"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "e9622c84c2a64421811f3efa211af3e5",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "017da53efe8e4e339c795a5c40a93164",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"s.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exploring the dataset we notice that it consists of two peaks that at different points change position and height. In oder to measure the position, height and width of the two peaks at all position we will create a ``Model`` that consists of 2 gaussian functions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[back to top] \n",
"\n",
"Creating a model now is simple - just pass the spectrum to the function \n",
"> `model_reference = signal_reference.create_model()`\n",
"\n",
"Let's reference the model by \"`m`\"."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"m = s.create_model()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look what's inside:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" # | Attribute Name | Component Name | Component Type\n",
"---- | ------------------- | ------------------- | -------------------"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.components"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see, the model is still empty. That will not always be the case - for some types of signals, an automatic background component is added when creating a model, hence it's always good to check.\n",
"\n",
"We can plot the model in exactly the same way as the signal:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The only difference from the model plot is that each data point is displayed individually. \n",
"\n",
"[back to top] \n",
"\n",
"To do anything with the model, we should __create__ some __components__ and add them. Let's create two gaussians, referenced as \"g1\" and \"g2\":\n",
"\n",
"-----------------\n",
"P.S.: keep in mind that creating a component is a function - hence there should be brackets at the end! Such as \n",
"> `our_component_reference = hs.model.components1D.example_component()`"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"g1 = hs.model.components1D.GaussianHF()\n",
"g2 = hs.model.components1D.GaussianHF()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[back to top] \n",
"\n",
"... and __add the components to__ our __model__. For that there are generally two ways:\n",
"\n",
"Individually\n",
"> `our_model_reference.append(our_component_reference)`\n",
"\n",
"or in lists (i.e. grouped by square brackets)\n",
"> `our_model_reference.extend([first_component_reference, second_component_reference])`"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"m.extend([g1, g2])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's check how the model looks now:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" # | Attribute Name | Component Name | Component Type\n",
"---- | ------------------- | ------------------- | -------------------\n",
" 0 | GaussianHF | GaussianHF | GaussianHF\n",
" 1 | GaussianHF_0 | GaussianHF_0 | GaussianHF"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.components"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[back to top] \n",
"\n",
"For our convenience we can __rename__ the __components__ as we choose, for example \"wide\" and \"narrow\" (note that the \"g1\" and \"g2\" are only references we created for them, not names of the components)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"g1.name = \"wide\"\n",
"g2.name = \"narrow\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can look at the model again to see the result"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" # | Attribute Name | Component Name | Component Type\n",
"---- | ------------------- | ------------------- | -------------------\n",
" 0 | wide | wide | GaussianHF\n",
" 1 | narrow | narrow | GaussianHF"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.components"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[back to top] \n",
"\n",
"To finally see the full structure (the one we looked at here ), we can __print all of the parameter values__ of all components of the model."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Model1D: Two gaussians current_component_values: wide
Parameter Name Free \n",
" Value Std Min Max centre True 0 \n",
" fwhm True 1 \n",
" 0 height True 1 \n",
" 0
current_component_values: narrow
Parameter Name Free \n",
" Value Std Min Max centre True 0 \n",
" fwhm True 1 \n",
" 0 height True 1 \n",
" 0
"
],
"text/plain": [
"Model1D: Two gaussians\n",
"current_component_values: wide\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 0.0 | None | None | None\n",
" fwhm | True | 1.0 | None | 0.0 | None\n",
" height | True | 1.0 | None | 0.0 | None\n",
"\n",
"current_component_values: narrow\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 0.0 | None | None | None\n",
" fwhm | True | 1.0 | None | 0.0 | None\n",
" height | True | 1.0 | None | 0.0 | None\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m.print_current_values()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To access the values, we have to look inside the components for the parameters. It can simply be done by following the pattern:\n",
"> `some_component_reference.parameter_name.value`\n",
"\n",
"In this case the component references are the __g1__ and __g2__, while parameter names are __centre__, __A__ and __sigma__."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At this point it is good practice to store the model so that, if something goes wrong, we can go back to this stage:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"m.store(name=\"new\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"├── ground_truth\n",
"│ ├── components\n",
"│ │ ├── narrow\n",
"│ │ └── wide\n",
"│ ├── date = 2021-04-20 12:47:51\n",
"│ └── dimensions = (32, 32|1024)\n",
"└── new\n",
" ├── components\n",
" │ ├── narrow\n",
" │ └── wide\n",
" ├── date = 2021-04-20 12:48:53\n",
" └── dimensions = (32, 32|1024)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.signal.models"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that there is another model stored in the signal, `ground truth`. We'll put it to use at end of this tutorial."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g1.fwhm.value"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that we can access the component more conveniently using its name as follows:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.components.wide.fwhm.value"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[back to top] \n",
"\n",
"We can __set parameter values__ in exactly the same way. Let set `g1` `sigma` value to 30:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"m.components.wide.fwhm.value = 30"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Model1D: Two gaussians current_component_values: wide
Parameter Name Free \n",
" Value Std Min Max centre True 0 \n",
" fwhm True 30 \n",
" 0 height True 1 \n",
" 0
current_component_values: narrow
Parameter Name Free \n",
" Value Std Min Max centre True 0 \n",
" fwhm True 1 \n",
" 0 height True 1 \n",
" 0
"
],
"text/plain": [
"Model1D: Two gaussians\n",
"current_component_values: wide\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 0.0 | None | None | None\n",
" fwhm | True | 30.0 | None | 0.0 | None\n",
" height | True | 1.0 | None | 0.0 | None\n",
"\n",
"current_component_values: narrow\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 0.0 | None | None | None\n",
" fwhm | True | 1.0 | None | 0.0 | None\n",
" height | True | 1.0 | None | 0.0 | None\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m.print_current_values()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For convenience, we can also __set values \"in bulk\"__ for all components in the model. The required command is\n",
"> `m.set_parameters_value`\n",
"\n",
"Set the area (\"A\" parameter) of both peaks to 500"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"m.set_parameters_value('height', 100)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Model1D: Two gaussians current_component_values: wide
Parameter Name Free \n",
" Value Std Min Max centre True 0 \n",
" fwhm True 30 \n",
" 0 height True 100 \n",
" 0
current_component_values: narrow
Parameter Name Free \n",
" Value Std Min Max centre True 0 \n",
" fwhm True 1 \n",
" 0 height True 100 \n",
" 0
"
],
"text/plain": [
"Model1D: Two gaussians\n",
"current_component_values: wide\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 0.0 | None | None | None\n",
" fwhm | True | 30.0 | None | 0.0 | None\n",
" height | True | 100.0 | None | 0.0 | None\n",
"\n",
"current_component_values: narrow\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 0.0 | None | None | None\n",
" fwhm | True | 1.0 | None | 0.0 | None\n",
" height | True | 100.0 | None | 0.0 | None\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m.print_current_values()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Indexing the model and fitting a single spectrum"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will start by analyzing the data at one single pixel. For that we can using the same indexing syntax that we use for signals."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"m00 = m.inav[0, 0]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "cbe76fe1a4d3439caa8f761a550027be",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m00.plot(plot_components=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to increase the chances of obtaining a good fit to the data, we must provide better starting parameters."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We could do that interactively, using ``m.gui()`` or manually as follows:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"m00.components.narrow.centre.value = 60\n",
"m00.components.wide.centre.value = 50"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are now ready to fit"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" covar: array([[ 1.76830147e-04, -5.11658338e-05, 1.93802041e-04,\n",
" -8.01526059e-06, -8.68573149e-05, -3.93832136e-04],\n",
" [-5.11658338e-05, 1.08993808e-03, -1.49141316e-03,\n",
" -3.06548331e-05, 1.62328408e-04, 7.76505163e-04],\n",
" [ 1.93802041e-04, -1.49141316e-03, 5.07437902e-03,\n",
" 5.16094662e-05, -7.30358575e-04, -3.23763439e-03],\n",
" [-8.01526059e-06, -3.06548331e-05, 5.16094662e-05,\n",
" 1.21034752e-04, -2.78305323e-06, -1.31480558e-05],\n",
" [-8.68573149e-05, 1.62328408e-04, -7.30358575e-04,\n",
" -2.78305323e-06, 7.92559428e-04, -2.15838794e-03],\n",
" [-3.93832136e-04, 7.76505163e-04, -3.23763439e-03,\n",
" -1.31480558e-05, -2.15838794e-03, 3.62907692e-02]])\n",
" fun: array([-0.28860998, -1.12330872, 1.04291008, ..., -4.09065073,\n",
" -2.22072033, -2.34996863])\n",
" message: 'Both actual and predicted relative reductions in the sum of squares\\n are at most 0.000000'\n",
" nfev: 64\n",
" status: 1\n",
" success: True\n",
" x: array([ 49.08134201, 59.87208342, 139.92132633, 60.00915957,\n",
" 5.90457142, 48.64318731])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m00.fit()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The fit (notice that the model got updated in the figure) looks good!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that the value of the parameters have changed to their optimal value. Also notice that the standard deviation has been estimated too."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Model1D: Two gaussians current_component_values: wide
Parameter Name Free \n",
" Value Std Min Max centre True 49.0813 \n",
" 0.125441 fwhm True 59.8721 \n",
" 0.311431 0 height True 139.921 \n",
" 0.671974 0
current_component_values: narrow
Parameter Name Free \n",
" Value Std Min Max centre True 60.0092 \n",
" 0.103781 fwhm True 5.90457 \n",
" 0.265569 0 height True 48.6432 \n",
" 1.79704 0
"
],
"text/plain": [
"Model1D: Two gaussians\n",
"current_component_values: wide\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 49.0813420 | 0.12544082 | None | None\n",
" fwhm | True | 59.8720834 | 0.31143087 | 0.0 | None\n",
" height | True | 139.921326 | 0.67197358 | 0.0 | None\n",
"\n",
"current_component_values: narrow\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 60.0091595 | 0.10378050 | None | None\n",
" fwhm | True | 5.90457141 | 0.26556856 | 0.0 | None\n",
" height | True | 48.6431873 | 1.79704452 | 0.0 | None\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m00.print_current_values()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But how to know how good is the fit? "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Once the fit was performed, chi-squared ($\\chi^2$), degrees of freedom and reduced chi-squared ($\\chi^2_\\nu$) of the fit are automatically calculated.\n",
"\n",
"They are accessible with, respectively:\n",
"> `m2.chisq`\n",
"\n",
"> `m2.dof`\n",
"\n",
"> `m2.red_chisq`\n",
"\n",
"Let's have a look at reduced $\\chi^2$ by plotting it"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([89.07346101])"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m00.red_chisq.data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That's far too big! (A good fit should have $a\\chi^2_\\nu$ of around 1.)\n",
"\n",
"The issue is that we haven't defined the variance of the noise:"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" \n",
" \n",
" General\n",
" \n",
" \n",
" \n",
" title = Two gaussians \n",
" \n",
" \n",
" \n",
" \n",
" Signal\n",
" \n",
" \n",
" \n",
" \n",
" \n",
" "
],
"text/plain": [
"├── General\n",
"│ └── title = Two gaussians\n",
"└── Signal\n",
" ├── binned = False\n",
" └── signal_type = "
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m00.signal.metadata"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For that we can use the following ``Signal`` method:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"m00.signal.estimate_poissonian_noise_variance()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's now fit. Because the noise variance is available, HyperSpy will now perform weighted non-linear least squares automatically."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" covar: array([[ 1.05592398e-02, -3.91479407e-03, 1.34613574e-02,\n",
" -4.90584075e-04, -5.85925231e-03, -2.25958693e-02],\n",
" [-3.91479407e-03, 5.63446391e-02, -1.23981408e-01,\n",
" -1.92875392e-03, 1.65734689e-02, 6.84912325e-02],\n",
" [ 1.34613574e-02, -1.23981408e-01, 5.62520683e-01,\n",
" 5.64066839e-03, -8.52446453e-02, -3.32862216e-01],\n",
" [-4.90584075e-04, -1.92875392e-03, 5.64066839e-03,\n",
" 1.82595481e-02, -2.24068762e-03, -1.43013956e-03],\n",
" [-5.85925231e-03, 1.65734689e-02, -8.52446453e-02,\n",
" -2.24068762e-03, 1.11382133e-01, -3.78334532e-01],\n",
" [-2.25958693e-02, 6.84912325e-02, -3.32862216e-01,\n",
" -1.43013956e-03, -3.78334532e-01, 5.85821303e+00]])\n",
" fun: array([-0.18588423, -0.35635426, 0.09923745, ..., -1.06540541,\n",
" -0.68143743, -0.71105147])\n",
" message: 'Both actual and predicted relative reductions in the sum of squares\\n are at most 0.000000'\n",
" nfev: 29\n",
" status: 1\n",
" success: True\n",
" x: array([ 49.00805359, 59.46045475, 138.94771078, 60.01140505,\n",
" 5.9548883 , 48.58265848])"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m00.fit()"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1.03117735])"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m00.red_chisq.data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That's much better!"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Model1D: Two gaussians current_component_values: wide
Parameter Name Free \n",
" Value Std Min Max centre True 49.0081 \n",
" 0.104296 fwhm True 59.4605 \n",
" 0.240924 0 height True 138.948 \n",
" 0.761242 0
current_component_values: narrow
Parameter Name Free \n",
" Value Std Min Max centre True 60.0114 \n",
" 0.137151 fwhm True 5.95489 \n",
" 0.338736 0 height True 48.5827 \n",
" 2.45661 0
"
],
"text/plain": [
"Model1D: Two gaussians\n",
"current_component_values: wide\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 49.0080535 | 0.10429646 | None | None\n",
" fwhm | True | 59.4604547 | 0.24092372 | 0.0 | None\n",
" height | True | 138.947710 | 0.76124160 | 0.0 | None\n",
"\n",
"current_component_values: narrow\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 60.0114050 | 0.13715077 | None | None\n",
" fwhm | True | 5.95488830 | 0.33873575 | 0.0 | None\n",
" height | True | 48.5826584 | 2.45660792 | 0.0 | None\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m00.print_current_values()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that the value of the parameters and their standard deviation has changed. The previous values were biased because we haven't defined the noise variance. These values should be more accurate."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can obtain an even more accurate result by using the current model to better estimate the noise variance:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Model1D: Two gaussians current_component_values: wide
Parameter Name Free \n",
" Value Std Min Max centre True 49.06 \n",
" 0.104386 fwhm True 59.9619 \n",
" 0.243351 0 height True 139.74 \n",
" 0.764604 0
current_component_values: narrow
Parameter Name Free \n",
" Value Std Min Max centre True 59.9998 \n",
" 0.139023 fwhm True 5.98386 \n",
" 0.341362 0 height True 48.501 \n",
" 2.45872 0
"
],
"text/plain": [
"Model1D: Two gaussians\n",
"current_component_values: wide\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 49.0600457 | 0.10438558 | None | None\n",
" fwhm | True | 59.9618538 | 0.24335118 | 0.0 | None\n",
" height | True | 139.740317 | 0.76460426 | 0.0 | None\n",
"\n",
"current_component_values: narrow\n",
"Active: True\n",
"Parameter Name | Free | Value | Std | Min | Max\n",
"============== | ===== | ========== | ========== | ========== | ==========\n",
" centre | True | 59.9998497 | 0.13902337 | None | None\n",
" fwhm | True | 5.98386161 | 0.34136212 | 0.0 | None\n",
" height | True | 48.5009772 | 2.45872209 | 0.0 | None\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m00.signal.estimate_poissonian_noise_variance(expected_value=m00.as_signal())\n",
"m00.fit()\n",
"m00.print_current_values()"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1.04536884])"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m00.red_chisq.data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting the first line"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's now analyze the first line before attempting to fit the whole dataset"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"ml = m.inav[:, 0]"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "c669b649ad554be8a270b3f1b04d00e8",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "b7ae2a41d57041acb21bd6327a9cff12",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ml.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that the parameters of the first pixels that we have estimated are already set.\n",
"\n",
"Like before, we must estimate the noise variance"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"ml.signal.estimate_poissonian_noise_variance()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to fit the whole line we must use the ``multifit()`` method"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/francisco/Git/hyperspy/hyperspy/model.py:1567: VisibleDeprecationWarning: The 'iterpath' default will change from 'flyback' to 'serpentine' in HyperSpy version 2.0. Change 'iterpath' to other than None to suppress this warning.\n",
" warnings.warn(\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "5825b0ee35bd447d9743f0ae73a4e65e",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
" 0%| | 0/32 [00:00,\n",
" ]"
]
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hs.plot.plot_images([narrow_centre_value, narrow_centre_std], label=[\"centre\", \"centre std\"], axes_decor=\"off\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice how the standard deviation image has a contrast? Is that expected? If yes, what should it be correlated with?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's now verify that the standard deviation estimation is correct. We know that, if correct, 66% percent of the residuals must fall between a 1 standard deviation interval. Let's use this property to verify the result:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The ground truth is actually stored in the signal:\n"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"├── first_line_fitted\n",
"│ ├── components\n",
"│ │ ├── narrow\n",
"│ │ └── wide\n",
"│ ├── date = 2021-04-20 12:49:48\n",
"│ └── dimensions = (32, 32|1024)\n",
"├── fitted_with_MLpoisson\n",
"│ ├── components\n",
"│ │ ├── narrow\n",
"│ │ └── wide\n",
"│ ├── date = 2021-04-20 13:00:09\n",
"│ └── dimensions = (32, 32|1024)\n",
"├── ground_truth\n",
"│ ├── components\n",
"│ │ ├── narrow\n",
"│ │ └── wide\n",
"│ ├── date = 2021-04-20 12:47:51\n",
"│ └── dimensions = (32, 32|1024)\n",
"└── new\n",
" ├── components\n",
" │ ├── narrow\n",
" │ └── wide\n",
" ├── date = 2021-04-20 12:48:53\n",
" └── dimensions = (32, 32|1024)"
]
},
"execution_count": 94,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.signal.models"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [],
"source": [
"narrow_centre_gt = m.signal.models.restore(\"ground truth\").components.narrow.centre.as_signal()"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [],
"source": [
"residuals = (narrow_centre_gt - narrow_centre_value).data"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [],
"source": [
"residuals_in_1sigma = len(residuals[(residuals > -narrow_centre_std.data) & (residuals < narrow_centre_std.data)])"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"68.9453125"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"100 * residuals_in_1sigma / np.prod(residuals.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That is very close to 66% percent, so it works!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Appendix I: User define components interesting components"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets say we have a slightly stranger signal that we want to fit, like this one:"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"s = hs.load('wobbly_peak.hspy')"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
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" try {\n",
" // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
" callback(fig, msg);\n",
" } catch (e) {\n",
" console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
" }\n",
" }\n",
" };\n",
"}\n",
"\n",
"// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
"mpl.findpos = function(e) {\n",
" //this section is from http://www.quirksmode.org/js/events_properties.html\n",
" var targ;\n",
" if (!e)\n",
" e = window.event;\n",
" if (e.target)\n",
" targ = e.target;\n",
" else if (e.srcElement)\n",
" targ = e.srcElement;\n",
" if (targ.nodeType == 3) // defeat Safari bug\n",
" targ = targ.parentNode;\n",
"\n",
" // jQuery normalizes the pageX and pageY\n",
" // pageX,Y are the mouse positions relative to the document\n",
" // offset() returns the position of the element relative to the document\n",
" var x = e.pageX - $(targ).offset().left;\n",
" var y = e.pageY - $(targ).offset().top;\n",
"\n",
" return {\"x\": x, \"y\": y};\n",
"};\n",
"\n",
"/*\n",
" * return a copy of an object with only non-object keys\n",
" * we need this to avoid circular references\n",
" * http://stackoverflow.com/a/24161582/3208463\n",
" */\n",
"function simpleKeys (original) {\n",
" return Object.keys(original).reduce(function (obj, key) {\n",
" if (typeof original[key] !== 'object')\n",
" obj[key] = original[key]\n",
" return obj;\n",
" }, {});\n",
"}\n",
"\n",
"mpl.figure.prototype.mouse_event = function(event, name) {\n",
" var canvas_pos = mpl.findpos(event)\n",
"\n",
" if (name === 'button_press')\n",
" {\n",
" this.canvas.focus();\n",
" this.canvas_div.focus();\n",
" }\n",
"\n",
" var x = canvas_pos.x * mpl.ratio;\n",
" var y = canvas_pos.y * mpl.ratio;\n",
"\n",
" this.send_message(name, {x: x, y: y, button: event.button,\n",
" step: event.step,\n",
" guiEvent: simpleKeys(event)});\n",
"\n",
" /* This prevents the web browser from automatically changing to\n",
" * the text insertion cursor when the button is pressed. We want\n",
" * to control all of the cursor setting manually through the\n",
" * 'cursor' event from matplotlib */\n",
" event.preventDefault();\n",
" return false;\n",
"}\n",
"\n",
"mpl.figure.prototype._key_event_extra = function(event, name) {\n",
" // Handle any extra behaviour associated with a key event\n",
"}\n",
"\n",
"mpl.figure.prototype.key_event = function(event, name) {\n",
"\n",
" // Prevent repeat events\n",
" if (name == 'key_press')\n",
" {\n",
" if (event.which === this._key)\n",
" return;\n",
" else\n",
" this._key = event.which;\n",
" }\n",
" if (name == 'key_release')\n",
" this._key = null;\n",
"\n",
" var value = '';\n",
" if (event.ctrlKey && event.which != 17)\n",
" value += \"ctrl+\";\n",
" if (event.altKey && event.which != 18)\n",
" value += \"alt+\";\n",
" if (event.shiftKey && event.which != 16)\n",
" value += \"shift+\";\n",
"\n",
" value += 'k';\n",
" value += event.which.toString();\n",
"\n",
" this._key_event_extra(event, name);\n",
"\n",
" this.send_message(name, {key: value,\n",
" guiEvent: simpleKeys(event)});\n",
" return false;\n",
"}\n",
"\n",
"mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
" if (name == 'download') {\n",
" this.handle_save(this, null);\n",
" } else {\n",
" this.send_message(\"toolbar_button\", {name: name});\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
" this.message.textContent = tooltip;\n",
"};\n",
"mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
"\n",
"mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
"\n",
"mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
" // Create a \"websocket\"-like object which calls the given IPython comm\n",
" // object with the appropriate methods. Currently this is a non binary\n",
" // socket, so there is still some room for performance tuning.\n",
" var ws = {};\n",
"\n",
" ws.close = function() {\n",
" comm.close()\n",
" };\n",
" ws.send = function(m) {\n",
" //console.log('sending', m);\n",
" comm.send(m);\n",
" };\n",
" // Register the callback with on_msg.\n",
" comm.on_msg(function(msg) {\n",
" //console.log('receiving', msg['content']['data'], msg);\n",
" // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
" ws.onmessage(msg['content']['data'])\n",
" });\n",
" return ws;\n",
"}\n",
"\n",
"mpl.mpl_figure_comm = function(comm, msg) {\n",
" // This is the function which gets called when the mpl process\n",
" // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
"\n",
" var id = msg.content.data.id;\n",
" // Get hold of the div created by the display call when the Comm\n",
" // socket was opened in Python.\n",
" var element = $(\"#\" + id);\n",
" var ws_proxy = comm_websocket_adapter(comm)\n",
"\n",
" function ondownload(figure, format) {\n",
" window.open(figure.imageObj.src);\n",
" }\n",
"\n",
" var fig = new mpl.figure(id, ws_proxy,\n",
" ondownload,\n",
" element.get(0));\n",
"\n",
" // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
" // web socket which is closed, not our websocket->open comm proxy.\n",
" ws_proxy.onopen();\n",
"\n",
" fig.parent_element = element.get(0);\n",
" fig.cell_info = mpl.find_output_cell(\"
\");\n",
" if (!fig.cell_info) {\n",
" console.error(\"Failed to find cell for figure\", id, fig);\n",
" return;\n",
" }\n",
"\n",
" var output_index = fig.cell_info[2]\n",
" var cell = fig.cell_info[0];\n",
"\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_close = function(fig, msg) {\n",
" var width = fig.canvas.width/mpl.ratio\n",
" fig.root.unbind('remove')\n",
"\n",
" // Update the output cell to use the data from the current canvas.\n",
" fig.push_to_output();\n",
" var dataURL = fig.canvas.toDataURL();\n",
" // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
" // the notebook keyboard shortcuts fail.\n",
" IPython.keyboard_manager.enable()\n",
" $(fig.parent_element).html('
')\n",
" nav_element.attr('style', 'width: 100%');\n",
" this.root.append(nav_element);\n",
"\n",
" // Define a callback function for later on.\n",
" function toolbar_event(event) {\n",
" return fig.toolbar_button_onclick(event['data']);\n",
" }\n",
" function toolbar_mouse_event(event) {\n",
" return fig.toolbar_button_onmouseover(event['data']);\n",
" }\n",
"\n",
" for(var toolbar_ind in mpl.toolbar_items){\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) { continue; };\n",
"\n",
" var button = $('
');\n",
" var button = $('= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] == html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"}\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel != null) {\n",
" IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
"}\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"s.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's (as the name implies) composed of a sinus + gaussian + 2nd degree polynomial. However we don't have a `sin` component in the in-build library, so we'll just write our own:"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"sin = hs.model.components1D.Expression('A*sin(b*x + c)',\n",
" name='sin',)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then just create and add all the additional components we might need: a gaussian and a polynomial"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": true,
"jupyter": {
"outputs_hidden": true
}
},
"outputs": [],
"source": [
"m = s.create_model()\n",
"gaus = hs.model.components1D.Gaussian()\n",
"poly = hs.model.components1D.Polynomial(2)\n",
"m.extend([sin, gaus, poly])"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Components\tParameter\tValue\n",
"sin\n",
"\t\tA\t0\n",
"\t\tb\t0\n",
"\t\tc\t0\n",
"Gaussian\n",
"\t\tA\t1\n",
"\t\tcentre\t0\n",
"\t\tsigma\t1\n",
"Polynomial\n",
"\t\tcoefficients[0]\t0\n",
"\t\tcoefficients[1]\t0\n",
"\t\tcoefficients[2]\t0\n"
]
}
],
"source": [
"m.print_current_values()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The initial values do not seem to be very useful, so let's just plot the model, turn on the widgets, and we'll play until things seem close enough:"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"application/javascript": [
"/* Put everything inside the global mpl namespace */\n",
"window.mpl = {};\n",
"\n",
"\n",
"mpl.get_websocket_type = function() {\n",
" if (typeof(WebSocket) !== 'undefined') {\n",
" return WebSocket;\n",
" } else if (typeof(MozWebSocket) !== 'undefined') {\n",
" return MozWebSocket;\n",
" } else {\n",
" alert('Your browser does not have WebSocket support.' +\n",
" 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
" 'Firefox 4 and 5 are also supported but you ' +\n",
" 'have to enable WebSockets in about:config.');\n",
" };\n",
"}\n",
"\n",
"mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
" this.id = figure_id;\n",
"\n",
" this.ws = websocket;\n",
"\n",
" this.supports_binary = (this.ws.binaryType != undefined);\n",
"\n",
" if (!this.supports_binary) {\n",
" var warnings = document.getElementById(\"mpl-warnings\");\n",
" if (warnings) {\n",
" warnings.style.display = 'block';\n",
" warnings.textContent = (\n",
" \"This browser does not support binary websocket messages. \" +\n",
" \"Performance may be slow.\");\n",
" }\n",
" }\n",
"\n",
" this.imageObj = new Image();\n",
"\n",
" this.context = undefined;\n",
" this.message = undefined;\n",
" this.canvas = undefined;\n",
" this.rubberband_canvas = undefined;\n",
" this.rubberband_context = undefined;\n",
" this.format_dropdown = undefined;\n",
"\n",
" this.image_mode = 'full';\n",
"\n",
" this.root = $('
');\n",
" this._root_extra_style(this.root)\n",
" this.root.attr('style', 'display: inline-block');\n",
"\n",
" $(parent_element).append(this.root);\n",
"\n",
" this._init_header(this);\n",
" this._init_canvas(this);\n",
" this._init_toolbar(this);\n",
"\n",
" var fig = this;\n",
"\n",
" this.waiting = false;\n",
"\n",
" this.ws.onopen = function () {\n",
" fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
" fig.send_message(\"send_image_mode\", {});\n",
" if (mpl.ratio != 1) {\n",
" fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
" }\n",
" fig.send_message(\"refresh\", {});\n",
" }\n",
"\n",
" this.imageObj.onload = function() {\n",
" if (fig.image_mode == 'full') {\n",
" // Full images could contain transparency (where diff images\n",
" // almost always do), so we need to clear the canvas so that\n",
" // there is no ghosting.\n",
" fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
" }\n",
" fig.context.drawImage(fig.imageObj, 0, 0);\n",
" };\n",
"\n",
" this.imageObj.onunload = function() {\n",
" this.ws.close();\n",
" }\n",
"\n",
" this.ws.onmessage = this._make_on_message_function(this);\n",
"\n",
" this.ondownload = ondownload;\n",
"}\n",
"\n",
"mpl.figure.prototype._init_header = function() {\n",
" var titlebar = $(\n",
" '
');\n",
" var titletext = $(\n",
" '
');\n",
" titlebar.append(titletext)\n",
" this.root.append(titlebar);\n",
" this.header = titletext[0];\n",
"}\n",
"\n",
"\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
"\n",
"}\n",
"\n",
"\n",
"mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
"\n",
"}\n",
"\n",
"mpl.figure.prototype._init_canvas = function() {\n",
" var fig = this;\n",
"\n",
" var canvas_div = $('
');\n",
"\n",
" canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
"\n",
" function canvas_keyboard_event(event) {\n",
" return fig.key_event(event, event['data']);\n",
" }\n",
"\n",
" canvas_div.keydown('key_press', canvas_keyboard_event);\n",
" canvas_div.keyup('key_release', canvas_keyboard_event);\n",
" this.canvas_div = canvas_div\n",
" this._canvas_extra_style(canvas_div)\n",
" this.root.append(canvas_div);\n",
"\n",
" var canvas = $('
')\n",
" nav_element.attr('style', 'width: 100%');\n",
" this.root.append(nav_element);\n",
"\n",
" // Define a callback function for later on.\n",
" function toolbar_event(event) {\n",
" return fig.toolbar_button_onclick(event['data']);\n",
" }\n",
" function toolbar_mouse_event(event) {\n",
" return fig.toolbar_button_onmouseover(event['data']);\n",
" }\n",
"\n",
" for(var toolbar_ind in mpl.toolbar_items) {\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) {\n",
" // put a spacer in here.\n",
" continue;\n",
" }\n",
" var button = $('');\n",
" nav_element.append(status_bar);\n",
" this.message = status_bar[0];\n",
"}\n",
"\n",
"mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
" // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
" // which will in turn request a refresh of the image.\n",
" this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
"}\n",
"\n",
"mpl.figure.prototype.send_message = function(type, properties) {\n",
" properties['type'] = type;\n",
" properties['figure_id'] = this.id;\n",
" this.ws.send(JSON.stringify(properties));\n",
"}\n",
"\n",
"mpl.figure.prototype.send_draw_message = function() {\n",
" if (!this.waiting) {\n",
" this.waiting = true;\n",
" this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
" }\n",
"}\n",
"\n",
"\n",
"mpl.figure.prototype.handle_save = function(fig, msg) {\n",
" var format_dropdown = fig.format_dropdown;\n",
" var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
" fig.ondownload(fig, format);\n",
"}\n",
"\n",
"\n",
"mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
" var size = msg['size'];\n",
" if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
" fig._resize_canvas(size[0], size[1]);\n",
" fig.send_message(\"refresh\", {});\n",
" };\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
" var x0 = msg['x0'] / mpl.ratio;\n",
" var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
" var x1 = msg['x1'] / mpl.ratio;\n",
" var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
" x0 = Math.floor(x0) + 0.5;\n",
" y0 = Math.floor(y0) + 0.5;\n",
" x1 = Math.floor(x1) + 0.5;\n",
" y1 = Math.floor(y1) + 0.5;\n",
" var min_x = Math.min(x0, x1);\n",
" var min_y = Math.min(y0, y1);\n",
" var width = Math.abs(x1 - x0);\n",
" var height = Math.abs(y1 - y0);\n",
"\n",
" fig.rubberband_context.clearRect(\n",
" 0, 0, fig.canvas.width, fig.canvas.height);\n",
"\n",
" fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
" // Updates the figure title.\n",
" fig.header.textContent = msg['label'];\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
" var cursor = msg['cursor'];\n",
" switch(cursor)\n",
" {\n",
" case 0:\n",
" cursor = 'pointer';\n",
" break;\n",
" case 1:\n",
" cursor = 'default';\n",
" break;\n",
" case 2:\n",
" cursor = 'crosshair';\n",
" break;\n",
" case 3:\n",
" cursor = 'move';\n",
" break;\n",
" }\n",
" fig.rubberband_canvas.style.cursor = cursor;\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_message = function(fig, msg) {\n",
" fig.message.textContent = msg['message'];\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
" // Request the server to send over a new figure.\n",
" fig.send_draw_message();\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
" fig.image_mode = msg['mode'];\n",
"}\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function() {\n",
" // Called whenever the canvas gets updated.\n",
" this.send_message(\"ack\", {});\n",
"}\n",
"\n",
"// A function to construct a web socket function for onmessage handling.\n",
"// Called in the figure constructor.\n",
"mpl.figure.prototype._make_on_message_function = function(fig) {\n",
" return function socket_on_message(evt) {\n",
" if (evt.data instanceof Blob) {\n",
" /* FIXME: We get \"Resource interpreted as Image but\n",
" * transferred with MIME type text/plain:\" errors on\n",
" * Chrome. But how to set the MIME type? It doesn't seem\n",
" * to be part of the websocket stream */\n",
" evt.data.type = \"image/png\";\n",
"\n",
" /* Free the memory for the previous frames */\n",
" if (fig.imageObj.src) {\n",
" (window.URL || window.webkitURL).revokeObjectURL(\n",
" fig.imageObj.src);\n",
" }\n",
"\n",
" fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
" evt.data);\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" }\n",
" else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
" fig.imageObj.src = evt.data;\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" }\n",
"\n",
" var msg = JSON.parse(evt.data);\n",
" var msg_type = msg['type'];\n",
"\n",
" // Call the \"handle_{type}\" callback, which takes\n",
" // the figure and JSON message as its only arguments.\n",
" try {\n",
" var callback = fig[\"handle_\" + msg_type];\n",
" } catch (e) {\n",
" console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
" return;\n",
" }\n",
"\n",
" if (callback) {\n",
" try {\n",
" // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
" callback(fig, msg);\n",
" } catch (e) {\n",
" console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
" }\n",
" }\n",
" };\n",
"}\n",
"\n",
"// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
"mpl.findpos = function(e) {\n",
" //this section is from http://www.quirksmode.org/js/events_properties.html\n",
" var targ;\n",
" if (!e)\n",
" e = window.event;\n",
" if (e.target)\n",
" targ = e.target;\n",
" else if (e.srcElement)\n",
" targ = e.srcElement;\n",
" if (targ.nodeType == 3) // defeat Safari bug\n",
" targ = targ.parentNode;\n",
"\n",
" // jQuery normalizes the pageX and pageY\n",
" // pageX,Y are the mouse positions relative to the document\n",
" // offset() returns the position of the element relative to the document\n",
" var x = e.pageX - $(targ).offset().left;\n",
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"And then fit it and look at the results!"
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"text": [
"Components\tParameter\tValue\n",
"sin\n",
"\t\tA\t-3\n",
"\t\tb\t0.100033\n",
"\t\tc\t-0.707963\n",
"Gaussian\n",
"\t\tA\t2999\n",
"\t\tcentre\t149.95\n",
"\t\tsigma\t49.9833\n",
"Polynomial\n",
"\t\tcoefficients[0]\t-2.19049e-11\n",
"\t\tcoefficients[1]\t0.06002\n",
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"## Appendix II: Generating the synthetic data"
]
},
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"metadata": {},
"source": [
"[back to top] \n"
]
},
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"cell_type": "code",
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" 0%| | 0/1024 [00:00\n",
"### Wobbly peak\n",
"[back to top] \n"
]
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"import numpy as np\n",
"import hyperspy.api as hs\n",
"\n",
"k = 1\n",
"alpha = 15\n",
"amp = 3\n",
"\n",
"gaus_position = 15\n",
"gaus_width = 5\n",
"gaus_A = 300\n",
"\n",
"gradient = 0.6\n",
"offset= 3\n",
"\n",
"sin_component = hs.model.components1D.Expression('A * sin(k*x + alpha)', name='sin', k=k,\n",
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"\n",
"poly = hs.model.components1D.Polynomial(1)\n",
"\n",
"poly.coefficients.value = (gradient, offset)\n",
"\n",
"axis = np.linspace(0, 30, 3000, dtype='double')\n",
"\n",
"result = sin_component.function(axis)+ gaus.function(axis) + poly.function(axis)\n",
"s = hs.signals.Signal1D(result)\n",
"s.axes_manager[0].name = 'x'\n",
"s.axes_manager[0].scale = 0.1\n",
"s.axes_manager[0].offset = 0\n",
"\n",
"s.metadata.General.author = 'Tomas Ostasevicius'\n",
"s.metadata.General.title = 'Sin + poly(2) + Gaussian'\n",
"s.save('wobbly_peak', overwrite=True)"
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