#!/usr/bin/env python
# geotecha - A software suite for geotechncial engineering
# Copyright (C) 2013  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 vertical drains 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 Speccon1dVR(speccon1d.Speccon1d):
    """Multilayer consolidation with vertical drains using the spectral
    Galerkin method.

    Features:

     - Multiple layers.
     - Vertical and radial drainage in a unit cell.
       (radial drainage uses the eta method).
     - Material properties that are constant in time but piecewsie linear with
       depth.
     - Surcharge and vacuum loading.
     - Non-zero top and bottom pore pressure boundary conditions.
     - Pumping from a point source (point source in 1D is pumping from line
       at fixed depth).
     - Pore pressure at specified depths a function of time.
     - Surcharge/Vacuum/Boundary Conditions/Pumping/Fixed Pore Pressures vary
       with time in a piecewise-linear function mulitplied by a cosine
       function of time.

       - Surcharge and Vacuum loads 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.
       - Average excess pore pressure between two depths.
       - Settlement between two depths.
       - Charts and csv output available.
     - Program can be run as script or in a python interpreter.


    .. 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) and pumping velocities (see `pumping` below).
    mvref : float, optional
        Reference value of volume compressibility mv (used with `H` in
        settlement calculations). Default mvref=1.0.  Note mvref will be used
        to normalise pumping velocities (see `pumping` below).
    kvref : float, optional
        Reference value of vertical permeability kv (only used for pretty
        output). Default kvref=1.0.
    khref : float, optional
        Reference value of horizontal permeability kh (only used for
        pretty output). Default khref=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
    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
    mv : PolyLine, optional
        Normalised volume compressibility PolyLine(depth, mv).
    kh : PolyLine, optional
        Normalised horizontal permeability PolyLine(depth, kh).
    kv : PolyLine , optional
        Normalised vertical permeability 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.
    vacuum_vs_depth : list of Polyline, optinal
        Vacuum variation with depth. PolyLine(depth, multiplier).
    vacuum_vs_time : list of Polyline, optional
        Vacuum magnitude variation with time. Polyline(time, magnitude).
    vacuum_omega_phase : list of 2 element tuples, optional
        (omega, phase) to define cyclic variation of vacuum. i.e.
        mag_vs_time * cos(omega*t + phase). If vacuum_omega_phase is None
        then cyclic component will be ignored.  If vacuum_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.
    fixed_ppress : list of 3 element tuple, optional
        (zfixed, pseudo_k, PolyLine(time, magnitude)).  zfixed is the
        normalised z at which pore pressure is fixed. pseudo_k is a
        permeability-like coefficient that controls how quickly the pore
        pressure reduces to the fixed value (pseudo_k should be as high as
        possible without causing numerical difficulties). If the third
        element of the tuple is None then the pore pressure will be fixed at
        zero rather than a prescribed mag_vs_time PolyLine.
    fixed_ppress_omega_phase : list of 2 element tuples, optional
        (omega, phase) to define cyclic variation of fixed ppress. i.e.
        mag_vs_time * cos(omega*t + phase). If fixed_ppress _omega_phase is
        None then cyclic component will be ignored.  If
        fixed_ppress_omega_phase is a list then if any member is None then
        cyclic component will not be applied for that load combo.
    pumping : list of 2 element tuple
        (zpump, mag_vs_time).  `zpump` is the normalised
        z at which pumping takes place. The mag_vs_time polyline should be
        the actual pumping velocity.  Within the program the actual pumping
        velocity will be normalised by dividing by (mvref * H).
        Negative values of vp will pump fluid out of the model, positive
        values of vp will pump fluid into the model.
    pumping_omega_phase : list of 2 element tuples, optional
        (omega, phase) to define cyclic variation of pumping velocity. i.e.
        mag_vs_time * cos(omega*t + phase). If pumping_omega_phase is
        None then cyclic component will be ignored.  If pumping_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 pore pressure plot.
        avp                 dict of prop to pass to 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 : 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 : 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 permeability.
     - :math:`k_h` is horizontal permeability.
     - :math:`m_v` is volume compressibility.
     - :math:`\\eta` is the radial drainage parameter
       :math:`\\eta = \\frac{2}{r_e^2 \\mu}`.
     - :math:`r_e` is influence radius of drain.
     - :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**

    The equation governing excess pore pressure at normalised depth
    :math:`Z` and time :math:`t`, :math:`u\\left({Z, t}\\right)`,  is:

    .. math::
        \\overline{m}_v u,_t
        + dT_h\\overline{k}_h\\overline{\\eta}u
        - dT_v\\left({\\overline{k}_v u,_Z}\\right),_Z
        + k_f u \\delta \\left({Z-Z_f}\\right)
        = \\overline{m}_v \\sigma,_t
        + dT_h\\overline{k}_h\\overline{\\eta}u_w
        - v_p\\delta\\left({Z-Z_p}\\right)
          / \\left({H m_{v\\textrm{ref}}}\\right)
        + k_f u_f \\delta \\left({Z-Z_f}\\right)
    where

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

    .. 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`.

    :math:`v_p` is the pumping velocity at depth :math:`Z_p`. :math:`u_f` is
    the fixed pore pressure at depth :math:`Z_f`. :math:`k_f` controls how
    quickly the 'fixed' pore pressure responds to changes (use a very high
    value for 'instantaneuous` response.)



    **Non-zero Boundary conditions**

    The following two sorts of boundary conditions 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:

    .. 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 mvref kvref khref etref dTh dTv mv kh kv et '
            'surcharge_vs_depth surcharge_vs_time '
            'vacuum_vs_depth vacuum_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 '
            'fixed_ppress surcharge_omega_phase vacuum_omega_phase '
            'fixed_ppress_omega_phase top_omega_phase bot_omega_phase '
            'pumping pumping_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,
            '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': 'speccon1dvr_'
            }

        self._attributes_that_should_be_lists= (
            'surcharge_vs_depth surcharge_vs_time surcharge_omega_phase '
            'vacuum_vs_depth vacuum_vs_time vacuum_omega_phase '
            'top_vs_time top_omega_phase '
            'bot_vs_time bot_omega_phase '
            'fixed_ppress fixed_ppress_omega_phase '
            'pumping pumping_omega_phase').split()

        self._attributes_that_should_have_same_x_limits = [
            'mv kv kh et surcharge_vs_depth vacuum_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(),
            'vacuum_vs_depth vacuum_vs_time'.split(),
            'vacuum_vs_time vacuum_omega_phase'.split(),
            'top_vs_time top_omega_phase'.split(),
            'bot_vs_time bot_omega_phase'.split(),
            'fixed_ppress_omega_phase fixed_ppress'.split(),
            'pumping pumping_omega_phase'.split()]

        self._attributes_to_force_same_len = [
            "surcharge_vs_time surcharge_omega_phase".split(),
            "vacuum_vs_time vacuum_omega_phase".split(),
            "fixed_ppress fixed_ppress_omega_phase".split(),
            "top_vs_time top_omega_phase".split(),
            "bot_vs_time bot_omega_phase".split(),
            "pumping pumping_omega_phase".split()]

        self._zero_or_all = [
            'dTh kh et'.split(),
            'dTv kv'.split(),
            'surcharge_vs_depth surcharge_vs_time'.split(),
            'vacuum_vs_depth vacuum_vs_time'.split()]
        self._at_least_one = [
            ['mv'],
            'dTh dTv'.split(),
            'kh kv'.split(),
            ('surcharge_vs_time vacuum_vs_time top_vs_time '
                'bot_vs_time fixed_ppress pumping').split(),
            ['tvals'],
            'ppress_z avg_ppress_z_pairs settlement_z_pairs'.split()]

        self._one_implies_others = [
            'vacuum_vs_time dTh kh et'.split(),
            'vacuum_vs_depth dTh kh et'.split(),
            ('surcharge_omega_phase surcharge_vs_depth '
                'surcharge_vs_time').split(),
            'vacuum_omega_phase vacuum_vs_depth vacuum_vs_time'.split(),
            'fixed_ppress_omega_phase fixed_ppress'.split(),
            'top_omega_phase top_vs_time'.split(),
            'bot_omega_phase bot_vs_time'.split(),
            'pumping_omega_phase pumping'.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.etref = self._attribute_defaults.get('etref', None)
        self.dTh = None
        self.dTv = None
        self.mv = None
        self.kh = None
        self.kv = None
        self.et = None
        self.surcharge_vs_depth = None
        self.surcharge_vs_time = None
        self.surcharge_omega_phase = None

        self.vacuum_vs_depth = None
        self.vacuum_vs_time = None
        self.vacuum_omega_phase = None
        self.top_vs_time = None
        self.top_omega_phase = None
        self.bot_vs_time = None
        self.bot_omega_phase = None
        self.fixed_ppress_omega_phase = None
        self.fixed_ppress = None
        self.pumping = None
        self.pumping_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._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 (i.e. prepare plots and data for csv files)"""

        header1 = ("program: speccon1d_vr; 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)

        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)

        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 = 0\: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 gam matrix from the terms involving time derivatives of
        u(Z,t).

        Creates the :math:`\Gam` matrix which occurs in the following
        equation:

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

       `self.gam` is created.

        """

        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 the psi matrix from the terms involving spatial (or no)
        derivatives of u(Z,t).

        Creates the :math:`\Psi` matrix which occurs in the following
        equation:

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

        `self.psi` is created.

        """

        self.psi = np.zeros((self.neig, self.neig))
        #kv part
        if sum([v is None for v in [self.kv, self.dTv]])==0:
            self.psi -= (self.dTv / self.dT *
                integ.pdim1sin_D_aDf_linear(self.m, self.kv,
                                implementation=self.implementation))
        #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 += (self.dTh / self.dT *
                integ.pdim1sin_abf_linear(self.m, self.kh, self.et,
                                          implementation=self.implementation))
        #fixed pore pressure part
        if not self.fixed_ppress is None:
            for (zfixed, pseudo_k, mag_vs_time) in self.fixed_ppress:
                self.psi += (pseudo_k / self.dT *
                np.sin(self.m[:, np.newaxis] * zfixed) *
                np.sin(self.m[np.newaxis, :] * zfixed))

        self.psi[np.abs(self.psi) < 1e-8]=0.0
        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}\\prime
            +\\mathbf{\\Psi A}=
            \\textrm{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)

        """

        Igam_psi = np.dot(np.linalg.inv(self.gam), self.psi)

        self.eigs, self.v = np.linalg.eig(Igam_psi)

        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_vacuum : vacuum 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 sum([v is None for v in [self.vacuum_vs_depth,
                                    self.vacuum_vs_time, self.et,
                                    self.kh,self.dTh]])==0:
            if self.dTh!=0:
                self._make_E_Igamv_the_vacuum()
                self.E_Igamv_the += self.E_Igamv_the_vacuum
        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
        if not self.fixed_ppress is None:
            self._make_E_Igamv_the_fixed_ppress()
            self.E_Igamv_the +=self.E_Igamv_the_fixed_ppress
        if not self.pumping is None:
            self._make_E_Igamv_the_pumping()
            self.E_Igamv_the += self.E_Igamv_the_pumping

        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 _make_E_Igamv_the_vacuum(self):
        """Make the vacuum loading matrices

        Make the E*inverse(gam*v)*theta part of solution u=phi*vE*inverse(gam*v)*theta.
        The contribution of each vacuum load is added and put in
        `self.E_Igamv_the_vacuum`. `self.E_Igamv_the_vacuum` 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_vacuum

        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_vacuum` which is
        the :math:`\\mathbf{E}\\left(\\mathbf{\\Gamma v}\\right)^{-1}\\mathbf{\\theta}`
        part of the solution for all vacuum loads

        """

#        self.E_Igamv_the_vacuum = self.dTh * speccon1d.dim1sin_E_Igamv_the_abmag_bilinear(self.m, self.eigs, self.kh, self.et,
#                                                                        self.vacuum_vs_depth, self.vacuum_vs_time, self.tvals, self.Igamv, self.dT)
        self.E_Igamv_the_vacuum = (self.dTh *
            speccon1d.dim1sin_E_Igamv_the_abmag_bilinear(self.m,
                self.eigs, self.tvals, self.Igamv, self.kh, self.et,
                self.vacuum_vs_depth, self.vacuum_vs_time,
                self.vacuum_omega_phase, self.dT,
                implementation=self.implementation))
#        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)
        return

    def _make_E_Igamv_the_fixed_ppress(self):
        """Make the fixed pore pressure loading matrices

        Make the E*inverse(gam*v)*theta part of solution u=phi*vE*inverse(gam*v)*theta.
        The contribution of each fixed ppress load is added and put in
        `self.E_Igamv_the_fixed_ppress`. `self.E_Igamv_the_fixed_ppress` 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_fixed_ppress

        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_fixed_ppress` will create `self.E_Igamv_the_fixed_ppress` which is
        the :math:`\\mathbf{E}\\left(\\mathbf{\\Gamma v}\\right)^{-1}\\mathbf{\\theta}`
        part of the solution for all fixed pore pressure loads.

        """

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

        if not self.fixed_ppress is None:
            zvals = [v[0] for v in self.fixed_ppress]
            pseudo_k = [v[1] for v in self.fixed_ppress]
            mag_vs_time = [v[2] for v in self.fixed_ppress]
            self.E_Igamv_the_fixed_ppress += (
                speccon1d.dim1sin_E_Igamv_the_deltamag_linear(
                self.m, self.eigs, self.tvals, self.Igamv,
                zvals, pseudo_k, mag_vs_time,
                self.fixed_ppress_omega_phase, self.dT,
                implementation=self.implementation))

    def _make_E_Igamv_the_pumping(self):
        """Make the pumping loading matrices

        Make the E*inverse(gam*v)*theta part of solution u=phi*vE*inverse(gam*v)*theta.
        The contribution of each pumping load is added and put in
        `self.E_Igamv_the_pumping`. `self.E_Igamv_the_pumping` 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_pumping

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

        """

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

        if not self.pumping is None:
            zvals = [v[0] for v in self.pumping]
            pseudo_k = [1 for v in self.pumping]
#            mag_vs_time = [v[1] for v in self.pumping]
            #dividing by mvref*H is because input pumping velocities need to
            # normalised
            mag_vs_time = [v[1] / (self.mvref * self.H) for v in self.pumping]
            self.E_Igamv_the_pumping += (
                speccon1d.dim1sin_E_Igamv_the_deltamag_linear(self.m,
                    self.eigs, self.tvals, self.Igamv, zvals, pseudo_k,
                    mag_vs_time, self.pumping_omega_phase, self.dT,
                    implementation=self.implementation))

    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

        Create self.E_Igamv_the_BC.

        """
        self.E_Igamv_the_BC = np.zeros((self.neig, len(self.tvals)))
        #mv * du/dt component
        #self.E_Igamv_the_BC -= speccon1d.dim1sin_E_Igamv_the_BC_aDfDt_linear(self.drn, self.m, self.eigs, self.mv, self.top_vs_time, self.bot_vs_time, self.tvals, self.Igamv, self.dT)

        bot_vs_time = self._normalised_bot_vs_time()

        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))

        #dTh * kh * et * u component
        if sum([v is None for v in [self.et, self.kh, self.dTh]])==0:
            if self.dTh!=0:
#                self.E_Igamv_the_BC -= self.dTh  * speccon1d.dim1sin_E_Igamv_the_BC_abf_linear(self.drn, self.m, self.eigs, self.kh, self.et, self.top_vs_time, bot_vs_time, self.tvals, self.Igamv, self.dT)
                self.E_Igamv_the_BC -= (self.dTh  *
                    speccon1d.dim1sin_E_Igamv_the_BC_abf_linear(self.drn,
                        self.m, self.eigs, self.tvals, self.Igamv, self.kh,
                        self.et, self.top_vs_time, bot_vs_time,
                        self.top_omega_phase, self.bot_omega_phase,
                        self.dT,
                        implementation=self.implementation))

        #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.kv, self.top_vs_time, bot_vs_time, self.tvals, self.Igamv, self.dT)
                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, self.kv,
                        self.top_vs_time, bot_vs_time,
                        self.top_omega_phase, self.bot_omega_phase, self.dT,
                        implementation=self.implementation))

        #the pseudo_k * delta(z-zfixed)*u component, i.e. the fixed_ppress part
        if not self.fixed_ppress is None:
            zvals = [v[0] for v in self.fixed_ppress]
            pseudo_k = [v[1] for v in self.fixed_ppress]
            self.E_Igamv_the_BC -= (
                speccon1d.dim1sin_E_Igamv_the_BC_deltaf_linear(self.drn,
                    self.m, self.eigs, self.tvals, self.Igamv, zvals,
                    pseudo_k, 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

        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()
        self.por= speccon1d.dim1sin_f(self.m, self.ppress_z,
                        self.tvals[self.ppress_z_tval_indexes],
                        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)
        return

    def _make_avp(self):
        """Calculate average pore pressure

        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()
        self.avp = speccon1d.dim1sin_avgf(self.m, self.avg_ppress_z_pairs,
                self.tvals[self.avg_ppress_z_pairs_tval_indexes],
                self.v_E_Igamv_the[:,self.avg_ppress_z_pairs_tval_indexes],
                self.drn, self.top_vs_time, bot_vs_time,
                self.top_omega_phase, self.bot_omega_phase)
        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_por(self):
        """Prepare plot of 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):
        """prepare plot of 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_set(self):
        """Prepare plot of 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):
        """Prepare all 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
        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)

        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)

        #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):
        """Prepare material property plots"""
        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.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.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):
        """Prepare plots of loading."""

        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.vacuum_vs_time is None:
            load_names.append('vac')
            ylabels.append('Vacuum')
            load_triples.append(
                [(vs_time, vs_depth, omega_phase) for
                    vs_time, vs_depth, omega_phase  in
                    zip(self.vacuum_vs_time, self.vacuum_vs_depth,
                    self.vacuum_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)])

        if not self.fixed_ppress is None:
            load_names.append('fixed p')
            ylabels.append('Fixed ppress')
            fixed_ppress_triples=[]
            for (zfixed, pseudo_k,
                     vs_time), omega_phase in zip(self.fixed_ppress,
                                                self.fixed_ppress_omega_phase):

                if vs_time is None:
                    vs_time = PolyLine([self.tvals[0], self.tvals[-1]], [0,0])

                vs_depth = ([zfixed], [1])
                fixed_ppress_triples.append((vs_time,vs_depth, omega_phase))

            load_triples.append(fixed_ppress_triples)

        if not self.pumping is None:
            #TODO: maybe multiply mag_vs_time by H and mvref to atual pumping
            #velocity rather than normalised.
            # gradient rather than normalised.
            load_names.append('pump')
            ylabels.append('Pumping velocity')
            pumping_triples=[]
            for (zpump, vs_time), omega_phase in zip(self.pumping,
                                                    self.pumping_omega_phase):
                vs_depth = ([zpump], [1])
                pumping_triples.append((vs_time, vs_depth, omega_phase))

            load_triples.append(pumping_triples)

        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_vr as script."""
    a = GenericInputFileArgParser(obj=Speccon1dVR,
                                  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()
