Esempio n. 1
0
def covariance_matrix(epsrel=0.0, verbosity=2):
    """Estimate model parameter errors via the covariance matrix technique.

    Note that the covariance matrix error estimate is always of lower quality than Monte Carlo simulations.


    @param epsrel:          Any columns of R which satisfy |R_{kk}| <= epsrel |R_{11}| are considered linearly-dependent and are excluded from the covariance matrix, where the corresponding rows and columns of the covariance matrix are set to zero.
    @type epsrel:           float
    @keyword verbosity:     The amount of information to print.  The higher the value, the greater the verbosity.
    @type verbosity:        int
    """

    # Test if the current data pipe exists.
    check_pipe()

    # The specific analysis API object.
    api = return_api()

    # Loop over the models.
    for model_info in api.model_loop():
        # Get the Jacobian and weighting matrix.
        jacobian, weights = api.covariance_matrix(model_info=model_info,
                                                  verbosity=verbosity)

        # Calculate the covariance matrix.
        pcov = statistics.multifit_covar(J=jacobian, weights=weights)

        # To compute one standard deviation errors on the parameters, take the square root of the diagonal covariance.
        sd = sqrt(diag(pcov))

        # Loop over the parameters.
        index = 0
        for name in api.get_param_names(model_info):
            # Set the parameter error.
            api.set_error(index, sd[index], model_info=model_info)

            # Increment the parameter index.
            index = index + 1
Esempio n. 2
0
def minimise_minfx(E=None):
    """Estimate r2eff and errors by minimising with minfx.

    @keyword E:     The Exponential function class, which contain data and functions.
    @type E:        class
    @return:        Packed list with optimised parameter, parameter error set to 'inf', chi2, iter_count, f_count, g_count, h_count, warning
    @rtype:         list
    """

    # Check that the C modules have been compiled.
    if not C_module_exp_fn:
        raise RelaxError(
            "Relaxation curve fitting is not available.  Try compiling the C modules on your platform."
        )

    # Initial guess for minimisation. Solved by linear least squares.
    x0 = asarray(E.estimate_x0_exp(times=E.times, values=E.values))

    if E.c_code:
        # Minimise with C code.

        # Initialise the function to minimise.
        scaling_list = [1.0, 1.0]
        model = Relax_fit_opt(model='exp',
                              num_params=len(x0),
                              values=E.values,
                              errors=E.errors,
                              relax_times=E.times,
                              scaling_matrix=scaling_list)

        # Define function to minimise for minfx.
        t_func = model.func
        t_dfunc = model.dfunc
        t_d2func = model.d2func
        args = ()

    else:
        # Minimise with minfx.
        # Define function to minimise for minfx.
        t_func = E.func_exp_chi2
        t_dfunc = E.func_exp_chi2_grad
        t_d2func = None
        # All args to function. Params are packed out through function, then other parameters.
        args = (E.times, E.values, E.errors)

    # Minimise.
    results_minfx = generic_minimise(func=t_func,
                                     dfunc=t_dfunc,
                                     d2func=t_d2func,
                                     args=args,
                                     x0=x0,
                                     min_algor=E.min_algor,
                                     min_options=E.min_options,
                                     func_tol=E.func_tol,
                                     grad_tol=E.grad_tol,
                                     maxiter=E.max_iterations,
                                     A=E.A,
                                     b=E.b,
                                     full_output=True,
                                     print_flag=0)

    # Unpack
    param_vector, chi2, iter_count, f_count, g_count, h_count, warning = results_minfx

    # Extract.
    r2eff, i0 = param_vector

    # Get the Jacobian.
    if E.c_code == True:
        if E.chi2_jacobian:
            # Use the chi2 Jacobian from C.
            jacobian_matrix_exp = transpose(
                asarray(model.jacobian_chi2(param_vector)))
            weights = ones(E.errors.shape)

        else:
            # Use the direct Jacobian from C.
            jacobian_matrix_exp = transpose(
                asarray(model.jacobian(param_vector)))
            weights = 1. / E.errors**2

    elif E.c_code == False:
        if E.chi2_jacobian:
            # Use the chi2 Jacobian from python.
            jacobian_matrix_exp = E.func_exp_chi2_grad_array(
                params=param_vector,
                times=E.times,
                values=E.values,
                errors=E.errors)
            weights = ones(E.errors.shape)

        else:
            # Use the direct Jacobian from python.
            jacobian_matrix_exp = E.func_exp_grad(params=param_vector,
                                                  times=E.times)
            weights = 1. / E.errors**2

    pcov = multifit_covar(J=jacobian_matrix_exp, weights=weights)

    # To compute one standard deviation errors on the parameters, take the square root of the diagonal covariance.
    param_vector_error = sqrt(diag(pcov))

    # Pack to list.
    results = [
        param_vector, param_vector_error, chi2, iter_count, f_count, g_count,
        h_count, warning
    ]

    # Return, including errors.
    return results
Esempio n. 3
0
def minimise_minfx(E=None):
    """Estimate r2eff and errors by minimising with minfx.

    @keyword E:     The Exponential function class, which contain data and functions.
    @type E:        class
    @return:        Packed list with optimised parameter, parameter error set to 'inf', chi2, iter_count, f_count, g_count, h_count, warning
    @rtype:         list
    """

    # Check that the C modules have been compiled.
    if not C_module_exp_fn:
        raise RelaxError("Relaxation curve fitting is not available.  Try compiling the C modules on your platform.")

    # Initial guess for minimisation. Solved by linear least squares.
    x0 = asarray( E.estimate_x0_exp(times=E.times, values=E.values) )

    if E.c_code:
        # Minimise with C code.

        # Initialise the function to minimise.
        scaling_list = [1.0, 1.0]
        model = Relax_fit_opt(model='exp', num_params=len(x0), values=E.values, errors=E.errors, relax_times=E.times, scaling_matrix=scaling_list)

        # Define function to minimise for minfx.
        t_func = model.func
        t_dfunc = model.dfunc
        t_d2func = model.d2func
        args=()

    else:
        # Minimise with minfx.
        # Define function to minimise for minfx.
        t_func = E.func_exp_chi2
        t_dfunc = E.func_exp_chi2_grad
        t_d2func = None
        # All args to function. Params are packed out through function, then other parameters.
        args=(E.times, E.values, E.errors)

    # Minimise.
    results_minfx = generic_minimise(func=t_func, dfunc=t_dfunc, d2func=t_d2func, args=args, x0=x0, min_algor=E.min_algor, min_options=E.min_options, func_tol=E.func_tol, grad_tol=E.grad_tol, maxiter=E.max_iterations, A=E.A, b=E.b, full_output=True, print_flag=0)

    # Unpack
    param_vector, chi2, iter_count, f_count, g_count, h_count, warning = results_minfx

    # Extract.
    r2eff, i0 = param_vector

    # Get the Jacobian.
    if E.c_code == True:
        if E.chi2_jacobian:
            # Use the chi2 Jacobian from C.
            jacobian_matrix_exp = transpose(asarray( model.jacobian_chi2(param_vector) ) )
            weights = ones(E.errors.shape)

        else:
            # Use the direct Jacobian from C.
            jacobian_matrix_exp = transpose(asarray( model.jacobian(param_vector) ) )
            weights = 1. / E.errors**2

    elif E.c_code == False:
        if E.chi2_jacobian:
            # Use the chi2 Jacobian from python.
            jacobian_matrix_exp = E.func_exp_chi2_grad_array(params=param_vector, times=E.times, values=E.values, errors=E.errors)
            weights = ones(E.errors.shape)

        else:
            # Use the direct Jacobian from python.
            jacobian_matrix_exp = E.func_exp_grad(params=param_vector, times=E.times)
            weights = 1. / E.errors**2

    pcov = multifit_covar(J=jacobian_matrix_exp, weights=weights)

    # To compute one standard deviation errors on the parameters, take the square root of the diagonal covariance.
    param_vector_error = sqrt(diag(pcov))

    # Pack to list.
    results = [param_vector, param_vector_error, chi2, iter_count, f_count, g_count, h_count, warning]

    # Return, including errors.
    return results
Esempio n. 4
0
def estimate_r2eff_err(spin_id=None, epsrel=0.0, verbosity=1):
    """This will estimate the R2eff and i0 errors from the covariance matrix Qxx.  Qxx is calculated from the Jacobian matrix and the optimised parameters.

    @keyword spin_id:       The spin identification string.
    @type spin_id:          str
    @param epsrel:          Any columns of R which satisfy |R_{kk}| <= epsrel |R_{11}| are considered linearly-dependent and are excluded from the covariance matrix, where the corresponding rows and columns of the covariance matrix are set to zero.
    @type epsrel:           float
    @keyword verbosity:     The amount of information to print.  The higher the value, the greater the verbosity.
    @type verbosity:        int
    """

    # Check that the C modules have been compiled.
    if not C_module_exp_fn:
        raise RelaxError(
            "Relaxation curve fitting is not available.  Try compiling the C modules on your platform."
        )

    # Perform checks.
    check_model_type(model=MODEL_R2EFF)

    # Loop over the spins.
    for cur_spin, mol_name, resi, resn, cur_spin_id in spin_loop(
            selection=spin_id, full_info=True, return_id=True,
            skip_desel=True):
        # Generate spin string.
        spin_string = generate_spin_string(spin=cur_spin,
                                           mol_name=mol_name,
                                           res_num=resi,
                                           res_name=resn)

        # Raise Error, if not optimised.
        if not (hasattr(cur_spin, 'r2eff') and hasattr(cur_spin, 'i0')):
            raise RelaxError(
                "Spin %s does not contain optimised 'r2eff' and 'i0' values.  Try execute: minimise.execute(min_algor='Newton', constraints=False)"
                % (spin_string))

        # Raise warning, if gradient count is 0.  This could point to a lack of minimisation first.
        if hasattr(cur_spin, 'g_count'):
            if getattr(cur_spin, 'g_count') == 0.0:
                text = "Spin %s contains a gradient count of 0.0.  Is the R2eff parameter optimised?  Try execute: minimise.execute(min_algor='Newton', constraints=False)" % (
                    spin_string)
                warn(RelaxWarning("%s." % text))

        # Print information.
        if verbosity >= 1:
            # Individual spin block section.
            top = 2
            if verbosity >= 2:
                top += 2
            subsection(file=sys.stdout,
                       text="Estimating R2eff error for spin: %s" %
                       spin_string,
                       prespace=top)

        # Loop over each spectrometer frequency and dispersion point.
        for exp_type, frq, offset, point, ei, mi, oi, di in loop_exp_frq_offset_point(
                return_indices=True):
            # The parameter key.
            param_key = return_param_key_from_data(exp_type=exp_type,
                                                   frq=frq,
                                                   offset=offset,
                                                   point=point)

            # Extract values.
            r2eff = getattr(cur_spin, 'r2eff')[param_key]
            i0 = getattr(cur_spin, 'i0')[param_key]

            # Pack data
            param_vector = [r2eff, i0]

            # The peak intensities, errors and times.
            values = []
            errors = []
            times = []
            for time in loop_time(exp_type=exp_type,
                                  frq=frq,
                                  offset=offset,
                                  point=point):
                values.append(
                    average_intensity(spin=cur_spin,
                                      exp_type=exp_type,
                                      frq=frq,
                                      offset=offset,
                                      point=point,
                                      time=time))
                errors.append(
                    average_intensity(spin=cur_spin,
                                      exp_type=exp_type,
                                      frq=frq,
                                      offset=offset,
                                      point=point,
                                      time=time,
                                      error=True))
                times.append(time)

            # Convert to numpy array.
            values = asarray(values)
            errors = asarray(errors)
            times = asarray(times)

            # Initialise data in C code.
            scaling_list = [1.0, 1.0]
            model = Relax_fit_opt(model='exp',
                                  num_params=len(param_vector),
                                  values=values,
                                  errors=errors,
                                  relax_times=times,
                                  scaling_matrix=scaling_list)

            # Use the direct Jacobian from function.
            jacobian_matrix_exp = transpose(
                asarray(model.jacobian(param_vector)))
            weights = 1. / errors**2

            # Get the co-variance
            pcov = multifit_covar(J=jacobian_matrix_exp, weights=weights)

            # To compute one standard deviation errors on the parameters, take the square root of the diagonal covariance.
            param_vector_error = sqrt(diag(pcov))

            # Extract values.
            r2eff_err, i0_err = param_vector_error

            # Copy r2eff dictionary, to r2eff_err dictionary. They have same keys to the dictionary,
            if not hasattr(cur_spin, 'r2eff_err'):
                setattr(cur_spin, 'r2eff_err',
                        deepcopy(getattr(cur_spin, 'r2eff')))
            if not hasattr(cur_spin, 'i0_err'):
                setattr(cur_spin, 'i0_err', deepcopy(getattr(cur_spin, 'i0')))

            # Set error.
            cur_spin.r2eff_err[param_key] = r2eff_err
            cur_spin.i0_err[param_key] = i0_err

            # Get other relevant information.
            chi2 = getattr(cur_spin, 'chi2')

            # Print information.
            print_strings = []
            if verbosity >= 1:
                # Add print strings.
                point_info = "%s at %3.1f MHz, for offset=%3.3f ppm and dispersion point %-5.1f, with %i time points." % (
                    exp_type, frq / 1E6, offset, point, len(times))
                print_strings.append(point_info)

                par_info = "r2eff=%3.3f r2eff_err=%3.4f, i0=%6.1f, i0_err=%3.4f, chi2=%3.3f.\n" % (
                    r2eff, r2eff_err, i0, i0_err, chi2)
                print_strings.append(par_info)

                if verbosity >= 2:
                    time_info = ', '.join(map(str, times))
                    print_strings.append('For time array: ' + time_info +
                                         '.\n\n')

            # Print info
            if len(print_strings) > 0:
                for print_string in print_strings:
                    print(print_string),
Esempio n. 5
0
def estimate_r2eff_err(spin_id=None, epsrel=0.0, verbosity=1):
    """This will estimate the R2eff and i0 errors from the covariance matrix Qxx.  Qxx is calculated from the Jacobian matrix and the optimised parameters.

    @keyword spin_id:       The spin identification string.
    @type spin_id:          str
    @param epsrel:          Any columns of R which satisfy |R_{kk}| <= epsrel |R_{11}| are considered linearly-dependent and are excluded from the covariance matrix, where the corresponding rows and columns of the covariance matrix are set to zero.
    @type epsrel:           float
    @keyword verbosity:     The amount of information to print.  The higher the value, the greater the verbosity.
    @type verbosity:        int
    """

    # Check that the C modules have been compiled.
    if not C_module_exp_fn:
        raise RelaxError("Relaxation curve fitting is not available.  Try compiling the C modules on your platform.")

    # Perform checks.
    check_model_type(model=MODEL_R2EFF)

    # Loop over the spins.
    for cur_spin, mol_name, resi, resn, cur_spin_id in spin_loop(selection=spin_id, full_info=True, return_id=True, skip_desel=True):
        # Generate spin string.
        spin_string = generate_spin_string(spin=cur_spin, mol_name=mol_name, res_num=resi, res_name=resn)

        # Raise Error, if not optimised.
        if not (hasattr(cur_spin, 'r2eff') and hasattr(cur_spin, 'i0')):
            raise RelaxError("Spin %s does not contain optimised 'r2eff' and 'i0' values.  Try execute: minimise.execute(min_algor='Newton', constraints=False)"%(spin_string))

        # Raise warning, if gradient count is 0.  This could point to a lack of minimisation first.
        if hasattr(cur_spin, 'g_count'):
            if getattr(cur_spin, 'g_count') == 0.0:
                text = "Spin %s contains a gradient count of 0.0.  Is the R2eff parameter optimised?  Try execute: minimise.execute(min_algor='Newton', constraints=False)" %(spin_string)
                warn(RelaxWarning("%s." % text))

        # Print information.
        if verbosity >= 1:
            # Individual spin block section.
            top = 2
            if verbosity >= 2:
                top += 2
            subsection(file=sys.stdout, text="Estimating R2eff error for spin: %s"%spin_string, prespace=top)

        # Loop over each spectrometer frequency and dispersion point.
        for exp_type, frq, offset, point, ei, mi, oi, di in loop_exp_frq_offset_point(return_indices=True):
            # The parameter key.
            param_key = return_param_key_from_data(exp_type=exp_type, frq=frq, offset=offset, point=point)

            # Extract values.
            r2eff = getattr(cur_spin, 'r2eff')[param_key]
            i0 = getattr(cur_spin, 'i0')[param_key]

            # Pack data
            param_vector = [r2eff, i0]

            # The peak intensities, errors and times.
            values = []
            errors = []
            times = []
            for time in loop_time(exp_type=exp_type, frq=frq, offset=offset, point=point):
                values.append(average_intensity(spin=cur_spin, exp_type=exp_type, frq=frq, offset=offset, point=point, time=time))
                errors.append(average_intensity(spin=cur_spin, exp_type=exp_type, frq=frq, offset=offset, point=point, time=time, error=True))
                times.append(time)

            # Convert to numpy array.
            values = asarray(values)
            errors = asarray(errors)
            times = asarray(times)

            # Initialise data in C code.
            scaling_list = [1.0, 1.0]
            model = Relax_fit_opt(model='exp', num_params=len(param_vector), values=values, errors=errors, relax_times=times, scaling_matrix=scaling_list)

            # Use the direct Jacobian from function.
            jacobian_matrix_exp = transpose(asarray( model.jacobian(param_vector) ) )
            weights = 1. / errors**2

            # Get the co-variance
            pcov = multifit_covar(J=jacobian_matrix_exp, weights=weights)

            # To compute one standard deviation errors on the parameters, take the square root of the diagonal covariance.
            param_vector_error = sqrt(diag(pcov))

            # Extract values.
            r2eff_err, i0_err = param_vector_error

            # Copy r2eff dictionary, to r2eff_err dictionary. They have same keys to the dictionary,
            if not hasattr(cur_spin, 'r2eff_err'):
                setattr(cur_spin, 'r2eff_err', deepcopy(getattr(cur_spin, 'r2eff')))
            if not hasattr(cur_spin, 'i0_err'):
                setattr(cur_spin, 'i0_err', deepcopy(getattr(cur_spin, 'i0')))

            # Set error.
            cur_spin.r2eff_err[param_key] = r2eff_err
            cur_spin.i0_err[param_key] = i0_err

            # Get other relevant information.
            chi2 = getattr(cur_spin, 'chi2')

            # Print information.
            print_strings = []
            if verbosity >= 1:
                # Add print strings.
                point_info = "%s at %3.1f MHz, for offset=%3.3f ppm and dispersion point %-5.1f, with %i time points." % (exp_type, frq/1E6, offset, point, len(times))
                print_strings.append(point_info)

                par_info = "r2eff=%3.3f r2eff_err=%3.4f, i0=%6.1f, i0_err=%3.4f, chi2=%3.3f.\n" % ( r2eff, r2eff_err, i0, i0_err, chi2)
                print_strings.append(par_info)

                if verbosity >= 2:
                    time_info = ', '.join(map(str, times))
                    print_strings.append('For time array: '+time_info+'.\n\n')

            # Print info
            if len(print_strings) > 0:
                for print_string in print_strings:
                    print(print_string),