self.calc_As()
            self.calc_part_factor()

            _, s = elapsed(t1)
            logger.info('Eigenvalue analysis finished in {:s}.'.format(s))

            if not self.system.files.no_output:
                self.report()
                if system.options.get('state_matrix') is True:
                    self.export_state_matrix()

            if self.config.plot:
                self.plot()

            succeed = True

        if not succeed:
            system.exit_code += 1
        return succeed

    def plot(self, mu=None, fig=None, ax=None, left=-6, right=0.5, ymin=-8, ymax=8, damping=0.05,
             line_width=0.5, dpi=150, show=True, latex=True):
        """
        Plot utility for eigenvalues in the S domain.
        """
        mpl.rc('font', family='Times New Roman', size=12)

        if mu is None:
            mu = self.mu
        mu_real = mu.real()
        mu_imag = mu.imag()
        p_mu_real, p_mu_imag = list(), list()
        z_mu_real, z_mu_imag = list(), list()
        n_mu_real, n_mu_imag = list(), list()

        for re, im in zip(mu_real, mu_imag):
            if re == 0:
                z_mu_real.append(re)
                z_mu_imag.append(im)
            elif re > 0:
                p_mu_real.append(re)
                p_mu_imag.append(im)
            elif re < 0:
                n_mu_real.append(re)
                n_mu_imag.append(im)

        if len(p_mu_real) > 0:
            logger.warning(
                'System is not stable due to %d positive eigenvalues.', len(p_mu_real))
        else:
            logger.info(
                'System is small-signal stable in the initial neighborhood.')

        if latex:
            set_latex()

        if fig is None or ax is None:
            fig, ax = plt.subplots(dpi=dpi)

        ax.scatter(n_mu_real, n_mu_imag, marker='x', s=40, linewidth=0.5, color='black')
        ax.scatter(z_mu_real, z_mu_imag, marker='o', s=40, linewidth=0.5, facecolors='none', edgecolors='black')
        ax.scatter(p_mu_real, p_mu_imag, marker='x', s=40, linewidth=0.5, color='black')
        ax.axhline(linewidth=0.5, color='grey', linestyle='--')
        ax.axvline(linewidth=0.5, color='grey', linestyle='--')

        # plot 5% damping lines
        xin = np.arange(left, 0, 0.01)
        yneg = xin / damping
        ypos = - xin / damping

        ax.plot(xin, yneg, color='grey', linewidth=line_width, linestyle='--')
        ax.plot(xin, ypos, color='grey', linewidth=line_width, linestyle='--')
        ax.set_xlabel('Real')
        ax.set_ylabel('Imaginary')
        ax.set_xlim(left=left, right=right)
        ax.set_ylim(ymin, ymax)

        if show is True:
            plt.show()
        return fig, ax

    def export_state_matrix(self):
        """
        Export state matrix to a ``<CaseName>_As.mat`` file with the variable name ``As``, where
        ``<CaseName>`` is the test case name.

        State variable names are stored in variables ``x_name`` and ``x_tex_name``.

        Returns
        -------
        bool
            True if successful
        """
        system = self.system
        out = {'As': self.As,
               'x_name': np.array(system.dae.x_name, dtype=np.object),
               'x_tex_name': np.array(system.dae.x_tex_name, dtype=np.object),
               }

        scipy.io.savemat(system.files.mat, mdict=out)
        logger.info('State matrix saved to "%s"', system.files.mat)
        return True

    def report(self, x_name=None, **kwargs):
        """
        Save eigenvalue analysis reports.

        Returns
        -------
        None
        """
        if x_name is None:
            x_name = self.x_name

        text, header, rowname, data = list(), list(), list(), list()

        neig = len(self.mu)
        mu_real = self.mu.real()
        mu_imag = self.mu.imag()
        n_positive = sum(1 for x in mu_real if x > 0)
        n_zeros = sum(1 for x in mu_real if x == 0)
        n_negative = sum(1 for x in mu_real if x < 0)

        numeral = []
        for idx, item in enumerate(range(neig)):
            if mu_real[idx] == 0:
                marker = '*'
            elif mu_real[idx] > 0:
                marker = '**'
            else:
                marker = ''
            numeral.append('#' + str(idx + 1) + marker)

        # compute frequency, un-damped frequency and damping
        freq = [0] * neig
        ufreq = [0] * neig
        damping = [0] * neig
        for idx, item in enumerate(self.mu):
            if item.imag == 0:
                freq[idx] = 0
                ufreq[idx] = 0
                damping[idx] = 0
            else:
                ufreq[idx] = abs(item) / 2 / pi
                freq[idx] = abs(item.imag / 2 / pi)
                damping[idx] = -div(item.real, abs(item)) * 100

        # obtain most associated variables
        var_assoc = []
        for prow in range(neig):
            temp_row = self.part_fact[prow, :]
            name_idx = list(temp_row).index(max(temp_row))
            var_assoc.append(x_name[name_idx])

        pf = []
        for prow in range(neig):
            temp_row = []
            for pcol in range(neig):
                temp_row.append(round(self.part_fact[prow, pcol], 5))
            pf.append(temp_row)

        # opening info section
        text.append(report_info(self.system))
        header.append(None)
        rowname.append(None)
        data.append(None)
        text.append('')

        header.append([''])
        rowname.append(['EIGENVALUE ANALYSIS REPORT'])
        data.append('')

        text.append('STATISTICS\n')
        header.append([''])
        rowname.append(['Positives', 'Zeros', 'Negatives'])
        data.append([n_positive, n_zeros, n_negative])

        text.append('EIGENVALUE DATA\n')
        header.append([
            'Most Associated',
            'Real',
            'Imag.',
            'Damped Freq.',
            'Frequency',
            'Damping [%]'])
        rowname.append(numeral)
        data.append(
            [var_assoc,
             list(mu_real),
             list(mu_imag),
             freq,
             ufreq,
             damping])

        n_cols = 7  # columns per block
        n_block = int(ceil(neig / n_cols))

        if n_block <= 100:
            for idx in range(n_block):
                start = n_cols * idx
                end = n_cols * (idx + 1)
                text.append('PARTICIPATION FACTORS [{}/{}]\n'.format(
                    idx + 1, n_block))
                header.append(numeral[start:end])
                rowname.append(x_name)
                data.append(pf[start:end])

        dump_data(text, header, rowname, data, self.system.files.eig)
        logger.info('Report saved to "%s".', self.system.files.eig)
Module for eigenvalue analysis. Eigenvalue analysis routine # internal flags and storage Return state matrix and store to ``self.As``.          Notes         -----         For systems in the mass-matrix formulation,          .. math ::              T \dot{x} = f(x, y) \\             0 = g(x, y)          Assume `T` is non-singular, the state matrix is calculated from          .. math ::              A_s = T^{-1} (f_x - f_y * g_y^{-1} * g_x)          Returns         -------         kvxopt.matrix             state matrix Kernel function for calculating state matrix. reorder As by moving rows and cols associated with zero time constants to the end.          Returns `fx`, `fy`, `gx`, `gy`, `Tf`. # swap the variable names # compute the permutation matrix for `As` containing non-states Solve eigenvalues of the state matrix ``self.As``          Returns         -------         None Compute participation factor of states in eigenvalues.          Returns         ------- # participation factor Print out a summary to ``logger.info``. Find the indices of non-states in x. Run small-signal stability analysis. Plot utility for eigenvalues in the S domain. # plot 5% damping lines Export state matrix to a ``<CaseName>_As.mat`` file with the variable name ``As``, where         ``<CaseName>`` is the test case name.          State variable names are stored in variables ``x_name`` and ``x_tex_name``.          Returns         -------         bool             True if successful Save eigenvalue analysis reports.          Returns         -------         None # compute frequency, un-damped frequency and damping # obtain most associated variables # opening info section # columns per block