#!/usr/bin/env python
# geotecha - A software suite for geotechncial engineering
# Copyright (C) 2018  Rohan T. Walker (rtrwalker@gmail.com)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see http://www.gnu.org/licenses/gpl.html.

"""
Multilayer consolidation with stone columns including vertical and
radial drainage using the spectral Galerkin method.

"""
from __future__ import division, print_function

import geotecha.plotting.one_d #import MarkersDashesColors as MarkersDashesColors
import time
import numpy as np
import matplotlib
import matplotlib.pyplot as plt

import geotecha.speccon.speccon1d as speccon1d
import geotecha.piecewise.piecewise_linear_1d as pwise
from geotecha.piecewise.piecewise_linear_1d import PolyLine
import geotecha.speccon.integrals as integ
import geotecha.mathematics.transformations as transformations
from geotecha.inputoutput.inputoutput import GenericInputFileArgParser


class Speccon1dVRC(speccon1d.Speccon1d):
    """Multilayer consolidation with stone columns including vertical and
    radial drainage in the column, using the spectral Galerkin method.

    Features:

     - Multiple layers.
     - Vertical and radial drainage in a unit cell.
       (radial drainage uses the eta method).
     - Finite vertical and radial permeability in the column.
     - Material properties that are constant in time but piecewsie linear with
       depth (including column permeability and stiffness). Soil-column
       stiffness is modelled using a lumped soil/column volume compressibilty
       (mv).
     - Surcharge loading (vacuum loading is via specifying non-zero negative
       pore pressure at top and bottom of drain.
     - Non-zero top and bottom pore pressure boundary conditions (top and
       bottom pore pressures are the same in the column and soil).
     - Surcharge/Boundary Conditions/vary
       with time in a piecewise-linear function multiplied by a cosine
       function of time.

       - Surcharge can also vary piecewise linear with depth.
         The depth dependence does not vary with time.
       - Mulitple loads will be combined using superposition.
     - Subset of Python syntax available in input files/strings allowing
       basic calculations within input files.
     - Output:

       - Excess pore pressure at depth in soil and column.
       - Average excess pore pressure between two depths (in soil, column and
         overall).
       - Settlement between two depths.
       - Charts and csv output available.
     - Program can be run as script or in a python interpreter.
     - Note there is no pumping or fixed pore pressure functionality.


    .. warning::
        The 'Parameters' and 'Attributes' sections below require further
        explanation.  The parameters listed below are not used to explicitly
        initialize the object.  Rather they are defined in either a
        multi-line string or a file-like object using python syntax; the
        file/string is then used to initialize the object using the
        `reader` parameter. As well as simple assignment statements
        (H = 1, drn = 0 etc.), the input file/string can contain basic
        calculations (z = np.linspace(0, H, 20) etc.).  Not all of the
        listed parameters are needed. The user should pick an appropriate
        combination of attributes for their analysis (minimal explicit
        checks on input data will be performed).
        Each  'parameter' will be turned into an attribute that
        can be accessed using conventional python dot notation, after the
        object has been initialised.  The attributes listed below are
        calculated values (i.e. they could be interpreted as results) which
        are accessible using dot notation after all calculations are
        complete.


    Parameters
    ----------
    H : float, optional
        Total height of soil profile. Default H=1.0. Note that even though
        this program deals with normalised depth values it is important to
        enter the correct H valu, as it is used when plotting, outputing
        data and in normalising gradient boundary conditions (see
        `bot_vs_time` below).
    mvref : float, optional
        Reference value of volume compressibility mv (used with `H` in
        settlement calculations). Default mvref=1.0.
    kvref : float, optional
        Reference value of vertical permeability kv  in soil
        (only used for pretty output). Default kvref=1.0.
    khref : float, optional
        Reference value of horizontal permeability kh in soil (only used for
        pretty output). Default khref=1.0.
    kvcref : float, optional
        Reference value of vertical permeability kvc  in column
        (only used for pretty output). Default kvcref=1.0.
    khcref : float, optional
        Reference value of horizontal permeability khc in column (only used for
        pretty output). Default khcref=1.0.
    etref : float, optional
        Reference value of lumped drain parameter et (only used for pretty
        output). Default etref=1.0.  et = 2 / (mu * re^2) where mu is
        smear-zone/geometry parameter and re is radius of influence of
        vertical drain.
    drn : {0, 1}, optional
        drainage boundary condition. Default drn=0.
        0 = Pervious top pervious bottom (PTPB).
        1 = Pervious top impoervious bottom (PTIB).
    dT : float, optional
        Convienient normaliser for time factor multiplier. Default dT=1.0.
    neig : int, optional
        Number of series terms to use in solution. Default neig=2. Don't use
        neig=1.
    dTv : float, optional
        Vertical reference time factor multiplier.  dTv is calculated with
        the chosen reference values of kv and mv: dTv = kv /(mv*gamw) / H ^ 2
    dTvc : float, optional
        Well reference time factor multiplier.  dTvc is calculated with
        the chosen reference values of kvc and mv:
        dTvc = kvc /(mv*gamw) / H ^ 2
    dTh : float, optional
        horizontal reference time factor multiplier.  dTh is calculated with
        the reference values of kh, et, and mv: dTh = kh / (mv * gamw) * et
    dThc : float, optional
        Horizontal reference time factor multiplier in column.
        dThc is calculated with
        the reference values of khc, and mv: dThc = 8*khc / (mv * gamw) /rc**2.
    mv : PolyLine
        Normalised volume compressibility PolyLine(depth, mv).  The mv here
        is the value of ms / (1 + alp * (Y - 1)) normalised by mvref.  Y is
        column to soil stiffness ratio ms/mc or Ec/Es. alp = 1/n**2 where
        n is the ratio between influence radius and column radius n=re/rw.
    kh : PolyLine, optional
        Normalised horizontal permeability in soil PolyLine(depth, kh).
    kv : PolyLine , optional
        Normalised vertical permeability in soil PolyLine(depth, kv).
    khc : PolyLine, optional
        Normalised horizontal permeability in column PolyLine(depth, kh).
    kvc : PolyLine , optional
        Normalised vertical permeability in column PolyLine(depth, kv).
    et : PolyLine, optional
        Normalised vertical drain parameter PolyLine(depth, et).
        et = 2 / (mu * re^2) where mu is smear-zone/geometry parameter and re
        is radius of influence of vertical drain.
    surcharge_vs_depth : list of Polyline, optional
        Surcharge variation with depth. PolyLine(depth, multiplier).
    surcharge_vs_time : list of Polyline, optional
        Surcharge magnitude variation with time. PolyLine(time, magnitude).
    surcharge_omega_phase : list of 2 element tuples, optional
        (omega, phase) to define cyclic variation of surcharge. i.e.
        mag_vs_time * cos(omega*t + phase). If surcharge_omega_phase is None
        then cyclic component will be ignored.  If surcharge_omega_phase is a
        list then if any member is None then cyclic component will not be
        applied for that load combo.
    top_vs_time : list of Polyline, optional
        Top p.press variation with time. Polyline(time, magnitude).
    top_omega_phase : list of 2 element tuples, optional
        (omega, phase) to define cyclic variation of top BC. i.e.
        mag_vs_time * cos(omega*t + phase). If top_omega_phase is None
        then cyclic component will be ignored.  If top_omega_phase is a
        list then if any member is None then cyclic component will not be
        applied for that load combo.
    bot_vs_time : list of Polyline, optional
        Bottom p.press variation with time. Polyline(time, magnitude).
        When drn=1, i.e. PTIB, bot_vs_time is equivilent to saying
        D[u(H,t), z] = bot_vs_time. Within the program the actual gradient
        will be normalised with depth by multiplying H.
    bot_omega_phase : list of 2 element tuples, optional
        (omega, phase) to define cyclic variation of bot BC. i.e.
        mag_vs_time * cos(omega*t + phase). If bot_omega_phase is None
        then cyclic component will be ignored.  If bot_omega_phase is a
        list then if any member is None then cyclic component will not be
        applied for that load combo.
    ppress_z : list_like of float, optional
        Normalised z to calculate pore pressure at.
    avg_ppress_z_pairs : list of two element list of float, optional
        Nomalised zs to calculate average pore pressure between
        e.g. average of all profile is [[0,1]].
    settlement_z_pairs : list of two element list of float, optional
        Normalised depths to calculate normalised settlement between.
        e.g. surface settlement would be [[0, 1]].
    tvals : list of float
        Times to calculate output at.
    ppress_z_tval_indexes : list/array of int, slice, optional
        Indexes of `tvals` at which to calculate ppress_z. i.e. only calculate
        ppress_z at a subset of the `tvals` values.
        Default ppress_z_tval_indexes=slice(None, None) i.e. use all the
        `tvals`.
    avg_ppress_z_pairs_tval_indexes : list/array of int, slice, optional
        Indexes of `tvals` at which to calculate avg_ppress_z_pairs.
        i.e. only calc avg_ppress_z_pairs at a subset of the `tvals` values.
        Default avg_ppress_z_pairs_tval_indexes=slice(None, None) i.e. use
        all the `tvals`.
    settlement_z_pairs_tval_indexes : list/array of int, slice, optional
        Indexes of `tvals` at which to calculate settlement_z_pairs.
        i.e. only calc settlement_z_pairs at a subset of the `tvals` values.
        Default settlement_z_pairs_tval_indexes=slice(None, None) i.e. use
        all the `tvals`.
    implementation : ['scalar', 'vectorized','fortran'], optional
        Where possible use the stated implementation type.  'scalar'=
        python loops (slowest), 'vectorized' = numpy (fast), 'fortran' =
        fortran extension (fastest).  Note only some functions have multiple
        implementations.
    RLzero : float, optional
        Reduced level of the top of the soil layer.  If RLzero is not None
        then all depths (in plots and results) will be transformed to an RL
        by RL = RLzero - z*H.  If RLzero is None (i.e. the default) then all
        depths will be reported  z*H (i.e. positive numbers).
    plot_properties : dict of dict, optional
        Dictionary that overrides some of the plot properties.
        Each member of `plot_properties` will correspond to one of the plots.

        ==================  ============================================
        plot_properties     description
        ==================  ============================================
        por                 dict of prop to pass to overall pore
                            pressure plot.
        porc                dict of prop to pass to soil pore pressure
                            plot.
        pors                dict of prop to pass to average pore
                            pressure plot.
        avp                 dict of prop to pass to overall average
                            pore pressure plot.
        avps                dict of prop to pass to soil average
                            pore pressure plot.
        avpc                dict of prop to pass to c average
                            pore pressure plot.
        set                 dict of prop to pass to settlement plot.
        load                dict of prop to pass to loading plot.
        material            dict of prop to pass to materials plot.
        ==================  ============================================
        see geotecha.plotting.one_d.plot_vs_depth and
        geotecha.plotting.one_d.plot_vs_time for options to specify in
        each plot dict.
    save_data_to_file : True/False, optional
        If True data will be saved to file.  Default save_data_to_file=False
    save_figures_to_file : True/False
        If True then figures will be saved to file.
        Default save_figures_to_file=False
    show_figures : True/False, optional
        If True the after calculation figures will be shown on screen.
        Default show_figures=False.
    directory : string, optional
        Path to directory where files should be stored.
        Default directory=None which
        will use the current working directory.  Note if you keep getting
        directory does not exist errors then try putting an r before the
        string definition. i.e. directory = r'C:\\Users\\...'
    overwrite : True/False, optional
        If True then existing files will be overwritten.
        Default overwrite=False.
    prefix : string, optional
         Filename prefix for all output files.  Default prefix= 'out'
    create_directory : True/Fase, optional
        If True a new sub-folder with name based on  `prefix` and an
        incremented number will contain the output
        files. Default create_directory=True.
    data_ext : string, optional
        File extension for data files. Default data_ext='.csv'
    input_ext : string, optional
        File extension for original and parsed input files. default = ".py"
    figure_ext : string, optional
        File extension for figures.  Can be any valid matplotlib option for
        savefig. Default figure_ext=".eps". Others include 'pdf', 'png'.
    title : str, optional
        A title for the input file.  This will appear at the top of data files.
        Default title=None, i.e. no title.
    author : str, optional
        Author of analysis. Default author='unknown'.


    Attributes
    ----------
    por, porc, pors : ndarray, only present if ppress_z is input
        Calculated pore pressure at depths corresponding to `ppress_z` and
        times corresponding to `tvals`.  This is an output array of
        size (len(ppress_z), len(tvals[ppress_z_tval_indexes])).
    avp, avpc, avps : ndarray, only present if avg_ppress_z_pairs is input
        Calculated average pore pressure between depths corresponding to
        `avg_ppress_z_pairs` and times corresponding to `tvals`.  This is an
        output array of size
        (len(avg_ppress_z_pairs), len(tvals[avg_ppress_z_pairs_tval_indexes])).
    set : ndarray, only present if settlement_z_pairs is input
        Settlement between depths corresponding to `settlement_z_pairs` and
        times corresponding to `tvals`.  This is an output array of size
        (len(avg_ppress_z_pairs), len(tvals[settlement_z_pairs_tval_indexes]))


    Notes
    -----
    **Gotchas**

    All the loading terms e.g. surcharge_vs_time, surcharge_vs_depth,
    surcharge_omega_phase can be either a single value or a list of values.
    The corresponding lists that define a load must have the same length
    e.g. if specifying multiple surcharge loads then surcharge_vs_time and
    surcharge_vs_depth must be lists of the same length such that
    surcharge_vs_time[0] can be paired with surcharge_vs_depth[0],
    surcharge_vs_time[1] can be paired with surcharge_vs_depth[1], etc.

    **Material and geometric properties**

     - :math:`k_v` is vertical soil permeability.
     - :math:`k_h` is horizontal soilpermeability.
     - :math:`k_{vc}` is vertical permeability in column.
     - :math:`k_{hc}` is horizontal permeability in column.
     - :math:`m_s` is the volume compressibility in the soil.
     - :math:`m_c` is the volume compressibility in the column.
     - :math:`m_v` is lumped volume compressibility.
       :math:`m_v=m_s/(1+\\alpha(Y-1))`.  Stiffness ratio
       :math:`Y=m_s/m_c=E_c/E_s`. Also :math:`\\alpha=1/n^2`.
     - :math:`\\eta` is the radial drainage parameter
       :math:`\\eta = \\frac{2}{r_e^2 \\mu}`.
     - :math:`r_e` is influence radius of drain.
     - :math:`r_w` is drain radius.
     - :math:`n=r_e/r_w` is ratio of influence radius to drain radius.
     - :math:`\\mu` is any of the smear zone geometry parameters dependent
       on the distribution of permeabilit in the smear zone (see
       geotecha.consolidation.smear_zones).
     - :math:`\\gamma_w` is the unit weight of water.
     - :math:`Z` is the nomalised depth (:math:`Z=z/H`).
     - :math:`H` is the total height of the soil profile.


    **Governing equation**
    Radially averaged soil and column pore pressures, :math:`u_s`,
    :math:`u_c` are related to the overall average pore pressure, :math:`u`
    by:

    .. math::
        u=\\left({1-\\alpha}\\right)u_s + \\alpha u_c

    where :math:`\\alpha=1-n^2=1-\\left({r_e/r_w}\\right)`. Equal strain in the
    soil and column requires:

    .. math::
        \\frac{\\varepsilon}{m_{vref}}=
            \\overline{m}_v \\left[{\\sigma
                                    -\\left({1-\\alpha}\\right)u_s
                                    -\\alpha u_c}\\right]

    Continuity of flow in the soil, column, and across the soil-column
    boundary respectively requires:

    .. math::
        \\frac{\\dot{\\varepsilon}}{m_{vref}}=
            dT_h\\overline{k}_h\\overline{\\eta}\\left({u_s-\\beta}\\right)
            - dT_v\\left({\\overline{k}_v u_s,_Z}\\right),_Z


    .. math::
        \\frac{\\dot{\\varepsilon}}{m_{vref}}=
            dT_{hc}\\overline{k}_{hc}\\left({u_c-\\beta}\\right)
            - dT_{vc}\\left({\\overline{k}_{vc} u_c,_Z}\\right),_Z

    .. math::
        \\frac{\\dot{\\varepsilon}}{m_{vref}}=
            \\left({1 - \\alpha}\\right) dT_v\\left({\\overline{k}_v u,_Z}\\right),_Z
            - \\alpha dT_{vc}\\left({\\overline{k}_{vc} u_c,_Z}\\right),_Z

    Each pore pressure value is a function of normalised depth
    :math:`Z` and time :math:`t`.  :math:`\\beta` is the pore pressure at the
    soil/column interface at a particular depth.


    where

    .. math::
        dT_v = \\frac{k_{v\\textrm{ref}}}
                     {H^2 m_{v\\textrm{ref}} \\gamma_w}
    .. math::
        dT_{vc} = \\frac{k_{vc\\textrm{ref}}}
                     {H^2 m_{v\\textrm{ref}} \\gamma_w}

    .. math::
        dT_{hc} = \\frac{8 k_{hc\\textrm{ref}}}
                     {m_{v\\textrm{ref}} \\gamma_w r_c^2}

    .. math::
        dT_h = \\frac{k_{h\\textrm{ref}} \\eta_{\\textrm{ref}}}
                     {m_{v\\textrm{ref}} \\gamma_w}

    .. math:: \\eta = \\frac{2}{r_e^2 \\mu}


    :math:`\\mu` is any of the smear zone geometry parameters dependent on
    the distribution of permeabilit in the smear zone (see
    geotecha.consolidation.smear_zones).


    The overline notation represents a depth dependent property normalised
    by the relevant reference property. e.g.
    :math:`\\overline{k}_v = k_v\\left({z}\\right) / k_{v\\textrm{ref}}`.

    A comma followed by a subscript represents differentiation with respect to
    the subscripted variable e.g.
    :math:`u,_Z = u\\left({Z,t}\\right) / \\partial Z`.



    **Non-zero Boundary conditions**

    The following two sorts of boundary conditions (identical in in both the
    soil and column) can be modelled:

    .. math::
        \\left.u\\left({Z,t}\\right)\\right|_{Z=0} = u^{\\textrm{top}}\\left({t}\\right)
        \\textrm{ and }
        \\left.u\\left({Z,t}\\right)\\right|_{Z=1} = u^{\\textrm{bot}}\\left({t}\\right)


    .. math::
        \\left.u\\left({Z,t}\\right)\\right|_{Z=0} = u^{\\textrm{top}}\\left({t}\\right)
        \\textrm{ and }
        \\left.u\\left({Z,t}\\right),_Z\\right|_{Z=1} = u^{\\textrm{bot}}\\left({t}\\right)


    The boundary conditions are incorporated by homogenising the governing
    equation with the following substitution (same process for the column and
    beta):

    .. math::
        u\\left({Z,t}\\right)
        = \\hat{u}\\left({Z,t}\\right) + u_b\\left({Z,t}\\right)

    where for the two types of non zero boundary boundary conditions:

    .. math::
        u_b\\left({Z,t}\\right)
        = u^{\\textrm{top}}\\left({t}\\right) \\left({1-Z}\\right)
        + u^{\\textrm{bot}}\\left({t}\\right) Z

    .. math::
        u_b\\left({Z,t}\\right)
        = u^{\\textrm{top}}\\left({t}\\right)
        + u^{\\textrm{bot}}\\left({t}\\right) Z

    **Time and depth dependence of loads/material properties**

    Soil properties do not vary with time.


    Loads are formulated as the product of separate time and depth
    dependant functions as well as a cyclic component:

    .. math:: \\sigma\\left({Z,t}\\right)=
                \\sigma\\left({Z}\\right)
                \\sigma\\left({t}\\right)
                \\cos\\left(\\omega t + \\phi\\right)

    :math:`\\sigma\\left(t\\right)` is a piecewise linear function of time
    that within the kth loading stage is defined by the load magnitude at
    the start and end of the stage:

    .. math::
        \\sigma\\left(t\\right)
        = \\sigma_k^{\\textrm{start}}
        + \\frac{\\sigma_k^{\\textrm{end}}
                 - \\sigma_k^{\\textrm{start}}}
                {t_k^{\\textrm{end}}
                 - t_k^{\\textrm{start}}}
        \\left(t - t_k^{\\textrm{start}}\\right)

    The depth dependence of loads and material property
    :math:`a\\left(Z\\right)` is a piecewise linear function
    with respect to :math:`Z`, that within a layer are defined by:

    .. math::
        a\\left(z\\right)
        = a_t + \\frac{a_b - a_t}{z_b - z_t}\\left(z - z_t\\right)

    with :math:`t` and :math:`b` subscripts representing 'top' and 'bottom' of
    each layer respectively.



    References
    ----------
    The genesis of this work is from research carried out by
    Dr. Rohan Walker, Prof. Buddhima Indraratna and others
    at the University of Wollongong, NSW, Austrlia, [1]_, [2]_, [3]_, [4]_.

    .. [1] Walker, Rohan. 2006. 'Analytical Solutions for Modeling Soft
           Soil Consolidation by Vertical Drains'. PhD Thesis, Wollongong,
           NSW, Australia: University of Wollongong.
    .. [2] Walker, R., and B. Indraratna. 2009. 'Consolidation Analysis of
           a Stratified Soil with Vertical and Horizontal Drainage Using the
           Spectral Method'. Geotechnique 59 (5) (January): 439-449.
           doi:10.1680/geot.2007.00019.
    .. [3] Walker, Rohan, Buddhima Indraratna, and Nagaratnam Sivakugan. 2009.
           'Vertical and Radial Consolidation Analysis of Multilayered
           Soil Using the Spectral Method'. Journal of Geotechnical and
           Geoenvironmental Engineering 135 (5) (May): 657-663.
           doi:10.1061/(ASCE)GT.1943-5606.0000075.
    .. [4] Walker, Rohan T. 2011. Vertical Drain Consolidation Analysis
           in One, Two and Three Dimensions'. Computers and
           Geotechnics 38 (8) (December): 1069-1077.
           doi:10.1016/j.compgeo.2011.07.006.

    """

    def _setup(self):

        self._attributes = (
            'H drn dT neig n '
            'mvref kvref kvcref khref khcref etref '
            'dTh dTv dTvc dThc '
            'mv kh kv et khc kvc '
            'surcharge_vs_depth surcharge_vs_time '
            'top_vs_time bot_vs_time '
            'ppress_z avg_ppress_z_pairs settlement_z_pairs tvals '
            'implementation ppress_z_tval_indexes '
            'avg_ppress_z_pairs_tval_indexes settlement_z_pairs_tval_indexes '
            'surcharge_omega_phase '
            'top_omega_phase bot_omega_phase '
            'RLzero '
            'prefix '

            ).split()

        self._attribute_defaults = {
            'H': 1.0, 'drn': 0, 'dT': 1.0, 'neig': 2, 'mvref':1.0,
            'kvref': 1.0, 'khref': 1.0, 'etref': 1.0,
            'kvcref': 1.0, 'khcref': 1.0,
            'implementation': 'vectorized',
            'ppress_z_tval_indexes': slice(None, None),
            'avg_ppress_z_pairs_tval_indexes': slice(None, None),
            'settlement_z_pairs_tval_indexes': slice(None, None),
            'prefix': 'speccon1dvrc_'
            }

        self._attributes_that_should_be_lists= (
            'surcharge_vs_depth surcharge_vs_time surcharge_omega_phase '
            'top_vs_time top_omega_phase '
            'bot_vs_time bot_omega_phase ').split()

        self._attributes_that_should_have_same_x_limits = [
            'mv kv kh kvc khc et surcharge_vs_depth'.split()]

        self._attributes_that_should_have_same_len_pairs = [
            'surcharge_vs_depth surcharge_vs_time'.split(),
            'surcharge_vs_time surcharge_omega_phase'.split(),
            'top_vs_time top_omega_phase'.split(),
            'bot_vs_time bot_omega_phase'.split()]

        self._attributes_to_force_same_len = [
            "surcharge_vs_time surcharge_omega_phase".split(),
            "top_vs_time top_omega_phase".split(),
            "bot_vs_time bot_omega_phase".split()]

        self._zero_or_all = [
            'dTv kv'.split(),
            'surcharge_vs_depth surcharge_vs_time'.split(),
            ]
        self._at_least_one = [
            ['dTh'],
            ['dThc'],
            ['dTvc'],
            ['dTv'],
            ['mv'],
            ['n'],
            ('surcharge_vs_time top_vs_time '
                'bot_vs_time').split(),
            ['tvals'],
            'ppress_z avg_ppress_z_pairs settlement_z_pairs'.split()]

        self._one_implies_others = [
            ('surcharge_omega_phase surcharge_vs_depth '
                'surcharge_vs_time').split(),
            'top_omega_phase top_vs_time'.split(),
            'bot_omega_phase bot_vs_time'.split(),
            'dTh kh et'.split(),
            'dThc khc'.split(),
            'dTvc kvc et'.split(),
            'dTv kv'.split(),]


        #these explicit initializations are just to make coding easier
        self.H = self._attribute_defaults.get('H', None)
        self.drn = self._attribute_defaults.get('drn', None)
        self.dT = self._attribute_defaults.get('dT', None)
        self.neig = self._attribute_defaults.get('neig', None)
        self.mvref = self._attribute_defaults.get('mvref', None)
        self.kvref = self._attribute_defaults.get('kvref', None)
        self.khref = self._attribute_defaults.get('khref', None)
        self.kvcref = self._attribute_defaults.get('kvcref', None)
        self.khcref = self._attribute_defaults.get('khcref', None)
        self.etref = self._attribute_defaults.get('etref', None)
        self.dTh = None
        self.dTv = None
        self.dThc = None
        self.dTvc = None
        self.mv = None
        self.kh = None
        self.kv = None
        self.khc = None
        self.kvc = None
        self.et = None
        self.n = None
        self.surcharge_vs_depth = None
        self.surcharge_vs_time = None
        self.surcharge_omega_phase = None

        self.top_vs_time = None
        self.top_omega_phase = None
        self.bot_vs_time = None
        self.bot_omega_phase = None


        self.ppress_z = None
        self.avg_ppress_z_pairs = None
        self.settlement_z_pairs = None
        self.tvals = None
        self.RLzero = None

        self.plot_properties = self._attribute_defaults.get('plot_properties',
                                                            None)

        self.ppress_z_tval_indexes = self._attribute_defaults.get(
                'ppress_z_tval_indexes', None)
        self.avg_ppress_z_pairs_tval_indexes = self._attribute_defaults.get(
                'avg_ppress_z_pairs_tval_indexes', None)
        self.settlement_z_pairs_tval_indexes = self._attribute_defaults.get(
                'settlement_z_pairs_tval_indexes', None)


        return

    def make_time_independent_arrays(self):
        """make all time independent arrays


        See Also
        --------
        self._make_m : make the basis function eigenvalues
        self._make_gam : make the mv dependent gamma matrix
        self._make_psi : make the kv, kh, et dependent psi matrix
        self._make_eigs_and_v : make eigenvalues, eigenvectors and I_gamv

        """


        self.alp = 1 / self.n**2


        self._make_m()
        self._make_gam()
        self._make_psi()
        self._make_eigs_and_v()

        return

    def make_time_dependent_arrays(self):
        """make all time dependent arrays

        See Also
        --------
        self.make_E_Igamv_the()

        """
        self.tvals = np.asarray(self.tvals)
        self.make_E_Igamv_the()
        self.v_E_Igamv_the = np.dot(self.v, self.E_Igamv_the)
        return





    def make_output(self):
        """make all output"""

        header1 = ("program: speccon1d_vrc; geotecha version: "
            "{}; author: {}; date: {}\n").format(self.version,
                self.author, time.strftime('%Y/%m/%d %H:%M:%S'))
        if not self.title is None:
            header1+= "{}\n".format(self.title)

        self._grid_data_dicts = []
        if not self.ppress_z is None:
            self._make_por()
            z = transformations.depth_to_reduced_level(
                np.asarray(self.ppress_z), self.H, self.RLzero)
            labels = ['{:.3g}'.format(v) for v in z]
            d = {'name': '_data_por',
                 'data': self.por.T,
                 'row_labels': self.tvals[self.ppress_z_tval_indexes],
                 'row_labels_label': 'Time',
                 'column_labels': labels,
                 'header': header1 + 'Pore pressure at depth'}
            self._grid_data_dicts.append(d)

            d = {'name': '_data_pors',
                 'data': self.pors.T,
                 'row_labels': self.tvals[self.ppress_z_tval_indexes],
                 'row_labels_label': 'Time',
                 'column_labels': labels,
                 'header': header1 + 'Pore pressure at depth in soil'}
            self._grid_data_dicts.append(d)

            d = {'name': '_data_porc',
                 'data': self.porc.T,
                 'row_labels': self.tvals[self.ppress_z_tval_indexes],
                 'row_labels_label': 'Time',
                 'column_labels': labels,
                 'header': header1 + 'Pore pressure at depth in column'}
            self._grid_data_dicts.append(d)

        if not self.avg_ppress_z_pairs is None:
            self._make_avp()
            z_pairs = transformations.depth_to_reduced_level(
                np.asarray(self.avg_ppress_z_pairs), self.H, self.RLzero)
            labels = ['{:.3g} to {:.3g}'.format(z1, z2) for z1, z2 in z_pairs]
            d = {'name': '_data_avp',
                 'data': self.avp.T,
                 'row_labels': self.tvals[self.avg_ppress_z_pairs_tval_indexes],
                 'row_labels_label': 'Time',
                 'column_labels': labels,
                 'header': header1 + 'Average pore pressure between depths'}
            self._grid_data_dicts.append(d)

            d = {'name': '_data_avps',
                 'data': self.avps.T,
                 'row_labels': self.tvals[self.avg_ppress_z_pairs_tval_indexes],
                 'row_labels_label': 'Time',
                 'column_labels': labels,
                 'header': header1 + 'Average soil pore pressure between depths'}
            self._grid_data_dicts.append(d)

            d = {'name': '_data_avpc',
                 'data': self.avpc.T,
                 'row_labels': self.tvals[self.avg_ppress_z_pairs_tval_indexes],
                 'row_labels_label': 'Time',
                 'column_labels': labels,
                 'header': header1 + 'Average column pore pressure between depths'}
            self._grid_data_dicts.append(d)

        if not self.settlement_z_pairs is None:
            self._make_set()
            z_pairs = transformations.depth_to_reduced_level(
                np.asarray(self.settlement_z_pairs), self.H, self.RLzero)
            labels = ['{:.3g} to {:.3g}'.format(z1, z2) for z1, z2 in z_pairs]
            d = {'name': '_data_set',
                 'data': self.set.T,
                 'row_labels': self.tvals[self.settlement_z_pairs_tval_indexes],
                 'row_labels_label': 'Time',
                 'column_labels': labels,
                 'header': header1 + 'settlement between depths'}
            self._grid_data_dicts.append(d)
        return


    def _make_m(self):
        """make the basis function eigenvalues

        m in u = sin(m * Z)

        Notes
        -----

        .. math:: m_i =\\pi*\\left(i+1-drn/2\\right)

        for :math:`i = 1\:to\:neig-1`

        """

        if sum(v is None for v in[self.neig, self.drn])!=0:
            raise ValueError('neig and/or drn is not defined')
        self.m = integ.m_from_sin_mx(np.arange(self.neig), self.drn)
        return


    def _make_gam(self):
        """make the mv dependant gam matrix

        """

        self.gam = integ.pdim1sin_af_linear(
                        self.m, self.mv, implementation=self.implementation)
        self.gam[np.abs(self.gam)<1e-8] = 0.0

        return


    def _make_psi(self):
        """make all the kv, kh, kvc, khc, et dependant psi matrices



        """

        #psi_sv, kv part
        if sum([v is None for v in [self.kv, self.dTv]])==0:
            self.psi_sv = (self.dTv / self.dT *
                integ.pdim1sin_D_aDf_linear(self.m, self.kv,
                    implementation=self.implementation))

        #psi_sh, kh & et part
        if sum([v is None for v in [self.kh, self.et, self.dTh]])==0:
            kh, et = pwise.polyline_make_x_common(self.kh, self.et)#
            self.psi_sh = (self.dTh / self.dT *
                integ.pdim1sin_abf_linear(self.m, self.kh, self.et,
                                          implementation=self.implementation))
        #psi_s
            self.psi_s = self.psi_sh - self.psi_sv

        #psi_cv, kvc part
        if sum([v is None for v in [self.kvc, self.dTvc]])==0:
            self.psi_cv = (self.dTvc / self.dT *
                integ.pdim1sin_D_aDf_linear(self.m, self.kvc,
                                        implementation=self.implementation))

        #psi_ch, khc
        if sum([v is None for v in [self.khc, self.dThc]])==0:
            self.psi_ch = (self.dThc / self.dT *
                integ.pdim1sin_af_linear(self.m, self.khc,
                                         implementation=self.implementation))
        #psi_c
            self.psi_c = self.psi_ch - self.psi_cv




        Ibet = np.bmat([[np.diag([1.0 - self.alp] * self.neig),
                         np.diag([self.alp] * self.neig),
                         np.zeros((self.neig, self.neig))],
                        [self.psi_s,
                         -self.psi_c ,
                         self.psi_ch - self.psi_sh ],
                        [self.psi_sh - self.alp * self.psi_sv,
                         self.alp * self.psi_cv,
                         -self.psi_sh]])

        Ibet = np.asarray(Ibet) # np.bmat returns an array

        self.bet = np.linalg.inv(Ibet)

        self.bet00 = self.bet[:self.neig, :self.neig]
        self.bet01 = self.bet[:self.neig, self.neig:2 * self.neig]
        self.bet02 = self.bet[:self.neig, 2 * self.neig:]

        self.bet10 = self.bet[self.neig: 2*self.neig, :self.neig]
        self.bet11 = self.bet[self.neig: 2*self.neig, self.neig:2 * self.neig]
        self.bet12 = self.bet[self.neig: 2*self.neig, 2 * self.neig:]

        self.bet20 = self.bet[2*self.neig:, :self.neig]
        self.bet21 = self.bet[2*self.neig:, self.neig:2 * self.neig]
        self.bet22 = self.bet[2*self.neig:, 2 * self.neig:]


        self.psi = (1 - self.alp) * np.dot(self.psi_sv, self.bet00)
        self.psi += self.alp * np.dot(self.psi_cv, self.bet10)
        self.psi *=-1.0


        return

    def _make_eigs_and_v(self):
        """make Igam_psi, v and eigs, and Igamv



        Finds the eigenvalues, `self.eigs`, and eigenvectors, `self.v` of
        inverse(gam)*psi.  Once found the matrix inverse(gamma*v), `self.Igamv`
        is determined.

        Notes
        -----
        From the original equation

        .. math:: \\mathbf{\\Gamma}\\mathbf{A}'=\\mathbf{\\Psi A}+loading\\:terms

        `self.eigs` and `self.v` are the eigenvalues and eigenvegtors of the matrix `self.Igam_psi`

        .. math:: \\left(\\mathbf{\\Gamma}^{-1}\\mathbf{\\Psi}\\right)

        """

        self.psi[np.abs(self.psi) < 1e-8] = 0.0
        Igam_psi = np.dot(np.linalg.inv(self.gam), self.psi)
        self.eigs, self.v = np.linalg.eig(Igam_psi)
        self.v = np.asarray(self.v)
        self.Igamv = np.linalg.inv(np.dot(self.gam, self.v))

        return

    def make_E_Igamv_the(self):
        """sum contributions from all loads

        Calculates all contributions to E*inverse(gam*v)*theta part of solution
        u=phi*vE*inverse(gam*v)*theta. i.e. surcharge, vacuum, top and bottom
        pore pressure boundary conditions. `make_load_matrices will create
        `self.E_Igamv_the`.  `self.E_Igamv_the`  is an array
        of size (neig, len(tvals)). So the columns are the column array
        E*inverse(gam*v)*theta calculated at each output time.  This will allow
        us later to do u = phi*v*self.E_Igamv_the

        See Also
        --------
        _make_E_Igamv_the_surcharge :  surchage contribution
        _make_E_Igamv_the_BC : top boundary pore pressure contribution
        _make_E_Igamv_the_bot : bottom boundary pore pressure contribution
        """

        self.E_Igamv_the = np.zeros((self.neig, len(self.tvals)))

        if sum([v is None for
                v in [self.surcharge_vs_depth, self.surcharge_vs_time]])==0:
            self._make_E_Igamv_the_surcharge()
            self.E_Igamv_the += self.E_Igamv_the_surcharge

        if not self.top_vs_time is None or not self.bot_vs_time is None:
            self._make_E_Igamv_the_BC()
            self.E_Igamv_the += self.E_Igamv_the_BC

        return

    def _make_E_Igamv_the_surcharge(self):
        """make the surcharge loading matrices

        Make the E*inverse(gam*v)*theta part of solution u=phi*vE*inverse(gam*v)*theta.
        The contribution of each surcharge load is added and put in
        `self.E_Igamv_the_surcharge`. `self.E_Igamv_the_surcharge` is an array
        of size (neig, len(tvals)). So the columns are the column array
        E*inverse(gam*v)*theta calculated at each output time.  This will allow
        us later to do u = phi*v*self.E_Igamv_the_surcharge

        Notes
        -----
        Assuming the load are formulated as the product of separate time and depth
        dependant functions:

        .. math:: \\sigma\\left({Z,t}\\right)=\\sigma\\left({Z}\\right)\\sigma\\left({t}\\right)

        the solution to the consolidation equation using the spectral method has
        the form:

        .. math:: u\\left(Z,t\\right)=\\mathbf{\\Phi v E}\\left(\\mathbf{\\Gamma v}\\right)^{-1}\\mathbf{\\theta}

        `_make_E_Igamv_the_surcharge` will create `self.E_Igamv_the_surcharge` which is
        the :math:`\\mathbf{E}\\left(\\mathbf{\\Gamma v}\\right)^{-1}\\mathbf{\\theta}`
        part of the solution for all surcharge loads

        """
        self.E_Igamv_the_surcharge = (
            speccon1d.dim1sin_E_Igamv_the_aDmagDt_bilinear(self.m,
                   self.eigs, self.tvals, self.Igamv, self.mv,
                   self.surcharge_vs_depth, self.surcharge_vs_time,
                   self.surcharge_omega_phase, self.dT,
                   implementation=self.implementation))

        return




    def _normalised_bot_vs_time(self):
        """Normalise bot_vs_time when drn=1, i.e. bot_vs_time is a gradient

        Multiplie each bot_vs_time PolyLine by self.H

        Returns
        -------
        bot_vs_time : list of Polylines, or None
            bot_vs_time normalised by H

        """

        if not self.bot_vs_time is None:
            if self.drn == 1:
                bot_vs_time = ([vs_time * self.H for
                                vs_time in self.bot_vs_time])
            else:
                bot_vs_time = self.bot_vs_time
        else:
            bot_vs_time = None
        return bot_vs_time

    def _make_E_Igamv_the_BC(self):
        """make the boundary condition loading matrices

        """
        self.E_Igamv_the_BC = np.zeros((self.neig, len(self.tvals)))
        bot_vs_time = self._normalised_bot_vs_time()


        #mv * du/dt component
        self.E_Igamv_the_BC -= (
            speccon1d.dim1sin_E_Igamv_the_BC_aDfDt_linear(
                self.drn, self.m, self.eigs, self.tvals,
                self.Igamv, self.mv, self.top_vs_time, bot_vs_time,
                self.top_omega_phase, self.bot_omega_phase, self.dT,
                implementation=self.implementation))


        G = np.diag([self.alp]*self.neig)
        G -= (1-self.alp) * self.psi_sv.dot((self.bet01 + self.alp*self.bet02))
        G -= self.alp * self.psi_cv.dot((self.bet11 + self.alp*self.bet12))

        #dTv * d/dZ(kv * du/dZ) component
        if sum([v is None for v in [self.kv, self.dTv]])==0:
            if self.dTv!=0:
                self.E_Igamv_the_BC += (self.dTv *
                    speccon1d.dim1sin_E_Igamv_the_BC_D_aDf_linear(
                        self.drn, self.m, self.eigs, self.tvals,
                        self.Igamv.dot(np.identity(self.neig, dtype=float)-G),
                        self.kv, self.top_vs_time,
                        bot_vs_time, self.top_omega_phase,
                        self.bot_omega_phase, self.dT,
                implementation=self.implementation))

        #dTvc * d/dZ(kvc * du/dZ) component
        if sum([v is None for v in [self.kvc, self.dTvc]])==0:
            if self.dTvc!=0:
                self.E_Igamv_the_BC += (self.dTvc *
                    speccon1d.dim1sin_E_Igamv_the_BC_D_aDf_linear(
                        self.drn, self.m, self.eigs, self.tvals,
                        self.Igamv.dot(np.identity(self.neig, dtype=float)-G),
                        self.kvc, self.top_vs_time,
                        bot_vs_time, self.top_omega_phase,
                        self.bot_omega_phase, self.dT,
                implementation=self.implementation))



    def _make_por(self):
        """make the pore pressure output, us, uc, and u

        makes `self.por`, the average pore pressure at depths corresponding to
        self.ppress_z and times corresponding to self.tvals.  `self.por`  has size
        (len(ppress_z), len(tvals)).

        Notes
        -----
        Solution to consolidation equation with spectral method for pore pressure at depth is :

        .. math:: u\\left(Z,t\\right)=\\mathbf{\\Phi v E}\\left(\\mathbf{\\Gamma v}\\right)^{-1}\\mathbf{\\theta}+u_{top}\\left({t}\\right)\\left({1-Z}\\right)+u_{bot}\\left({t}\\right)\\left({Z}\\right)

        For pore pressure :math:`\\Phi` is simply :math:`sin\\left({mZ}\\right)` for each value of m


        """

        bot_vs_time = self._normalised_bot_vs_time()
        tvals = self.tvals[self.ppress_z_tval_indexes]
        #average pore pressure at depth
        self.por = speccon1d.dim1sin_f(self.m, self.ppress_z,
            tvals,
            self.v_E_Igamv_the[:, self.ppress_z_tval_indexes],
            self.drn, self.top_vs_time, bot_vs_time,
            self.top_omega_phase, self.bot_omega_phase)

        #soil pore poressure at depth
        self.pors = speccon1d.dim1sin_f(self.m, self.ppress_z,
            tvals,
            self.bet00.dot(self.v_E_Igamv_the[:, self.ppress_z_tval_indexes]),
            self.drn, self.top_vs_time, bot_vs_time,
            self.top_omega_phase, self.bot_omega_phase)
        if not self.top_vs_time is None or not self.bot_vs_time is None:
            a = self.dTv * speccon1d.dim1sin_foft_Ipsiw_the_BC_D_aDf_linear(
                    self.drn, self.m, self.eigs,
                    tvals,
                    (self.bet01 + self.alp * self.bet02),
                    self.kv, self.top_vs_time, bot_vs_time,
                    self.top_omega_phase, self.bot_omega_phase)
            b = self.dTvc * speccon1d.dim1sin_foft_Ipsiw_the_BC_D_aDf_linear(
                    self.drn, self.m, self.eigs,
                    tvals,
                    (self.bet01 + self.alp * self.bet02),
                    self.kvc, self.top_vs_time, bot_vs_time,
                    self.top_omega_phase, self.bot_omega_phase)
            self.pors += speccon1d.dim1sin_f(self.m, self.ppress_z,
                                             tvals, a+b, self.drn)

        #column pore pressure at depth
        self.porc = speccon1d.dim1sin_f(self.m, self.ppress_z,
            tvals,
            self.bet10.dot(self.v_E_Igamv_the[:, self.ppress_z_tval_indexes]),
            self.drn, self.top_vs_time, bot_vs_time,
            self.top_omega_phase, self.bot_omega_phase)
        if not self.top_vs_time is None or not self.bot_vs_time is None:
            a = self.dTv * speccon1d.dim1sin_foft_Ipsiw_the_BC_D_aDf_linear(
                    self.drn, self.m, self.eigs,
                    tvals,
                    (self.bet11 + self.alp * self.bet12),
                    self.kv, self.top_vs_time, bot_vs_time,
                    self.top_omega_phase, self.bot_omega_phase)
            b = self.dTvc * speccon1d.dim1sin_foft_Ipsiw_the_BC_D_aDf_linear(
                    self.drn, self.m, self.eigs,
                    tvals,
                    (self.bet11 + self.alp * self.bet12),
                    self.kvc, self.top_vs_time, bot_vs_time,
                    self.top_omega_phase, self.bot_omega_phase)
            self.porc += speccon1d.dim1sin_f(self.m, self.ppress_z,
                                             tvals, a+b, self.drn)
        return




    def _make_avp(self):
        """calculate average pore pressure, for us uc and u

        makes `self.avp`, the average pore pressure at depths corresponding to
        self.avg_ppress_z_pairs and times corresponding to self.tvals.  `self.avp`  has size
        (len(ppress_z), len(tvals)).


        Notes
        -----
        The average pore pressure between Z1 and Z2 is given by:

        .. math:: \\overline{u}\\left(\\left({Z_1,Z_2}\\right),t\\right)=\\int_{Z_1}^{Z_2}{\\mathbf{\\Phi v E}\\left(\\mathbf{\\Gamma v}\\right)^{-1}\\mathbf{\\theta}+u_{top}\\left({t}\\right)\\left({1-Z}\\right)+u_{bot}\\left({t}\\right)\\left({Z}\\right)\,dZ}/\\left({Z_2-Z_1}\\right)

        """
        bot_vs_time = self._normalised_bot_vs_time()
        tvals = self.tvals[self.avg_ppress_z_pairs_tval_indexes]
        v_E_Igamv_the = self.v_E_Igamv_the[:self.neig, self.avg_ppress_z_pairs_tval_indexes]
        #average pore pressure at depth
        self.avp = speccon1d.dim1sin_avgf(self.m, self.avg_ppress_z_pairs,
            tvals,
            v_E_Igamv_the,
            self.drn, self.top_vs_time, bot_vs_time,
            self.top_omega_phase, self.bot_omega_phase)

        #soil pore poressure at depth
        self.avps = speccon1d.dim1sin_avgf(self.m, self.avg_ppress_z_pairs,
            tvals,
            self.bet00.dot(v_E_Igamv_the),
            self.drn, self.top_vs_time, bot_vs_time,
            self.top_omega_phase, self.bot_omega_phase)
        if not self.top_vs_time is None or not self.bot_vs_time is None:
            a = self.dTv * speccon1d.dim1sin_foft_Ipsiw_the_BC_D_aDf_linear(
                    self.drn, self.m, self.eigs,
                    tvals,
                    (self.bet01 + self.alp * self.bet02),
                    self.kv, self.top_vs_time, bot_vs_time,
                    self.top_omega_phase, self.bot_omega_phase)
            b = self.dTvc * speccon1d.dim1sin_foft_Ipsiw_the_BC_D_aDf_linear(
                    self.drn, self.m, self.eigs,
                    tvals,
                    (self.bet01 + self.alp * self.bet02),
                    self.kvc, self.top_vs_time, bot_vs_time,
                    self.top_omega_phase, self.bot_omega_phase)
            self.avps += speccon1d.dim1sin_avgf(self.m, self.avg_ppress_z_pairs,
                                             tvals, a+b, self.drn)

        #column pore pressure at depth
        self.avpc = speccon1d.dim1sin_avgf(self.m, self.avg_ppress_z_pairs,
            tvals,
            self.bet10.dot(v_E_Igamv_the),
            self.drn, self.top_vs_time, bot_vs_time,
            self.top_omega_phase, self.bot_omega_phase)
        if not self.top_vs_time is None or not self.bot_vs_time is None:
            a = self.dTv * speccon1d.dim1sin_foft_Ipsiw_the_BC_D_aDf_linear(
                    self.drn, self.m, self.eigs,
                    tvals,
                    (self.bet11 + self.alp * self.bet12),
                    self.kv, self.top_vs_time, bot_vs_time,
                    self.top_omega_phase, self.bot_omega_phase)
            b = self.dTvc * speccon1d.dim1sin_foft_Ipsiw_the_BC_D_aDf_linear(
                    self.drn, self.m, self.eigs,
                    tvals,
                    (self.bet11 + self.alp * self.bet12),
                    self.kvc, self.top_vs_time, bot_vs_time,
                    self.top_omega_phase, self.bot_omega_phase)
            self.avpc += speccon1d.dim1sin_avgf(self.m, self.avg_ppress_z_pairs,
                                             tvals, a+b, self.drn)


        return

    def _make_set(self):
        """calculate settlement

        makes `self.set`, the average pore pressure at depths corresponding to
        self.settlement_z_pairs and times corresponding to self.tvals.  `self.set`  has size
        (len(ppress_z), len(tvals)).


        Notes
        -----
        The average settlement between Z1 and Z2 is given by:

        .. math:: \\overline{\\rho}\\left(\\left({Z_1,Z_2}\\right),t\\right)=\\int_{Z_1}^{Z_2}{m_v\\left({Z}\\right)\\left({\\sigma\\left({Z,t}\\right)-u\\left({Z,t}\\right)}\\right)\\,dZ}


        .. math:: \\overline{\\rho}\\left(\\left({Z_1,Z_2}\\right),t\\right)=\\int_{Z_1}^{Z_2}{m_v\\left({Z}\\right)\\sigma\\left({Z,t}\\right)\\,dZ}+\\int_{Z_1}^{Z_2}{m_v\\left({Z}\\right)\\left({\\mathbf{\\Phi v E}\\left(\\mathbf{\\Gamma v}\\right)^{-1}\\mathbf{\\theta}+u_{top}\\left({t}\\right)\\left({1-Z}\\right)+u_{bot}\\left({t}\\right)\\left({Z}\\right)}\\right)\\,dZ}

        """

        bot_vs_time = self._normalised_bot_vs_time()
        z1 = np.asarray(self.settlement_z_pairs)[:,0]
        z2 = np.asarray(self.settlement_z_pairs)[:,1]

        self.set = -speccon1d.dim1sin_integrate_af(self.m,
                     self.settlement_z_pairs,
                     self.tvals[self.settlement_z_pairs_tval_indexes],
                     self.v_E_Igamv_the[:,self.settlement_z_pairs_tval_indexes],
                     self.drn, self.mv, self.top_vs_time, bot_vs_time,
                     self.top_omega_phase, self.bot_omega_phase)

        if not self.surcharge_vs_time is None:
            self.set += (
                pwise.pxa_ya_cos_multiply_integrate_x1b_x2b_y1b_y2b_multiply_x1c_x2c_y1c_y2c_between_super(
                    self.surcharge_vs_time, self.surcharge_vs_depth,
                    self.mv,
                    self.tvals[self.settlement_z_pairs_tval_indexes], z1, z2,
                    omega_phase = self.surcharge_omega_phase,
                    achoose_max=True))

        self.set *= self.H * self.mvref
        return


    def _plot_pors(self):
        """plot soil depth vs pore pressure for various times

        """
        t = self.tvals[self.ppress_z_tval_indexes]
        line_labels = ['{:.3g}'.format(v) for v in t]
        por_prop = self.plot_properties.pop('pors', dict())
        if not 'xlabel' in por_prop:
            por_prop['xlabel'] = 'Soil pore pressure'

        #to do
        fig_por = geotecha.plotting.one_d.plot_vs_depth(self.pors,
                                                        self.ppress_z,
                                      line_labels=line_labels, H = self.H,
                                      RLzero=self.RLzero,
                                      prop_dict=por_prop)
        return fig_por
    def _plot_porc(self):
        """plot column depth vs pore pressure for various times

        """
        t = self.tvals[self.ppress_z_tval_indexes]
        line_labels = ['{:.3g}'.format(v) for v in t]
        porc_prop = self.plot_properties.pop('porc', dict())
        if not 'xlabel' in porc_prop:
            porc_prop['xlabel'] = 'Column pore pressure'

        #to do
        fig_porc = geotecha.plotting.one_d.plot_vs_depth(self.porc,
                                                         self.ppress_z,
                                      line_labels=line_labels, H = self.H,
                                      RLzero=self.RLzero,
                                      prop_dict=porc_prop)
        return fig_porc

    def _plot_por(self):
        """plot depth vs pore pressure for various times

        """
        t = self.tvals[self.ppress_z_tval_indexes]
        line_labels = ['{:.3g}'.format(v) for v in t]
        por_prop = self.plot_properties.pop('por', dict())
        if not 'xlabel' in por_prop:
            por_prop['xlabel'] = 'Pore pressure'

        #to do
        fig_por = geotecha.plotting.one_d.plot_vs_depth(self.por,
                                                        self.ppress_z,
                                      line_labels=line_labels, H = self.H,
                                      RLzero=self.RLzero,
                                      prop_dict=por_prop)
        return fig_por

    def _plot_avp(self):
        """plot average pore pressure vs time for various depth intervals

        """

        t = self.tvals[self.avg_ppress_z_pairs_tval_indexes]
        z_pairs = transformations.depth_to_reduced_level(
            np.asarray(self.avg_ppress_z_pairs), self.H, self.RLzero)
        line_labels = ['{:.3g} to {:.3g}'.format(z1, z2) for z1, z2 in z_pairs]

        avp_prop = self.plot_properties.pop('avp', dict())
        if not 'ylabel' in avp_prop:
            avp_prop['ylabel'] = 'Average pore pressure'
        fig_avp = geotecha.plotting.one_d.plot_vs_time(t, self.avp.T,
                           line_labels=line_labels,
                           prop_dict=avp_prop)
        return fig_avp

    def _plot_avps(self):
        """plot average soil pore pressure vs time for various depth intervals

        """

        t = self.tvals[self.avg_ppress_z_pairs_tval_indexes]
        z_pairs = transformations.depth_to_reduced_level(
            np.asarray(self.avg_ppress_z_pairs), self.H, self.RLzero)
        line_labels = ['{:.3g} to {:.3g}'.format(z1, z2) for z1, z2 in z_pairs]

        avp_prop = self.plot_properties.pop('avps', dict())
        if not 'ylabel' in avp_prop:
            avp_prop['ylabel'] = 'Average soil pore pressure'
        fig_avp = geotecha.plotting.one_d.plot_vs_time(t, self.avps.T,
                           line_labels=line_labels,
                           prop_dict=avp_prop)
        return fig_avp

    def _plot_avpc(self):
        """plot average column pore pressure vs time for various depth intervals

        """

        t = self.tvals[self.avg_ppress_z_pairs_tval_indexes]
        z_pairs = transformations.depth_to_reduced_level(
            np.asarray(self.avg_ppress_z_pairs), self.H, self.RLzero)
        line_labels = ['{:.3g} to {:.3g}'.format(z1, z2) for z1, z2 in z_pairs]

        avp_prop = self.plot_properties.pop('avpc', dict())
        if not 'ylabel' in avp_prop:
            avp_prop['ylabel'] = 'Average column pore pressure'
        fig_avp = geotecha.plotting.one_d.plot_vs_time(t, self.avpc.T,
                           line_labels=line_labels,
                           prop_dict=avp_prop)
        return fig_avp

    def _plot_set(self):
        """plot settlement vs time for various depth intervals


        """
        t = self.tvals[self.settlement_z_pairs_tval_indexes]
        z_pairs = transformations.depth_to_reduced_level(
            np.asarray(self.settlement_z_pairs), self.H, self.RLzero)
        line_labels = ['{:.3g} to {:.3g}'.format(z1, z2) for z1, z2 in z_pairs]

        set_prop = self.plot_properties.pop('set', dict())
        if not 'ylabel' in set_prop:
            set_prop['ylabel'] = 'Settlement'
        fig_set = geotecha.plotting.one_d.plot_vs_time(t, self.set.T,
                           line_labels=line_labels,
                           prop_dict=set_prop)
        fig_set.gca().invert_yaxis()

        return fig_set

    def produce_plots(self):
        """produce plots of analysis"""

        geotecha.plotting.one_d.pleasing_defaults()

#        matplotlib.rcParams['figure.dpi'] = 80
#        matplotlib.rcParams['savefig.dpi'] = 80

        matplotlib.rcParams.update({'font.size': 11})
        matplotlib.rcParams.update({'font.family': 'serif'})

        self._figures=[]
        #por and porwell
        if not self.ppress_z is None:
            f=self._plot_por()
            title = 'fig_por'
            f.set_label(title)
            f.canvas.manager.set_window_title(title)
            self._figures.append(f)

            f=self._plot_pors()
            title = 'fig_pors'
            f.set_label(title)
            f.canvas.manager.set_window_title(title)
            self._figures.append(f)

            f=self._plot_porc()
            title = 'fig_porc'
            f.set_label(title)
            f.canvas.manager.set_window_title(title)
            self._figures.append(f)

        if not self.avg_ppress_z_pairs is None:
            f=self._plot_avp()
            title = 'fig_avp'
            f.set_label(title)
            f.canvas.manager.set_window_title(title)
            self._figures.append(f)

            f=self._plot_avps()
            title = 'fig_avps'
            f.set_label(title)
            f.canvas.manager.set_window_title(title)
            self._figures.append(f)

            f=self._plot_avpc()
            title = 'fig_avpc'
            f.set_label(title)
            f.canvas.manager.set_window_title(title)
            self._figures.append(f)

        #settle
        if not self.settlement_z_pairs is None:
            f=self._plot_set()
            title = 'fig_set'
            f.set_label(title)
            f.canvas.manager.set_window_title(title)
            self._figures.append(f)
        #loads
        f=self._plot_loads()
        title = 'fig_loads'
        f.set_label(title)
        f.canvas.manager.set_window_title(title)
        self._figures.append(f)

        #materials
        f=self._plot_materials()
        self._figures.append(f)
        title = 'fig_materials'
        f.set_label(title)
        f.canvas.manager.set_window_title(title)

    def _plot_materials(self):

        material_prop = self.plot_properties.pop('material', dict())

        z_x=[]
        xlabels=[]
        if not self.mv is None:
            z_x.append(self.mv)
            xlabels.append('$m_v/\\overline{{m}}_v$, $\\left'
                '(\\overline{{m}}_v={:g}\\right)$'.format(self.mvref))
        if not self.kv is None:
            z_x.append(self.kv)
            xlabels.append('$k_v/\\overline{{k}}_v$, $\\left(\\overline{{k}}_v={:g}\\right)$'.format(self.kvref))
        if not self.khc is None:
            z_x.append(self.kvc)
            xlabels.append('$k_{{vc}}/\\overline{{k}}_{{vc}}$, $\\left(\\overline{{k}}_{{vc}}={:g}\\right)$'.format(self.kvcref))
        if not self.kh is None:
            z_x.append(self.kh)
            xlabels.append('$k_h/\\overline{{k}}_h$, $\\left(\\overline{{k}}_h={:g}\\right)$'.format(self.khref))
        if not self.khc is None:
            z_x.append(self.khc)
            xlabels.append('$k_{{hc}}/\\overline{{k}}_{{hc}}$, $\\left(\\overline{{k}}_{{hc}}={:g}\\right)$'.format(self.khcref))
        if not self.et is None:
            z_x.append(self.et)
            xlabels.append('$\\eta/\\overline{{\\eta}}$, $\\left(\\overline{{\\eta}}={:g}\\right)$'.format(self.etref))


        return (geotecha.plotting.one_d.plot_single_material_vs_depth(z_x,
                            xlabels, H = self.H,
                            RLzero = self.RLzero,prop_dict = material_prop))
    def _plot_loads(self):
        """plot loads

        """

        load_prop = self.plot_properties.pop('load', dict())
        load_triples=[]
        load_names = []
        ylabels=[]
        #surcharge
        if not self.surcharge_vs_time is None:
            load_names.append('surch')
            ylabels.append('Surcharge')
            load_triples.append(
                [(vs_time, vs_depth, omega_phase) for
                    vs_time, vs_depth, omega_phase  in
                    zip(self.surcharge_vs_time, self.surcharge_vs_depth,
                    self.surcharge_omega_phase)])


        if not self.top_vs_time is None:
            load_names.append('top')
            ylabels.append('Top boundary')
            load_triples.append(
                [(vs_time, ([0],[1]), omega_phase) for
                    vs_time, omega_phase  in
                    zip(self.top_vs_time, self.top_omega_phase)])

        if not self.bot_vs_time is None:
            #TODO: maybe if drn = 1, multiply bot_vs_time by H to give actual
            # gradient rather than normalised.
            load_names.append('bot')
            ylabels.append('Bot boundary')
            load_triples.append(
                [(vs_time, ([1],[1]), omega_phase) for
                    vs_time, omega_phase  in
                    zip(self.bot_vs_time, self.bot_omega_phase)])

        return (geotecha.plotting.one_d.plot_generic_loads(load_triples, load_names,
                    ylabels=ylabels, H = self.H, RLzero=self.RLzero,
                    prop_dict=load_prop))


def main():
    """Run speccon1d_vrc as a script"""
    a = GenericInputFileArgParser(obj=Speccon1dVRC,
                                  methods=[('make_all', [], {})],
                                 pass_open_file=True)

    a.main()

if __name__ == '__main__':
#    import nose
#    nose.runmodule(argv=['nose', '--verbosity=3', '--with-doctest'])
##    nose.runmodule(argv=['nose', '--verbosity=3'])
    main()

