Plot

When the curves of a list run out of styles they start again from style 1. They cycle through all styles, at least three, or through the first “LineStyleCycle” styles. Two colors that alternate therefore need “LineStyleCycle”: {“LineStyle”, {Orange, Green}} alone gives orange, green, blue (the default style 3), orange, …; with {“LineStyleCycle”,2} it gives orange, green, orange, green, … “LineStyleCycle” can not be larger than the number of styles.

===== Waterfall plots =====

With “WaterfallShift” or “UseResonantEnergy” the curves of a list are drawn above each other: curve $n$ at WaterfallOffset + $(n-1)$ WaterfallShift, or at WaterfallOffset plus its resonant energy. The values are multiplied by “Scale” before they are shifted. With “UseResonantEnergy” the vertical axis reads the incoming energy of RIXS spectra, also when the incoming energies are not equally spaced. “UseResonantEnergy” needs a Spectra object and can not be combined with “Nrow” and “Ncolumn”.

===== Color maps =====

With {“ColorMap”,true} the curves of a list are drawn as a color map, a bitmap of “NPixelX” by “NPixelY” pixels inside the frame. Each curve lies at the height it would have in a waterfall plot, or, without the waterfall options, at its number $n$. The heights must increase or decrease from curve to curve, and a color map needs at least two curves on a common energy mesh: it can not be made of lists of points, and not combined with “Nrow” and “Ncolumn”. With “Interpolate” the map is interpolated linearly in energy and between neighboring curves; without it each pixel takes the nearest point, the boundary between two curves lies half way between them, and the pixels are drawn as sharp squares.

The value at a pixel is the imaginary part, or the real part with {“plotIm”,false}, after “Negate” and “Scale”. The built-in color scale goes from white to “Color” as “Saturation” times the value goes from 0 to 1. A “ColorFunction” f(Re, Im) gets both parts and returns red, green and blue, each from 0 to 1 (values outside are clipped); it can show the intensity on a scale of its own, a logarithmic scale, or the sign or the phase of a response function.

===== Grids of panels =====

A matrix valued response function, and a Spectra object with “Nrow” and “Ncolumn”, is drawn as a grid of panels, one curve each, with the first curve (the element $G_{11}$) in the top left corner, row by row. All panels share the plot range of the “Frame”. The off-diagonal panels can show a different vertical range: from $(Y_{min} - s)\, c$ to $(Y_{max} - s)\, c$, with $s$ = “ShiftOffDiagonal” and $c$ = “ScaleOffDiagonal”, so that $c < 1$ magnifies the off-diagonal elements by $1/c$. The numbers on the vertical axis are those of the diagonal panels. To draw some of the elements in one frame instead, select them with “SpectraStart”, “SpectraStep” and “SpectraStop”: the diagonal of an $N \times N$ matrix is element 1 and every $(N+1)$-th after it.

===== Example =====

Three peaks as a Spectra object and as a response function, several curves in one frame, a waterfall plot and a color map.

==== Input ==== <code Quanty Example.Quanty> -- a response function with three poles, at -2, 0.5 and 3 eV with weights 0.3, 0.5 and 0.2, -- and a spectrum made from it, broadened by a Lorentzian of 0.2 eV G = ResponseFunction.New({ {0, -2, 0.5, 3}, {0.3, 0.5, 0.2}, mu = 0, type = “ListOfPoles” }) S = ResponseFunction.ToSpectra(G, emin_-5_emax_5_ne_1000_gammal_0.2) -- write a Graphics object to an svg file that fills the window of a web browser function Save(pl, name) local file = io.open(name..“.svg”, “w”) file:write(Graphics.ToSVG(pl, relativesize_true)) file:close() end -- 1. without options: the real part red and the imaginary part blue, the vertical axis from -1 to 1 Save(Graphics.Plot(S), “Plot_1_default”) -- 2. the intensity -Im S, in a frame chosen by hand Frame = xmin_-4_xmax_4_ymin_-0.2_ymax_5.5_firstytick_0_dytick_1_xlabel_energy_ev_ylabel_intensity_xlmargin_0.1_yaxis_-10 Save(Graphics.Plot(S, plotre_false_negate_true_frame_frame), “Plot_2_intensity”) -- 3. the response function itself, broadened by a Lorentzian of 0.2 eV; the energies are those of the frame Save(Graphics.Plot(G, 0.2, frame_xmin_-4_xmax_4_ymin_-5.5_ymax_5.5_firstytick_-4_dytick_2_xlabel_energy_ev_ylabel_g_e_xlmargin_0.1}}), “Plot_3_response_function”) -- 4. four curves in one frame, the intensity broadened by 0.2, 0.3, 0.5 and 0.8 eV, alternating orange and green Curves = {} for k, Gamma in ipairs({0.2, 0.3, 0.5, 0.8}) do Curves[k] = ResponseFunction.ToSpectra(G, emin_-5_emax_5_ne_1000_gammal_gamma) end Orange = linewidth_0.003_linecolor_0xff8000 Green = linewidth_0.003_linecolor_0x00a000 Save(Graphics.Plot(Curves, plotre_false_negate_true_frame_frame_linestyle_orange_green, {“LineStyleCycle”,2}}), “Plot_4_several_curves”) -- 5. the same curves as a waterfall plot, in the default styles, made smaller by Scale and each shifted up by 2 from the one before Save(Graphics.Plot(Curves, plotre_false_negate_true_scale_0.35_waterfallshift_2_frame_xmin_-4_xmax_4_yticks_false_xaxis_-10_yaxis_-10_xlabel_energy_ev_ylabel_intensity_shifted_xlmargin_0.06}}), “Plot_5_waterfall”) -- 6. the levels split by Delta from 0 to 3 eV, as a color map with Delta on the vertical axis Series = {} for k = 0, 60 do local Delta = 0.05*k Series[k+1] = ResponseFunction.ToSpectra(ResponseFunction.New({ {0, -0.4*Delta, 0.6*Delta}, {0.4, 0.6}, mu = 0, type = “ListOfPoles” }), emin_-3_emax_3_ne_600_gammal_0.2) end Save(Graphics.Plot(Series, plotre_false_negate_true_waterfalloffset_0_waterfallshift_0.05_colormap_true_color_0x0000c0_saturation_0.2_npixelx_300_npixely_300_frame_xmin_-2_xmax_3_dytick_0.5_yformat_.1f_xaxis_-10_yaxis_-10_xlabel_energy_ev_ylabel_delta_ev_xlmargin_0.1}}), “Plot_6_color_map”) </code>

The script prints nothing; it writes the six plots as svg files. The plot without options shows the default vertical range from -1 to 1, which cuts the peaks. A Lorentzian of weight $w$ and full width $\Gamma$ is $2w/\Gamma$ high in $-\mathrm{Im}\,G$, here 3, 5 and 2. In the fourth plot the two styles alternate because of “LineStyleCycle”; the waterfall plot uses the default styles black, red and blue, which start again at the fourth curve.

===== Table of contents =====