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zqw0o-ui<pQz;Z>{2qsXiVLJY>dssSIr@FZuF9@twK%f4kZyJoM579T9D{1y*mtXX^ zc;VyO-<YQJDAE`rn##Xb4L5x!Uk%Tu^2>jNJH7Kekmo@Hn;zi4@0z*syQmO(93R<A zw*4XYY|V_{M9lvB39(iyf`;uvC2PgBG66hM^JR=KBjboZW|kY$`k9$~`HC33!p)l? NCDyA~_00`f{||j|GR^=1 diff --git a/Doc/DevRef/Multilayers.tex b/Doc/DevRef/Multilayers.tex index 4f52b5fb577..d9347c67ec8 100644 --- a/Doc/DevRef/Multilayers.tex +++ b/Doc/DevRef/Multilayers.tex @@ -656,7 +656,7 @@ Consider the equation which we ultimetaly need to solve for $i=0$, $f=J$. It is a \emph{split boundary problem} because the given amplitudes $t_i$, $r_f$ appear on different sides of the equation. -The homogeneous linear equation~\eqref{EMif} can be reorganized as +The homogeneous linear equation~\cref{EMif} can be reorganized as \begin{equation}\label{EWif} \begin{pmatrix}{t_f}\\ {r_i}\end{pmatrix} = W_{if} \begin{pmatrix}{t_i}\\ {r_f}\end{pmatrix}. @@ -668,7 +668,7 @@ Let us write matrix components as \begin{pmatrix} M_{tt} &M_{tr}\\ M_{rt} &M_{rr}\end{pmatrix}, \end{equation} and similarly for $W$. -Combining \eqref{EMif} and~\eqref{EWif}, +Combining \cref{EMif} and~\cref{EWif}, we can express $W$ as function of~$M$, \begin{equation}\label{EM2W} W = \mathcal{W}(M) @@ -691,7 +691,7 @@ If the total transfer matrix M = M_{01} \cdots M_{J-1,J} \end{equation} is given, and the boundary conditions are $t_0=1$ and $r_J=0$, -then \eqref{EWif} reduces to +then \cref{EWif} reduces to \begin{equation}\label{Etfri0J} \begin{array}{l@{}c@{}l} t_J &=& M_{tt}^{-1},\\[.3em] @@ -699,8 +699,8 @@ then \eqref{EWif} reduces to \end{array} \end{equation} If there is one single interface ($J=1$) -with $M=M_{01}=S_{01}$ given by~\eqref{ESab}, -then \eqref{Etfri0J} yields the standard Fresnel results, namely the transmitted amplitude +with $M=M_{01}=S_{01}$ given by~\cref{ESab}, +then \cref{Etfri0J} yields the standard Fresnel results, namely the transmitted amplitude \begin{equation}\label{EtFresnel} t_1 =\frac{2\kappa_0}{\kappa_0+\kappa_1}\eqqcolon t_{01}, \end{equation} @@ -710,7 +710,7 @@ and the reflected amplitude \end{equation} The newly introduced notation $t_{01}$ and $r_{01}$ identifies these as interface transmission and reflection coefficients. -The refraction matrix \eqref{ESab} can then be written as +The refraction matrix \cref{ESab} can then be written as \begin{equation}\label{ESab2} S_{ab} \coloneqq @@ -732,7 +732,7 @@ we readily verify that the incoming unit flux is conserved under reflection and %==================================================================================================% In general, the total transfer matrix is not known beforehand. -Straightforward evaluation of the product~\eqref{EM} is numerically unstable +Straightforward evaluation of the product~\cref{EM} is numerically unstable \cite[Sects.~III, IV]{StKK98}. It is therefore preferable to solve the split boundary problem through a recursion. Also, to compute scattering it is not sufficient to determine $r_0$ and $t_J$; @@ -740,11 +740,11 @@ the radiation amplitudes inside the inner layers are also needed. This is another good reason to use a recursive algorithm. We consider layers $a$, $b\coloneqq a+1$, $J$. -The transfer matrix \eqref{EM} obeys the recursion +The transfer matrix \cref{EM} obeys the recursion \begin{equation} M_{aJ}=M_{ab}\,M_{bJ}. \end{equation} -With the conversion functions \eqref{EM2W} and~\eqref{EW2M}, +With the conversion functions \cref{EM2W} and~\cref{EW2M}, we can derive a recursion for $W$: \begin{equation}\label{EWrecu} W_{aJ}=\mathcal{W}\left( M_{ab}\,\mathcal{M}\left(W_{bJ}\right)\right). @@ -767,11 +767,11 @@ This backward computation must then be followed by a forward computation of \iffalse However, determining the $W_{aJ}$ is not a goal in itself; we shall only evaluate them insofar as needed for computing -Ultimately, we want to apply~\eqref{EcWcP} to layers $i=0$, $f=J$, +Ultimately, we want to apply~\cref{EcWcP} to layers $i=0$, $f=J$, with $\U{r_J}=0$. Therefore, we only need to derive the $tt$ and $rt$ components of~$W_{0J}$, whereas the $tr$ and $rr$ components are irrelevant. -It turns out that this also holds for the inner terms of the recursion~\eqref{EWrecu}: +It turns out that this also holds for the inner terms of the recursion~\cref{EWrecu}: we only need the $tt$ and $rt$ components of the intermediate~$W_{0a}$. \fi @@ -781,7 +781,7 @@ the intermediate~$W_{0a}$. For the sake of numeric stability, it is advisable \emph{not} to compute the matrix~$M$ directly, -but to solve \eqref{E1Ap} through recursion. +but to solve \cref{E1Ap} through recursion. In early versions of BornAgain, we started from the bottom with $\tilde t_{J}=1$, and normalized the final result by division through $\tilde t_0$. @@ -810,13 +810,13 @@ This can easily be proven if the $\kappa_j$, and thereby the $r_{ab}$, are real. Old note from document Roughness.tex. A straight-forward implementation of the transfer matrix formulation accumulates all amplitudes -and then normalizes all of them in the final step via \eqref{EApml}. +and then normalizes all of them in the final step via \cref{EApml}. However, as soon as the amplitudes overflow this computational scheme breaks down and does not yield a valid result. By a small modification in the algorithm, this problem can be circumvented. -For this purpose, the global normalization \eqref{EApml} +For this purpose, the global normalization \cref{EApml} at the end of the computation can be replaced by a normalization \begin{align} \begin{pmatrix} @@ -826,14 +826,14 @@ t'_j \\ r'_j \end{pmatrix} \label{eq:normalization_step} \end{align} -that is carried out after every step \eqref{eq:amplitudes_computation} in the computation. +that is carried out after every step \cref{eq:amplitudes_computation} in the computation. This approach then keeps the amplitudes $t_j$ automatically equal to one, so that not only the boundary condition $t_0 = t'_0 = 1$ is automatically satisfied, but the amplitudes do not blow up towards infinity and hence the numerical problem remains well defined. At the end of the computation, however, there is still a renormalization step required in order to obtain the amplitudes $\left(t_j, r_j\right)^T$. This is accomplished by walking from the top of the sample to the bottom, -whereby all amplitudes are further scaled in order to meet the global normalization \eqref{EApml}. +whereby all amplitudes are further scaled in order to meet the global normalization \cref{EApml}. It must be mentioned though, that this algorithm still fails if a very thick layer is encountered. This will lead to the immediate underflow of $\delta$ and hence to an overflow of $\delta^* = 1/\delta$. @@ -993,11 +993,11 @@ TODO: Rework this fragment (ingested 29may23 from ba-intern/theory/Stratified.te For incident angles below the critical angle $\alpha_i < \alpha_c$ (also at interfaces inside the sample), the $k_z$-component of the wave vector turns imaginary. This situation then corresponds to an evanescent wave. -As a consequence, the phase factor $\delta$ \eqref{Ddell} +As a consequence, the phase factor $\delta$ \cref{Ddell} turns real and describes the exponential decrease of the amplitudes $t_j$, $r_j$ in the corresponding layer. For large layer thicknesses, this means that $\delta$ rapidly approaches zero, and its inverse becomes very large. -This leads to an increasingly ill-conditioned transfer matrix \eqref{Etransfer_matrix_BA}, until, +This leads to an increasingly ill-conditioned transfer matrix \cref{Etransfer_matrix_BA}, until, at some point, both quantities underflow or overflow, leading to invalid numerical results. As the simulation approaches this singular situation, the amplitudes $t_j$ and $r_j$ will diff --git a/Doc/DevRef/Polarized.tex b/Doc/DevRef/Polarized.tex index 4a31ddd7e5a..4ee6ae53af6 100644 --- a/Doc/DevRef/Polarized.tex +++ b/Doc/DevRef/Polarized.tex @@ -278,11 +278,11 @@ $\d \Psi_m/\d z \left(z_m\right) = \d \Psi_{m+1}/\d z \left(z_m\right)$ \\ p_m \exp{i \varphi_m} t_m - p_m \exp{-i \varphi_m} r_m &= p_{m+1} t_{m+1} - p_{m+1} r_{m+1} \label{eq:boundary2} \end{align} -By multiplying \eqref{eq:boundary2} from the left with $p_m^{-1}$, we find +By multiplying \cref{eq:boundary2} from the left with $p_m^{-1}$, we find \begin{align} \exp{i \varphi_m} t_m - \exp{-i \varphi_m} r_m &= p_m^{-1} p_{m+1} t_{m+1} - p_m^{-1} p_{m+1} r_{m+1} \label{eq:boundary2b} \,. \end{align} -Now from taking \eqref{eq:boundary1} + \eqref{eq:boundary2b} and \eqref{eq:boundary1} - \eqref{eq:boundary2b}, we find +Now from taking \cref{eq:boundary1} + \cref{eq:boundary2b} and \cref{eq:boundary1} - \cref{eq:boundary2b}, we find \begin{align} 2 \exp{i \varphi_m} t_m &= \left(1 + p_m^{-1} p_{m+1}\right) t_{m+1} + \left( 1 - p_m^{-1} p_{m+1} \right) r_{m+1} \\ @@ -300,7 +300,7 @@ t_m \\ r_m \left( 1 - p_m^{-1} p_{m+1} \right) t_{m+1} + \left( 1 + p_m^{-1} p_{m+1} \right) r_{m+1} \end{pmatrix} \,. \end{align} -This is the desired representation of the transfer matrix given in equations \eqref{eq:interface_transfer_matrix}. +This is the desired representation of the transfer matrix given in equations \cref{eq:interface_transfer_matrix}. \subsection{Parratt Formalism} @@ -353,12 +353,12 @@ and the Pauli vector~$\Pauli$. Spinors, like the field $\U{\Phi}(z)$, shall be underlined; $2\times2$ matrices that operate on spinors are underlined twice. -We redefine the vertical wave number $\kappa$, introduced in \eqref{Ekperp}, +We redefine the vertical wave number $\kappa$, introduced in \cref{Ekperp}, to account only for the nuclear potential, \begin{equation}\label{EkperpP} \kappa^2(z) \coloneqq k_\perp^2(z) \coloneqq K^2 - k_\parallel^2 -4\pi\overline{v}_\nucl(z), \end{equation} -whereas the wave equation \eqref{Ewz} shall be replaced by +whereas the wave equation \cref{Ewz} shall be replaced by \begin{equation}\label{EwzP} \Big( \partial_z^2 + \UU{p}^2(z) \Big) \U\Phi(z) = 0 \end{equation} @@ -390,7 +390,7 @@ For future reference, we note the inverse operator\footnote We consider a stratified sample where both $\overline{v}_\nucl(z)$ and $\v{B}(\r)$ are constant within one layer. -The vertical wavefunction is then given by the spinor analog of \eqref{Eupdn}. +The vertical wavefunction is then given by the spinor analog of \cref{Eupdn}. Within layer~$j$, the wavefunction is \begin{equation}\label{EPhijP} \U{\Phi_j}(z) @@ -398,15 +398,15 @@ Within layer~$j$, the wavefunction is \end{equation} with constant spinors $\U{t_j}$, $\U{r_j}$. The continuity conditions at the interface of layers -$a$ and $b\coloneqq a+1$ are analog to \eqref{Econtcond}. -In full analogy with~\eqref{EcMcP}, they can be resolved as +$a$ and $b\coloneqq a+1$ are analog to \cref{Econtcond}. +In full analogy with~\cref{EcMcP}, they can be resolved as \begin{equation}\label{EcMcP} \begin{pmatrix}\U{t_a}\\ \U{r_a}\end{pmatrix} = \WW{M}_{ab} \begin{pmatrix}\U{t_b}\\\U{r_b}\end{pmatrix}. \end{equation} The double wavey underline shall indicate that the transfer matrix is now of dimension $4\times4$. It is made of $2\times2$ blocks that consist of $2\times2$ matrices acting in spin space. -As in \eqref{EMDS}, it can be written as a product +As in \cref{EMDS}, it can be written as a product \begin{equation}\label{EMDSP} \WW{M}_{ab} = \WW{D}_{a}\, \WW{S}_{ab}. @@ -438,7 +438,7 @@ contains the phase-shift matrix \begin{equation}\label{EdeltaP} \UU{\delta_j} \coloneqq \e^{i d_j \UU{p_j}} \end{equation} -that generalizes~\eqref{Edeltaadef}. +that generalizes~\cref{Edeltaadef}. %==================================================================================================% \subsection{Evaluation of the phase factors}\label{Sphase} @@ -447,7 +447,7 @@ that generalizes~\eqref{Edeltaadef}. To make our implementation\footnote {In \T{MatrixRTCoefficients::computeDeltaMatrix}} transparent, let us explain the evaluation of -the phase-shift matrix~\eqref{EdeltaP} in some detail. +the phase-shift matrix~\cref{EdeltaP} in some detail. The matrix $\eB\Pauli$ has the eigenvalues $\pm 1$ and the normalized eigenvectors \begin{equation}\label{Ev1v2} \U{v}_+ = \frac{1}{\sqrt{2(1+\eBcomp_z)}} \begin{pmatrix} @@ -457,7 +457,7 @@ The matrix $\eB\Pauli$ has the eigenvalues $\pm 1$ and the normalized eigenvecto \end{equation} For readability, we have omitted the subscript $\v{B}$ from the components of~$\eB$. The matrix $\UU{p}$ has the eigenvalues $\lambda_\pm$, -and the same eigenvectors~\eqref{Ev1v2} as $\eB\Pauli$. +and the same eigenvectors~\cref{Ev1v2} as $\eB\Pauli$. We introduce the eigenvector matrix \begin{equation} \UU{Q} \coloneqq \left(\U{v}_+, \U{v}_-\right). @@ -467,7 +467,7 @@ Then $\UU{p}$ has the eigenvalue decomposition \UU{p} = \UU{Q} \, \begin{pmatrix}\lambda_+ & 0 \\ 0 & \lambda_-\end{pmatrix} \UU{Q}^\dagger, \end{equation} -and the phase-shift matrix \eqref{EdeltaP} can be written +and the phase-shift matrix \cref{EdeltaP} can be written \begin{equation}\label{EdP2} \UU\delta = @@ -475,7 +475,7 @@ and the phase-shift matrix \eqref{EdeltaP} can be written \end{equation} In the case $\v{B} = 0$, we have $\lambda_+=\lambda_-$, -which has for consequence that \eqref{EdP2} holds for whatever direction vector~$\eB$; +which has for consequence that \cref{EdP2} holds for whatever direction vector~$\eB$; the simplest choice is $\eB(B\!=\!0)\coloneqq\v{\hat z}$ so that $\UU{Q}=\UU{1}$. @@ -491,7 +491,7 @@ Their argument can be further simplified as follows. THE FOLLOWING WAS OUTCOMMENTED: -The homogeneous linear equation~\eqref{EcMcP} can be reorganized as +The homogeneous linear equation~\cref{EcMcP} can be reorganized as \begin{equation}\label{EcWcP} \begin{pmatrix}\U{t_f}\\ \U{r_i}\end{pmatrix} = \WW{W}_{if} \begin{pmatrix}\U{t_i}\\\U{r_f}\end{pmatrix} @@ -503,8 +503,8 @@ we write matrix components as \WW{W} \eqqcolon \begin{pmatrix} \UU{W}^{tt} &\UU{W}^{tr}\\[.2em] \UU{W}^{rt} &\UU{W}^{rr} \end{pmatrix}, \end{equation} -and similarly for matrix $\WW{M}$ of~\eqref{EcMcP}. -Combining \eqref{EcMcP} and~\eqref{EcWcP}, +and similarly for matrix $\WW{M}$ of~\cref{EcMcP}. +Combining \cref{EcMcP} and~\cref{EcWcP}, we can express $\WW{W}$ as function of~$\WW{M}$, \begin{equation}\label{EM2W} \WW{W}\left(\WW{M}\right) @@ -524,16 +524,16 @@ The transfer matrix obeys the recursion \begin{equation} \WW{M}_{0b}=\WW{M}_{0a}\,\WW{M}_{ab}. \end{equation} -With the conversions \eqref{EM2W} and~\eqref{EW2M}, +With the conversions \cref{EM2W} and~\cref{EW2M}, we can derive a recursion for $\WW{W}$: \begin{equation}\label{EWrecu} \WW{W}_{0b}=\WW{W}\left( \WW{M}\left(\WW{W}_{0a}\right)\,\WW{M}_{ab}\right). \end{equation} -Ultimately, we want to apply~\eqref{EcWcP} to layers $i=0$, $f=J$, +Ultimately, we want to apply~\cref{EcWcP} to layers $i=0$, $f=J$, with $\U{r_J}=0$. Therefore, we only need to derive the $tt$ and $rt$ components of~$\WW{W}_{0J}$, whereas the $tr$ and $rr$ components are irrelevant. -It turns out that this also holds for the inner terms of the recursion~\eqref{EWrecu}: +It turns out that this also holds for the inner terms of the recursion~\cref{EWrecu}: we only need the $tt$ and $rt$ components of the intermediate~$\WW{W}_{0a}$. @@ -632,14 +632,14 @@ If we consider the intensities right a the topmost interface of the sample at $z \U{r_0} = \UU{\mathcal{R}} \U{t_0} \,. \end{equation} Therefore, as soon as $\UU{\mathcal{R}}$ is known, it is trivial to perform a calculation for any desired incoming polarization state. -It is clear that \eqref{eq:R-matrix} is a system of two equations with four unknown variables. +It is clear that \cref{eq:R-matrix} is a system of two equations with four unknown variables. Hence if two pairs of incoming and reflected waves $\U{t_0}, \U{r_0}$ and $\U{t_0'}, \U{r_0'}$ are known, the reflection matrix can be determined (if they are linearly independent). Writing these four equations as a matrix \begin{equation} \label{eq:R-matrix2} \left( \U{r_0}, \U{r_0}' \right) = \UU{\mathcal{R}} \left( \U{t_0}, \U{t_0}' \right) \,, \end{equation} one can see that the inversion of this equation becomes trivial if the two incoming waves are chosen such that they are in a $+$ and $-$ polarization state. -If they are chosen differently, inverting equation \eqref{eq:R-matrix2} corresponds to the rotation of the incoming polarization vectors such that they become pure $+$ and $-$ waves. +If they are chosen differently, inverting equation \cref{eq:R-matrix2} corresponds to the rotation of the incoming polarization vectors such that they become pure $+$ and $-$ waves. If we perform polarization analysis, the analyzer will only pass a wave in the $\U{\Phi_f}$ polarization state. @@ -669,7 +669,7 @@ The same holds for non-perfect analyzers, where we call $|\boldsymbol{p}|$ the e \footnote{In PolarizedSpecular, Sec. 5.1, Dmitry claims this treatment of a non-perfect analyzer is not possible and suggests a different treatment. However i (rb) think that his argument is not correct.} -In order to compute the reflection coefficient for a mixed-state beam, equation \eqref{eq:intensity_polarization_analysis} needs to be rewritten in the density matrix formalism +In order to compute the reflection coefficient for a mixed-state beam, equation \cref{eq:intensity_polarization_analysis} needs to be rewritten in the density matrix formalism \begin{equation} \label{eq:intensity_trace} \Braket{ \U{\Phi_i} | \UU{\mathcal{R}}^{\dagger} | \Psi_f } \cdot @@ -681,7 +681,7 @@ In order to compute the reflection coefficient for a mixed-state beam, equation \end{equation} Here Tr denotes trace operation. $\Ket{ \U{\Phi_f}} \Bra{ \U{\Phi_f}}$ and $ \Ket{ \U{\Phi_i}} \Bra{ \U{\Phi_i}}$ are respective outer products for the $\U{\Phi_f}$ and $\U{\Phi_i}$ pure states and coincide with the corresponding density matrices. -To generalize expression \eqref{eq:intensity_trace} to mixed states of the incoming beam and polarization analyzer, one has to replace the explicit outer products with the density matrices $\UU{f_p}$, $\UU{f_a}$ that describe the polarizer and analyzer as defined in \eqref{eq:density_operators}. +To generalize expression \cref{eq:intensity_trace} to mixed states of the incoming beam and polarization analyzer, one has to replace the explicit outer products with the density matrices $\UU{f_p}$, $\UU{f_a}$ that describe the polarizer and analyzer as defined in \cref{eq:density_operators}. This will automatically take into account the averaging over all possible initial and final pure states of the system. Therefore, the final expression for $I_R$ reads \begin{equation} \label{eq:32} @@ -695,7 +695,7 @@ This expression should work for both a perfect and imperfect polarizer and analy It also seems to be consistent with Wildes \cite{Wil99,Wil06}, this paper was recommended as standard reference on this topic by Artur. It needs to be noted that the limit $\left| \vec a \right| = 0$ does not correspond to no polarization analysis (i.e. a very common experiment without polarization analysis). -Instead, if no polarization analysis is performed, writing \eqref{eq:intensity_no_polarization_analysis} in the density matrix formalism yields +Instead, if no polarization analysis is performed, writing \cref{eq:intensity_no_polarization_analysis} in the density matrix formalism yields \begin{equation} I_R = \left| \U{\Phi_r} \right|^2 = \Braket{ \U{\Phi_i} | \UU{\mathcal{R}}^\dagger \UU{\mathcal{R}} | \U{\Phi_i}} = \text{Tr}\left( \UU{f_p} \UU{\mathcal{R}}^\dagger \UU{\mathcal{R}} \right) \,, @@ -720,7 +720,7 @@ We combine the amplitude vectors for $+$ and $-$ polarization into a single matr \UU{R_j} &= \left( \U{r_j}^+, \U{r_j}^-\right) \,, \end{align} where the submatrices $\UU{T_j}$ and $\UU{R_j}$ are of dimension $2 \times 2$. -The recursion equation \eqref{eq:interface_transfer_matrix} can then be written simultaneously for both polarization states as +The recursion equation \cref{eq:interface_transfer_matrix} can then be written simultaneously for both polarization states as \begin{align} \begin{pmatrix} \UU{T_a} \\ \UU{R_a} @@ -742,7 +742,7 @@ Explicitly performing this multiplication yields two matrix recursion equations \\ \UU{R_a} &= \frac{1}{2} \UU{\delta_a} \left( \left(1 - \UU{P_{ab}} \right) \UU{T_{b}} + \left(1 + \UU{P_{ab}} \right) \UU{R_{b}} \right) \end{align} -After every step of the iteration \eqref{eq:total_transfer_matrix}, we want to rotate and normalize the polarization, such that we obtain the bottom boundary condition $\UU{T_a} = \UU{1}$. +After every step of the iteration \cref{eq:total_transfer_matrix}, we want to rotate and normalize the polarization, such that we obtain the bottom boundary condition $\UU{T_a} = \UU{1}$. For this purpose, we define the rotation matrix $\UU{S}$ as \begin{align} \UU{T'_a} &= \UU{T_a} \cdot \UU{S_a} = \UU{1} \,, @@ -784,7 +784,7 @@ Therefore, all rotations of the polarization need to be forward-propagated accor \text{for } & a \geq 1, \text{ where } \prod^{0}_{i = m-1} \UU{S_i} = \UU{S_{a-1}} \UU{S_{a-2}} \cdots \UU{S_0} \end{align} The proof of these relations can be done as follows. -In order to obtain the correct amplitudes in each layer, after every step of the recursion \eqref{eq:primed_recursion} the applied rotation needs to be propagated down through the bottom of the stack according to +In order to obtain the correct amplitudes in each layer, after every step of the recursion \cref{eq:primed_recursion} the applied rotation needs to be propagated down through the bottom of the stack according to \begin{align} & \text{for } m = N - 1 \dots 0 \hspace{2em} \text{\small outer iteration from bottom to top} \\ @@ -801,7 +801,7 @@ In order to obtain the correct amplitudes in each layer, after every step of the \textbf{Remark} -The defined $\UU{R'_m}$ is equal to the $\UU{X_m}$ in the Parratt formalism and equation \eqref{eq:primed_recursion}c is almost identical to the usual recursion in $\UU{X_m}$ \cite{KeRT08,KeRT03}, apart from the treatment of the phase factor. +The defined $\UU{R'_m}$ is equal to the $\UU{X_m}$ in the Parratt formalism and equation \cref{eq:primed_recursion}c is almost identical to the usual recursion in $\UU{X_m}$ \cite{KeRT08,KeRT03}, apart from the treatment of the phase factor. The second recursion equation in \cite{KeRT08,KeRT03} that yields the amplitudes is replaced by storing the intermediate $\UU{S_m}$. \T{Compute::SpecularMagnetic::topLayerR} @@ -942,7 +942,7 @@ This expression is evaluated via the eigenvalue decomposition \UU{Q^\dagger_{a}} \,, \end{align} -where we have defined $\UU{\sigma'_a} = \left(\pi/2\right)^{3/2} \UU{\sigma_a}$ and the transformation matrix $\UU Q$ is the same as in equation \eqref{eq:transformation_matrix_q}. +where we have defined $\UU{\sigma'_a} = \left(\pi/2\right)^{3/2} \UU{\sigma_a}$ and the transformation matrix $\UU Q$ is the same as in equation \cref{eq:transformation_matrix_q}. The case of zero magnetic field $\vec e_b = 0$ needs to be treated separately again, in that case we have \begin{align} @@ -1071,7 +1071,7 @@ This requires the decomposition of \U{\Phi_j}\left( z \right) &= \exp{i \UU{p_a} \left(z - z_{j-1} \right) } \U{t_j} + \exp{-i \UU{p_a} \left(z - z_{j-1} \right) } \U{r_j} \,, \end{align} into its eigenmodes. -In order to achieve this, we again apply the eigenvalue decomposition of $\UU{p_a}$, as it is also used in \eqref{eq:roughness_tanh_eigenvalue_decomposition}, where the transformation matrix is given by \eqref{eq:transformation_matrix_q} and the eigenvalues are of course $\lambda_+$ and $\lambda_-$ and we have +In order to achieve this, we again apply the eigenvalue decomposition of $\UU{p_a}$, as it is also used in \cref{eq:roughness_tanh_eigenvalue_decomposition}, where the transformation matrix is given by \cref{eq:transformation_matrix_q} and the eigenvalues are of course $\lambda_+$ and $\lambda_-$ and we have \begin{align} \exp{i \UU{p_j} z} &= \UU{Q} \cdot \exp {i \Lambda z } \cdot \UU{Q}^\dagger \\ @@ -1157,7 +1157,7 @@ For two layers, consistency between the scalar and polarized computation is chec \subsubsection{Magnetic field in the fronting medium} -As previously described in \cite{MaOB06}, it is reasonable to assume that the incoming beam penetrates the fronting medium of the sample assembly from a side. This results in $k_z$ being preserved even when there is a non-zero magnetic field in the fronting medium. To account for that in the calculations, one needs to replace $k_{0z}^2$ with $k_{0z}^2 + 4 \pi \check{\rho}_{front}$ in equation \eqref{eq:5}, with +As previously described in \cite{MaOB06}, it is reasonable to assume that the incoming beam penetrates the fronting medium of the sample assembly from a side. This results in $k_z$ being preserved even when there is a non-zero magnetic field in the fronting medium. To account for that in the calculations, one needs to replace $k_{0z}^2$ with $k_{0z}^2 + 4 \pi \check{\rho}_{front}$ in equation \cref{eq:5}, with $\check{\rho}_{front}$ being the SLD matrix for the fronting medium. It is also equivalent to subtracting the magnetic field of the fronting medium, $\boldsymbol{B}_{front}$, from the magnetic field of each layer, thus amending $\check{\rho}_{M}$: diff --git a/Doc/DevRef/Roughness.tex b/Doc/DevRef/Roughness.tex index 1cbb8ab7a87..3e211a147f7 100644 --- a/Doc/DevRef/Roughness.tex +++ b/Doc/DevRef/Roughness.tex @@ -52,8 +52,8 @@ Among the SLD profiles that can be solved analytically, the tanh profile is particularly important. A good summary of the solution can be found in Ch.~2.5 of Lekner \cite{Lek16}.\footnote {He credits Eckart (1930) and Epstein (1930) for the solution. -For a short summary, see also \S~25, exercise~3 in \cite{LL3}.} -While Lekner only considers the electromagnetic case with a profile $\epsilon(z)$, +For a short summary, see also \cite[\S~25, exercise~3]{LL3}.} +Whereas Lekner only considers the electromagnetic case with a profile $\epsilon(z)$, we summarize the theory in terms of $\kappa=\epsilon K^2 - k_\parallel^2$. We posit a profile @@ -62,8 +62,8 @@ We posit a profile = \frac{\kappa_a^2+\kappa_b^2}{2} + \frac{\kappa_b^2-\kappa_a^2}{2} \tanh\frac{z}{2\tau}. \end{equation} -In BornAgain, the profile is parameterized by a roughness length~$\sigma$ -that is related to our present parameter~$\tau$ through +The parameter~$\tau$ is related to the roughness length~$\sigma$ of the BornAgain API +through \begin{equation} \pi\tau = \left(\frac{\pi}{2}\right)^{3/2} \sigma. \end{equation} @@ -81,41 +81,55 @@ Here we only note the reflection coefficient \cite[Eq.~2.88]{Lek16} The phase $\varphi$ is a real number as long as $\kappa_a$ and $\kappa_b$ are real. The transmission coefficient $t_{ab}$ is communicated in \cite{AnMR88}. Using various properties of the Gamma and sinh functions, -one can verify flux conservation~\eqref{EConservation}. +one can verify flux conservation~\cref{EConservation}. %==================================================================================================% \subsection{Fresnel coefficients with roughness factor} %==================================================================================================% -In the limit $\tau\to0$, the phase factor $\varphi$ in \eqref{ErTanh} goes to zero. +In the limit $\tau\to0$, the phase factor $\varphi$ in \cref{ErTanh} goes to zero. For simplicity, we let $\varphi=0$ throughout. This approximation is equivalent to an adjustment of the interface position~$z_{ab}$ by an amount that can be expected to be small compared to the interface thickness~$\tau_{ab}$. -To rewrite~\eqref{ErTanh} in a form -inspired by the Fresnel reflection coefficient~\eqref{ErFresnel}, -we will use the identity +%-------------------------------------------------------------------------------- +\begin{figure}[tb] +\includegraphics[width=0.41\textwidth]{fig/funcplot/tanhc.ps} +\hfill +\includegraphics[width=0.41\textwidth]{fig/funcplot/FresnelReductionTanh.ps} +\caption{(a) Function tanhc. (b) Reflectivity reduction factor, +obtained by dividing \cref{ErTanh2} through the Fresnel reflectivity~\cref{EtFresnel}, +as function of $\kappa_a \tau$ for ratios +$\kappa_b / \kappa_a$ of 0.1, 0.2, 0.4, 0.9, 1.1, 2, and~5.} +\label{Ftanhc} +\end{figure} +%-------------------------------------------------------------------------------- + +To rewrite~\cref{ErTanh} in a form +inspired by the Fresnel reflection coefficient~\cref{ErFresnel}, +we use the identity \begin{equation} \frac{\sinh(x - y)}{\sinh(x + y)} = \frac{\sinh x \cosh y - \sinh y \cosh x}{\sinh x \cosh y + \sinh y \cosh x} - = \frac{\tanh y - \tanh x}{\tanh y + \tanh x}. + = \frac{\tanh y - \tanh x}{\tanh y + \tanh x} \end{equation} -We let $x\coloneqq \pi\tau\kappa_a$ and $y\coloneqq \pi\tau\kappa_b$. -We write $\text{tanhc} x \coloneqq (\tanh x)/x$, +with $x\coloneqq \pi\tau\kappa_a$ and $y\coloneqq \pi\tau\kappa_b$. +We write $\text{tanhc}\; x \coloneqq (\tanh x)/x$ (\cref{Ftanhc}a) and define the roughness factor \begin{equation}\label{ERba} -R_{ab} \coloneqq \sqrt{ \frac{\text{tanhc} \pi\tau\kappa_b}{\text{tanhc} \pi\tau\kappa_a } }. +R_{ab} \coloneqq \sqrt{ \frac{\text{tanhc}\; \pi\tau\kappa_b}{\text{tanhc}\; \pi\tau\kappa_a } }. \end{equation} -With all this, \eqref{ErTanh} can be cast as +With all this, \cref{ErTanh} can be cast as \begin{equation}\label{ErTanh2} r_{ab} = \frac{R_{ab}^{-1}\kappa_a - R_{ab} \kappa_b}{R_{ab}^{-1}\kappa_a + R_{ab}\kappa_b}, \end{equation} -which has the form of the Fresnel reflection coefficient~\eqref{ErFresnel}, +which has the form of the Fresnel reflection coefficient~\cref{ErFresnel}, except for the factors $R_{ab}^{-1}$ and $R_{ab}$. -For $\tau\to0$, these factors go to~1 so that \eqref{ErFresnel} is fully recovered. +For $\tau\to0$, these factors go to~1 so that \cref{ErFresnel} is fully recovered +(\cref{Ftanhc}b). Neglecting again the phase factor, we can compute the transmission coefficient -from \eqref{EConservation}. We obtain +from \cref{EConservation}. We obtain \begin{equation}\label{EtTanh2} t_{ab} = \frac{2\kappa_a}{R_{ab}^{-1}\kappa_a + R_{ab}\kappa_b}. \end{equation} @@ -123,10 +137,10 @@ from \eqref{EConservation}. We obtain Tests confirm that flux conservation is fulfilled at machine precision.\footnote {\textbf{TODO:} provide name of tests.} -Eq.~\eqref{ESab2}, +Eq.~\cref{ESab2}, which relates the refraction matrix to transmission and reflection coefficients, -remains valid for our modified coefficients \eqref{ErTanh2} and~\eqref{EtTanh2}. -Accordingly, \eqref{ESab} must be replaced by +remains valid for our modified coefficients \cref{ErTanh2} and~\cref{EtTanh2}. +Accordingly, \cref{ESab} must be replaced by \begin{equation}\label{ESabR} S_{ab} \coloneqq @@ -146,7 +160,7 @@ for the reflection coefficient: \begin{align}\label{ErNC} \tilde r_{ab} &= r_{ab} \, \e^{- 2 k_a k_b \sigma_{ab}^2}, \end{align} -where $r_{ab}$ is the Fresnel reflectivity \eqref{ErFresnel} of a sharp interface. +where $r_{ab}$ is the Fresnel reflectivity \cref{ErFresnel} of a sharp interface. This form can be obtained in various ways, with more or less hand-wavy arguments or approximations. As e.g.\ used by Tolan it can be obtained by averaging the Parrat recursion equations @@ -163,11 +177,11 @@ Currently BornAgain uses \begin{align}\label{EtNC} \tilde t_{ab} &= t_{ab}\, \e^{+\left( k_a - k_b \right)^2 \sigma_{ab}^2/2}, \end{align} -where $t_{ab}$ is the Fresnel coefficient \eqref{EtFresnel}. +where $t_{ab}$ is the Fresnel coefficient \cref{EtFresnel}. This is the result obtained by Tolan \cite[Eq.~2.35]{Tol99}, and is also given by de Boer \cite{BoLe96} as a result from formal perturbation theory in the limit of very small lateral correlation length. -With \eqref{ESab2}, we obtain the refraction matrix +With \cref{ESab2}, we obtain the refraction matrix \begin{align}\label{ESabGibaud} \tilde S_{ab} &= \frac{1}{2\kappa_a} \begin{pmatrix} \left( \kappa_a + \kappa_b \right) \NCm & @@ -180,9 +194,9 @@ which shows that the above is also consistent with \cite[Eq.~3.114]{GiVi09}. However, the total reflected and transmitted flux $\kappa_a|\tilde r_{ab}|^2+\kappa_b|\tilde t_{ab}|^2$, -computed as in \eqref{EConservation}, +computed as in \cref{EConservation}, is \emph{greater} than the incoming flux~$\kappa_a$. -This takes all credibility from \eqref{EtNC} and \eqref{ESabGibaud}. +This takes all credibility from \cref{EtNC} and \cref{ESabGibaud}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Scattering by a rough interface}\label{Sroughscatter} diff --git a/Doc/DevRef/fig/funcplot/FresnelReductionTanh.ps b/Doc/DevRef/fig/funcplot/FresnelReductionTanh.ps new file mode 100644 index 00000000000..36f530807ad --- /dev/null +++ b/Doc/DevRef/fig/funcplot/FresnelReductionTanh.ps @@ -0,0 +1,4935 @@ +%!PS-Adobe-1.0 EPSF-1.0 +%%BoundingBox: 7 602 258 788 +%%Comment: Bounding box extracted by bboxx +%%+: A program by Dov Grobgeld 2003 +%%Comment: Bounding box extracted by bboxx +%%+: A program by Dov Grobgeld 2003 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FRIDA: fast reliable interactive data analysis %% +%% wups18a.ps: graphic macros %% +%% (C) Joachim Wuttke 1990-2018 %% +%% http://www.messen-und-deuten.de/frida %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/WuGdict18a 400 dict def +WuGdict18a begin + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Generic and math operators +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Shortcuts: + +/np { newpath } bind def +/mv { moveto } bind def +/rm { rmoveto } bind def +/rl { rlineto } bind def +/li { lineto } bind def +/cp { closepath } bind def +/st { stroke } bind def +/x { exch } bind def +/gs { gsave } bind def +/gr { grestore } bind def +/G { gsave exec grestore } bind def + +%% Math operators: + +/twopi { 6.2831853072 } def + +/rnd { rand cvr 1 30 bitshift div 2 div 0 max 1 min } def % -> between 0 and 1 + +/min { 2 copy gt { x } if pop } def +/max { 2 copy lt { x } if pop } def + +/tan { dup sin x cos div } def +/cot { dup cos x sin div } def +/pol2xy{ 2 copy cos mul 3 1 roll sin mul } def % r phi | x y + +/eexp { 2.71828 x exp } def % "exp" is x^y, eexp is e^x +/tanh { 2.71828 x 2 copy exp 3 1 roll neg exp 2 copy sub 3 1 roll add div } def + +%% Loop: + +/iterate { % xi yi what dx dy num_repeats | - %% after each repeat, translates by (dx,dy) + gsave + 6 4 roll xym translate % what x_mv y_mv num_repeats + { % what x_mv y_mv + 3 copy + 3 2 roll + exec + xym translate + } repeat + pop pop pop + grestore +} def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Incremental path construction with persistent direction +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/NP { % x y [new path] + gsave translate np 0 0 mv } bind def +/EP { % [end path] + grestore } bind def +/L { % len rel_dir [line] + 90 mul rotate 0 2 copy rl translate } bind def +/A { % radius angle [arc segment] + /IPCa x 90 mul def /IPCr x def + IPCa 0 lt + { + 0 IPCr neg IPCr 90 90 IPCa add arcn + 0 IPCr neg translate IPCa rotate 0 IPCr translate + } { + 0 IPCr IPCr -90 -90 IPCa add arc + 0 IPCr translate IPCa rotate 0 IPCr neg translate + } ifelse + } def +/V { % size [simple arrow] - + gsave /IPCr x def np -.8 IPCr mul .6 IPCr mul mv + 0 0 li -.8 IPCr mul -.6 IPCr mul li st grestore + } def % size [arrow] +/Vc { % size [triangular unfilled arrow] - + gsave /IPCr x def np -.8 IPCr mul .6 IPCr mul mv + 0 0 li -.8 IPCr mul -.6 IPCr mul li cp { white fill } G st grestore + } def % + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Page coordinates +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/pt { .018567 mul} bind def % for line widths and font sizes, reason unclear +/cm {28.346456 mul} bind def % typographic_point -> cm + +/cmtranslate { % x y [] - + cm x cm x translate } bind def + +% Move origin from lower left (PostScript default) to upper left +/setnewpage { % xoff yoff + /yoffnewpage x def + /xoffnewpage x def +} def +/originUpperLeft_A4{ .7 28.3 cmtranslate } bind def +/goffsetA4 { ungscale originUpperLeft_A4 gscale } def +/newpage { + goffsetA4 + xoffnewpage yoffnewpage offset +} def + +% Set absolute global scale and relative symbol size +/defsiz { % size(cm) symbolsize(rel) | - + /ftot x def + /gsiz x cm 10 div def + gscale % within 'size', coordinates run from 0 to 10 + } def +/gscale { + gsiz dup scale + } def +/ungscale { + 1 gsiz div dup scale + } def + +% Symbol (and label?) size as sublinear function of figure size +/autolabel { % size(cm) | symbolsize(rel) + dup 7 div 2 add 4 mul % the simplest sublinear increase + x div % anticipate overall rescaling + } def + +% Aspect ratios +/gyld {0.447214 mul} bind def /Gyld {0.447214 div} bind def % sqrt(5) +/guld {0.547723 mul} bind def /Guld {0.547723 div} bind def % sqrt(3) +/gold {0.618034 mul} bind def /Gold {0.618034 div} bind def % goldener Schnitt +/gild {0.707107 mul} bind def /Gild {0.707107 div} bind def % sqrt(2) : DIN +/geld {0.759836 mul} bind def /Geld {0.759836 div} bind def % sqrt(sqrt(3)) +/gald {0.817765 mul} bind def /Gald {0.817765 div} bind def % sqrt sqrt sqrt 5 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Several frames per page +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/setpagegrid { % ncol nrow xoffnewframe yoffnewframe + /yoffnewframe x def + /xoffnewframe x def + /nrowpage x def + /ncolpage x def +} def +/iFrame 0 def +/nextFrame { + /iFrame iFrame 1 add def + iFrame nrowpage ncolpage mul mod 0 eq { + showpage gscale newpage + } { + iFrame ncolpage mod 0 eq { + xoffnewframe ncolpage 1 sub neg mul yoffnewframe offset + } { + xoffnewframe 0 offset + } ifelse + } ifelse + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Frame coordinates +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/defred { % x_reduction y_reduction label_reduction | - + /fmm x ftot mul def + /ymm x def + /xmm x def + + % conversion frame_coordinate -> global_coord + /xm {xmm mul} bind def + /ym {ymm mul} bind def + /fm {fmm mul} bind def + /xym {ym x xm x} bind def + + % prefer rescaling over explicit conversion (make more use of this !) + /mmscale { xmm ymm scale } bind def + /mmunscale { 1 xmm div 1 ymm div scale } bind def + + % graphic commands in frame coordinates + /offset { xym translate } bind def + /currentxy { currentpoint ymm div x xmm div x } bind def + /setline { pt fm setlinewidth [] 0 setdash } bind def + } def + +/stdred { % x_reduction y_reduction | - + 2 copy mul sqrt defred + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% World (= user application) coordinates +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/xSetCoord { % log min max | - + /wxmax x def + /wxmin x def + /wxlog x 0 eq not def + /wxdel wxmax wxmin wxlog { div log } { sub } ifelse def + /wxd { % dx(world) | dx(frame) + wxlog { log } if wxdel div 10 mul + } bind def + /wx { % x(world) | x(frame) + wxmin wxlog { div } { sub } ifelse + wxd + } bind def + } def +/ySetCoord { % log min max | - + /wymax x def + /wymin x def + /wylog x 0 eq not def + /wydel wymax wymin wylog { div log } { sub } ifelse def + /wyd { % dy(world) | dy(frame) + wylog { log } if wydel div 10 mul + } bind def + /wy { % y(world) | y(frame) + wymin wylog { div } { sub } ifelse + wyd + } bind def + } def +/hSetCoord { % log min max | - % for use in 2D plot + /whmax x def + /whmin x def + /whlog x 0 eq not def + /wH { % h(world) | h(col) + dup whmin lt { + pop -1 + } { + dup whmax gt { + pop 11 + } { + wh + } ifelse + } ifelse + } bind def + whlog { + /whdel whmax whmin div log def + /wh { whmin div log whdel div 10 mul } bind def % h(world) | h(col) + } { + /whdel whmax whmin sub def + /wh { whmin sub whdel div 10 mul } bind def % h(world) | h(col) + } ifelse + } def + +% pair conversion +/wxy { % x,y(world) -> x,y(frame) + wy x wx x + } def + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Colors %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Color operators: + +/setRGBcolor { + 3 { 255 div 3 1 roll } repeat setrgbcolor + } def + +/colormix { % weight(0..1) col1(R|G|B) col2(R|G|B) | col(R|G|B) + 7 -1 roll dup /weightA x def /weightB x 1 x sub def + 4 -1 roll weightA mul x weightB mul add 5 1 roll + 3 -1 roll weightA mul x weightB mul add 4 1 roll + 2 -1 roll weightA mul x weightB mul add 3 1 roll + } def + +/relcol { % i_col n_col | rel(0..1) : for one-dimensional choices + 1 sub div 0 max 1 min + } def + +%% Named colors: + +/black { 0 setgray } bind def +/white { 1 setgray } bind def + +/red { 255 0 0 setRGBcolor } bind def + +/siemensorange { 255 153 0 setRGBcolor } bind def +/siemensblue { 0 102 153 setRGBcolor } bind def +/siemenstext { 0 51 102 setRGBcolor } bind def +/siemensred { 165 0 33 setRGBcolor } bind def +/siemenspink { 221 102 102 setRGBcolor } bind def +/siemensgrey { 221 221 221 setRGBcolor } bind def +/siemensdark { 102 102 102 setRGBcolor } bind def +/siemensgreen { 33 153 102 setRGBcolor } bind def +/siemensyellow { 255 221 0 setRGBcolor } bind def + + +%% One-dimensional linear color choices: + +/iCol1 { % i i_max | - : default -2010, round the circle, RGBR + relcol dup 1 x % rel 1 rel + 360 mul 255 add cos 1 add dup mul neg .053 mul 1 add % modulate saturation + sethsbcolor + } def +/iCol2 { % i i_max | - : cyan - yellow - magenta + relcol 3 mul + dup 1 le { + dup 1 sub neg 0 3 2 roll } { + dup 2 le { + 1 sub dup 1 sub neg 0 3 1 roll } { + 2 sub dup 1 sub neg 0 3 0 roll } ifelse + } ifelse + 0 setcmykcolor + } def +/iCol3 { % i i_max | - : siemens + div /icnow x def + 165 1 icnow sub mul + 102 icnow mul + 33 120 icnow mul add setRGBcolor + } def +/iCol4 { % i i_max | - : red to blue (subsequence of old scheme iCol1) + relcol + 3 x sub 3 div 1 iCol1 + } def + + +%% One-dimensional color choice from given array: + +/iColA { % i i_max arr | - + /aCol x def + relcol + aCol length 1 sub mul % position within array + dup cvi dup 3 1 roll % idx pos idx + sub x % offset idx + 0 max aCol length 1 sub min % offset safe_idx + dup 1 add aCol length 1 sub min % offset i i+1 + aCol x get exec + 4 3 roll aCol x get exec colormix setRGBcolor + } def + +%% ditto with discontinuous values for h<0 and h>1 + +/iColAA { % i i_max arr {low_col} {hig_col} | - + 5 3 roll + div + dup 0 lt { + pop pop x pop exec + } { + dup 1 gt { + pop 3 1 roll pop pop exec + } { + 1 % arr {l} {h} i i_max + 5 2 roll pop pop + x 1 add x % ad-hoc correction for legacy definition of relcol + iColA + } ifelse + } ifelse + } def + +%% Color arrays for non-linear one-dimensional choices: + +/aCol1 [ % red-blue + { 255 0 0 } % 1 + { 240 10 10 } % 2 + { 220 40 40 } % 3 + { 205 65 90 } % 4 + { 195 80 130 } % 5 + { 180 110 180 } % 6 + { 165 120 185 } % 7 + { 150 130 190 } % 8 + { 130 150 210 } % 9 + { 110 125 220 } % 10 + { 85 105 230 } % 11 + { 70 90 255 } % 12 + { 0 0 255 } % 13 + ] def +/aCol2 [ % orange-red-blue-darkblue + { 255 180 0 } + { 255 160 0 } + { 255 120 0 } + { 255 70 0 } + { 255 0 0 } + { 220 30 30 } + { 220 70 60 } + { 220 100 110 } + { 200 130 130 } + { 200 130 160 } + { 180 110 180 } + { 165 110 185 } + { 150 130 190 } + { 130 150 210 } + { 100 120 220 } + { 85 105 230 } + { 70 90 255 } + { 0 0 255 } + { 0 0 180 } + { 10 10 150 } + { 30 30 130 } + ] def +/aCol3 [ % [fixed size: max_i=8] siemenscolors + { 165 0 33 } % siemensred + { 33 153 102 } % siemensgreen + { 0 102 153 } % siemensblue + { 0 51 102 } % siemenstext + { 255 153 0 } % siemensorange + { 102 102 102 } % siemensdark + { 255 221 0 } % siemensyellow + { 221 221 221 } % siemensgrey + { 221 102 102 } % siemenspink + ] def +/aCol4 [ % green-blue-brown + { 120 160 60 } + { 90 185 40 } + { 50 215 20 } + { 0 245 0 } + { 10 235 112 } + { 20 235 143 } + { 30 230 173 } + { 40 225 194 } + { 50 205 215 } + { 40 153 204 } + { 40 102 153 } + { 40 82 122 } + { 90 74 101 } + { 140 68 80 } + { 170 59 60 } + { 190 50 40 } + { 180 65 40 } + { 160 80 40 } + { 140 100 40 } + { 120 80 30 } + { 100 60 20 } + ] def +/aCol5 [ % [fixed size: max_i=7] old gnuplot default (see man gnuplot and rgb.txt) + { 255 0 0 } % red + { 0 255 0 } % green + { 0 0 255 } % blue + { 255 0 255 } % magenta + { 0 255 255 } % cyan + { 160 82 45 } % sienna + { 255 165 0 } % orange + { 255 127 80 } % coral + ] def +/aCol6 [ % heat plot + { 100 0 100 } % violet + { 60 30 130 } % dark blue + { 30 50 220 } % blue + { 50 150 100 } % green + { 150 200 100 } % green + { 215 255 50 } % green/yellow + { 255 255 0 } % yellow + { 255 125 0 } % orange + { 255 0 0 } % red + ] def +/aCol7 [ % [fixed size: max_i=8] default colors, modified from old gnuplot + { 80 80 255 } % blue + { 255 0 0 } % red + { 0 160 0 } % dark green + { 255 0 255 } % magenta + { 0 160 192 } % dark cyan + { 160 82 45 } % sienna + { 255 165 0 } % orange + { 255 127 80 } % coral + { 64 224 32 } % light greenish + ] def +/aCol8 [ % matplotlib's viridis: blue - green -yellow + { 64 0 79 } + { 72 36 117 } + { 65 68 135 } + { 53 95 141 } + { 42 120 142 } + { 33 145 140 } + { 34 168 132 } + { 68 191 112 } + { 122 209 81 } + { 189 223 38 } + { 239 218 34 } + ] def +/aCol9 [ % matplotlib's inferno: black - violet - red - orange - yellow + { 0 0 0 } + { 27 12 65 } + { 74 12 107 } + { 120 28 109 } + { 165 44 96 } + { 207 68 70 } + { 237 105 37 } + { 251 155 6 } + { 247 209 61 } + { 252 255 164 } + ] def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Fonts +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% extend font encoding +/ReEncode { % OldFont NewFont Encoding | - + /MyEncoding x def + x findfont % select OldFont + dup length dict begin + {def} forall + /Encoding MyEncoding def + currentdict + end + definefont pop % define as NewFont + } def + +% we assume that image scripts are Latin1 encoded +/Helvetica /MyFont ISOLatin1Encoding ReEncode +/Helvetica-Oblique /MyFont-Oblique ISOLatin1Encoding ReEncode +/Helvetica-Bold /MyFont-Bold ISOLatin1Encoding ReEncode +/Helvetica-BoldOblique /MyFont-BoldOblique ISOLatin1Encoding ReEncode + +/setPalatino { + /Palatino /MyFont ISOLatin1Encoding ReEncode + /Palatino-Italic /MyFont-Oblique ISOLatin1Encoding ReEncode + /Palatino-Bold /MyFont-Bold ISOLatin1Encoding ReEncode + /Palatino-BoldItalic /MyFont-BoldOblique ISOLatin1Encoding ReEncode + } def + +%% Preset standard styles: + +% scale and set font; define fontsize, fontheight +/setfontandsize { % font size | - + dup 0 le { pop 100 } if % fontsize <= 0 not allowed ! + /fontnonnil true def + pt fm dup /fontsize x def + x findfont + x scalefont + setfont + gsave % determine fontheight - from the cookbook : + np 0 0 mv (W) true charpath flattenpath + pathbbox % low_left_x, low_left_y, up_right_x, up_right_y + /fontheight x def + /fontwidth x def + pop pop + grestore + } def + +% standard settings for labelling axes +/numlabcol { black } def +/setnum { /MyFont 24 setfontandsize numlabcol } def +/setlab { /MyFont 24 setfontandsize numlabcol } def + +% user commands (free choice of fontsize, but fixed font family) +/setown { /MyFont x setfontandsize } def +/setbol { /MyFont-Bold x setfontandsize } def +/setboq { /MyFont-BoldOblique x setfontandsize } def +/setobl { /MyFont-Oblique x setfontandsize } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Text blocks +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/showif { % string | - : increment xwidth or plot string + prepare + { stringwidth pop xwidth add /xwidth x def } + { show } + ifelse + } def +/script { % matrix relpos_y | - + /yoffset x fontheight mul def + currentfont x makefont setfont + 0 yoffset rm + } def +/scred .71 def +/subsc { + showif + [scred 0 0 scred 0 0] -.2 script + } def +/supsc { + showif + [scred 0 0 scred 0 0] .6 script + } def +/endsc { + showif + regularfont setfont + 0 yoffset neg rm + } def +/grec { + showif + /Symbol findfont fontsize scalefont setfont + } def +/endgr { + showif + regularfont setfont + } def +/endall { + showif + regularfont setfont + } def +/build { % string xrel yrel obj | - : plot obj above/below string + /obj x def /yrelbui x def /xrelbui x def + dup showif + prepare + { pop } + { stringwidth pop xrelbui neg mul fontheight yrelbui mul % relpos for obj + currentpoint 4 2 roll % save position after string + rm obj pop % obj must end with () that will be pop'ed + mv % back to saved position + } + ifelse + } def +/gbuild { % string xrel yrel obj | - : plot obj above/below string + /obj x def /yrelbui x def /xrelbui x def + /Symbol findfont fontsize scalefont setfont + dup showif + prepare + { pop regularfont setfont } + { stringwidth pop xrelbui neg mul fontheight yrelbui mul % relpos for obj + currentpoint 4 2 roll % save position after string + regularfont setfont + rm obj pop % obj must end with () that will be pop'ed + mv % back to saved position + } + ifelse + } def +/hut { % ..) (<Char>) hut (.. %%% MISERABEL PROGRAMMIERT + x showif + 1.4 .6 {(\136) show ()} build + } def +/ghut { % ..) (<grec-Char>) ghut (.. %%% BREITE PASST NUR FUER Phi(t) + x showif + .8 .65 {(\136) show ()} gbuild + } def +/tilde { + x showif + 1. .6 {(~) show ()} build + } def +/gtilde { + x showif + 1. .6 {(~) show ()} gbuild + } def +/spce { % string n spce - ; insert n times ( ) + {showif ( )} repeat + } def + +% the following macros use the symbol/curve plotting mechanism +/pins { % string symins - ; symbol must be selected by pset + showif + ( ) showif ( ) .5 .5 { currentxy 0 p black ()} build ( ) showif + } def +/clenins { % string len clenins - ; curve must be selected by cset + x showif % I suppose that pins is preceeded by 8 spaces + dup ( ) stringwidth pop mul 2 add /xstrich x xmm div def + % length of inserted curve : + % -1 space : curve begins and ends in middle of ( ) + % +3 spaces: pins requires 3 times ( ) + ( ) 0 .5 { currentxy currentxy 0 ci x xstrich add x 0 cf () } build + 2 add {( ) showif} repeat + } def +/cins { % string symins - ; curve must be selected by cset + showif 8 % I suppose that pins is preceeded by 8 spaces + dup ( ) stringwidth pop mul 2 add /xstrich x xmm div 10 div def + % nov03, ohne zu verstehen, "10 div" eingefuegt + % length of inserted curve : + % -1 space : curve begins and ends in middle of ( ) + % +3 spaces: pins requires 3 times ( ) + ( ) 0 .5 { currentxy currentxy 0 ci x xstrich add x 0 cf () } build + 2 add {( ) showif} repeat + } def + +/block { % x y ob xrel yrel | - + /yrel x def /xrel x def /blabla x def + /ypos x ym def /xpos x xm def + /regularfont currentfont def /yoffset 0 def % initialize for security + /prepare true def /xwidth 0 def 0 0 mv % to prevent empty-path-error + blabla endall % first pass : determine xwidth + boxif { /boxwidth xwidth (M) stringwidth pop boxxr mul 2 mul add def + /boxheight fontheight 1 boxyr 2 mul add mul def + np xpos xwidth xrel mul sub boxwidth xwidth sub 2 div sub + ypos fontheight .5 boxyr add mul sub mv + boxwidth 0 rl 0 boxheight rl boxwidth neg 0 rl cp + boxproc + } if + xpos xwidth xrel mul sub ypos fontheight yrel mul sub mv + /prepare false def + blabla endall % second pass : plot + /boxif false def + } def +/rblock { % x y ang ob proc rblock - + 5 3 roll + gsave + xym translate + 3 2 roll rotate + 0 0 4 2 roll exec + grestore + } def + +/Box { % x y {exe} + /boxif true def + /boxproc x def /boxyr x def /boxxr x def + } def +/nBox { .6 .6 3 2 roll Box } def +/boxif false def +/textW { % obj | length : calculate only length. + /blabla x def + /regularfont currentfont def /yoffset 0 def % initialize for security + /prepare true def /xwidth 0 def 0 0 mv % to prevent empty-path-error + blabla endall + xwidth % has been determined + } def +/textw { % obj | y : dito, in 0..10-units + textW xmm div + } def + +% horizontal text: x y ob | - +/textLB { 0. 0. block } bind def +/textCB { .5 0. block } bind def +/textRB { 1. 0. block } bind def +/textLM { 0. .5 block } bind def +/textCM { .5 .5 block } bind def +/textRM { 1. .5 block } bind def +/textLT { 0. 1. block } bind def +/textCT { .5 1. block } bind def +/textRT { 1. 1. block } bind def + +% rotated text: x y ang ob | - +/rtextLB { {textLB} rblock } bind def +/rtextLM { {textLM} rblock } bind def +/rtextRB { {textRB} rblock } bind def +/rtextRM { {textRM} rblock } bind def +/rtextCM { {textCM} rblock } bind def + +%% Language selection: + +% preset +/language { % choose_this of_so_many | - % select current language + /langMax x def + /langChc x def + } def +1 1 language % default +% choose text from sequence +/langSel { % text_1 .. text_M | text_C : choose text, M=langMax, C=langChc + langMax dup langChc sub 1 add roll + langMax 1 sub { pop } repeat + } def + +%% Text composition shortcuts: + +/g { x grec endgr} bind def +/sb { x subsc endsc} bind def +/sp { x supsc endsc} bind def +/sbgr { x grec () subsc endsc () endgr} bind def +/spgr { x grec () supsc endsc () endgr} bind def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Coordinate Frame %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Layout presets: + +/xyTicLen {0.10 fm} def +/xyTacLen {0.20 fm} def +/txllen {0.20 fm} def +/tyllen {0.20 fm} def +/linsetAxx {black 0.7 setline} def +/linsetTic {black 0.7 setline} def +/linsetTac {black 0.7 setline} def +/linsetGri {black 0.4 setline} def + +%% Start-up commands: + +/Resets { + /yNumLengthL 0 def /yNumLengthH 0 def + /xNumHeightL .3 def /xNumHeightH 0 def + /xNumHeightRel 2.4 def + /aMean 5 def + black + } def +/BoxBackground { + 0 10 0 10 rect gsave setboxbackgroundcolor fill grestore +} def +/setboxbackgroundcolor { white } def + +/zValues { pop pop } def +/whiteframe { 1 0 0 10 10 graybox } def + +/abc {abclab setown abcx abcy 3 2 roll textCM} def % usage ((a)) abc +/abcset { % x y siz abcset - : preset for abc + /abclab x def /abcy x def /abcx x def + } def + +%% Ticks: + +% set tick array - internal macros +/tiputs { % rel_pos_of_tick | pos_of_tick : innermost routine for /taproc + tastep mul taloop add + } def +/taproclin { % (#tick/tack) | - : define /taproc for use in SetVec + 1 x div /tistep x def + /taproc { 0 tistep .999 { tiputs } for } def + } def +/taproclog { % (#ticks/tacks) | - : define /taproc for use in SetVec + dup 3 gt { pop /taproc { 1 1 9 { log tiputs } for } def + }{ dup 1 gt { pop /taproc { 0 tiputs 2 log tiputs 5 log tiputs } def + }{ dup 0 gt { pop /taproc { 0 tiputs } def + }{ neg taproclin + } ifelse } ifelse } ifelse + } def +/SetVec { % tafro tatoo nta /vector | - : set /vector + 4 1 roll + /nta x def /tatoo x def /tafro x def + /tastep tatoo tafro sub nta 1 sub div def + [ + 0 1 nta { + tastep mul tafro add /taloop x def + taproc exec + } for + ] def + } def +% set tick array - user commands +/SetTicVecLin { taproclin /TicVec SetVec } def +/SetTicVecLog { taproclog /TicVec SetVec } def + +% set tack-and-number array +/SetTacVec { % [ pos {label} pos {label} ... ] | - + /TacVec x def + } def + +% define axes + % note on angles : 0 = x-axis, 90 = y-axis +/OneAxx { % fro to xpos ypos aang tang | - : presets for Axx, Tic, Tac, Num + % store arguments + /tAng x def /aAng x def + /yPos x def /xPos x def + /aTo x def /aFro x def + % set constants + /xTicLen tAng cos xyTicLen mul def /yTicLen tAng sin xyTicLen mul def + /xTacLen tAng cos xyTacLen mul def /yTacLen tAng sin xyTacLen mul def + /xAng aAng cos def /yAng aAng sin def + /aMean aFro aTo add 2 div def + } def + +% draw axis (with parameters preset by OneAxx or ArrAxx) +/Axx { % - | - + linsetAxx + gsave + xPos yPos offset + mmscale + aAng rotate + % draw a line + aFro 0 np mv + aTo 0 li st + grestore + } def + +% draw ticks (positions given by SetTicVec, parameters preset by OneAxx/..) +/Tic { % - | - : draw tick as defined in TicProc + linsetTic + TicVec { + dup dup aFro lt x aTo gt or {pop} {TicProc} ifelse + } forall + } def +/TicProc { % aPos | - : default procedure to plot one tick + np + xPos yPos xym mv + dup xAng mul x yAng mul xym rm % eat argument, go to start pos. + xTicLen yTicLen rl st + } def +/xGric { % yFro yTo | - : draw a grid line (instead of an x tick) + linsetGri + TicVec { + 3 copy dup 5 -1 roll aFro lt x aTo gt or {pop pop pop} { + dup % y1 y2 x x + 4 -1 roll xym np mv % y2 x + x xym li st + } ifelse + } forall + pop pop + } def +/yGric { % xFro xTo | - : draw a grid line (instead of an y tick) + linsetGri + TicVec { + 3 copy dup 5 -1 roll aFro lt x aTo gt or {pop pop pop} { + dup % x1 x2 y y + 4 -1 roll x xym np mv % x2 y + xym li st + } ifelse + } forall + pop pop + } def + +% draw tacks (positions given by SetTacVec, parameters preset by OneAxx/..) +/TacExe { % Proc | - % Execute Proc for all pairs of elements of TacVec + % (but only if inside aFro..aTo) + /TacProc x def + /ispair true def % toggle: take pos, take label, take pos, take label ... + TacVec { + ispair + { + /aPos x def + /ispair false def + } { + aPos dup aFro lt x aTo gt or + {pop} {TacProc} ifelse + /ispair true def + } ifelse + } forall + } def +/Tac { + linsetTac + { pop xPos yPos xym mv + aPos dup xAng mul x yAng mul xym rm + xTacLen yTacLen rl st + } TacExe + } def +% special tack routines, only for rectangular axes +/xTacC { % : centered tack on x axis + linsetTac + { pop aPos xm yPos ym txllen 2 div sub np mv 0 txllen rl st } TacExe + } def +/xGrid { % : rule instead of tack on x axis + linsetTac + { pop aPos xm np yPos ym mv 0 10 xym rl st } TacExe + } def +/yTacC { % : centered tack on y axis + linsetTac + { pop xPos xm tyllen 2 div sub aPos ym np mv tyllen 0 rl st } TacExe + } def +/yGrid { % : rule instead of tack on low y axis + linsetTac + { pop aPos ym np xPos xm x mv 10 0 xym rl st } TacExe + } def + +% draw numbers (pos-txt pairs given by SetTacVec) +/Num { % Generic but useless. Adjust for your application. + setnum + fontheight ymm div yDisRel mul tAng sin mul /yDist x def + { dup textW xDisRel mul tAng cos mul /xDist x def + xPos aPos xAng mul add xDist sub + yPos aPos yAng mul add yDist sub 3 2 roll textCM + } TacExe + } def +/setnumDisRel { % xDisRel yDisRel | - : adjust just a little bit + /yDisRel x def /xDisRel x def + } def +1.2 1.2 setnumDisRel % default setting +% explicit Num routines for rectangular case +/xNumL { % : numbers on low x axis + setnum + { fontheight ymm div % conversion -> user_scale + dup /xNumHeightL x def + -.6 mul yPos add aPos x 3 2 roll textCT + } TacExe + } def +/xNumH { % : numbers on high x axis + setnum + { fontheight ymm div % conversion -> user_scale + dup /xNumHeightH x def + .6 mul yPos add aPos x 3 2 roll textCB + } TacExe + } def +/yNumL { % : numbers on low y axis + setnum + { fontsize -.3 mul xmm div xPos add aPos 3 2 roll textRM + xwidth dup yNumLengthL gt {/yNumLengthL x def} {pop} ifelse + } TacExe + } def +/yNumLD { % : calculate only yNumLength (used for adjustement) + setnum + { textW dup yNumLengthL gt {/yNumLengthL x def} {pop} ifelse + } TacExe + } def +/yDumL { % {(..)} yDumL : compare yNumLength with one arg (used for adjustement) + setnum + textW dup yNumLengthL gt {/yNumLengthL x def} {pop} ifelse + } def +/yNumH { % : numbers on high y axis + setnum + { fontsize .3 mul xmm div xPos add aPos 3 2 roll textLM + xwidth dup yNumLengthH gt {/yNumLengthH x def} {pop} ifelse + } TacExe + } def +/yNumHD { % : calculate only yNumLength (used for adjustement) + setnum + {textW dup yNumLengthH gt {/yNumLengthH x def} {pop} ifelse + } TacExe + } def +/yDumH { % {(..)} yDumH : compare yNumLength with one arg (used for adjustement) + setnum + textW dup yNumLengthH gt {/yNumLengthH x def} {pop} ifelse + } def + +% draw labels +/xCL { % xlabel | - ; plots coordinate name below the x-axis. + setlab + aMean xNumHeightL xNumHeightRel neg mul + 3 -1 roll textCT + } def +/xCH { % xlabel | - ; plots coordinate name above the x-axis. + setlab + aMean xNumHeightH xNumHeightRel mul 10 add + 3 -1 roll textCB + } def +/yCL { % ylabel | - ; plots coordinate name to the left of the y-axis. + gsave + setlab + yNumLengthL neg fontsize -.85 mul add % yNumLengthL calculated in yN + aMean ym translate + 0 0 mv + 90 rotate + 0 x 0 x textCB + grestore + } def +/YCH { % ylabel xpos | - ; plots coordinate name to the right of a vertical axis + gsave + setlab + yNumLengthH fontsize .85 mul add x xm add + aMean ym translate + 0 0 mv + 90 rotate + 0 x 0 x textCT + grestore + } def +/yCH { 10 YCH } def % ylabel | - ; plots coordinate name to the right of the y-axis. +/yCF { % ylabel | - ; plots coordinate name *falling* right of the y-axis. + gsave + setlab + yNumLengthH fontsize .85 mul add 10 xm add + aMEan ym translate + 0 0 mv + -90 rotate + 0 x 0 x textCB + grestore + } def + +/knautschy { % x0 y0 y_knau y_tot knautschy - : insert an S in dived y-axis + % the total height of the generated object is y_tot + % of which y_knau(.le. y_tot) is for the real knautsch, + % the remainder is for vertical prolongations. + x ym 4 div dup /tmpy x def 5 sqrt mul /tmpx x def + /tmpa x ym tmpy 4 mul sub 2 div def + np ym x xm x mv 0 tmpa rl tmpx tmpy rl tmpx -2 mul tmpy 2 mul rl + tmpx tmpy rl 0 tmpa rl st + } def +/separy { % x0 y0 sep lng ang lin - : insert an // in dived y-axis + setline + /spang x def + /splng x def + /spsep x def + 2 copy spsep sub gsave offset spang rotate + splng -.5 mul fm 0 np mv splng fm 0 rl st grestore + spsep add gsave offset spang rotate + splng -.5 mul fm 0 np mv splng fm 0 rl st grestore + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Data Plotting (Symbols and Curves) %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Initializations: + +% asymmetric error bars? +/err_asy false def % overwrite this if data are quadruples x y d- d+ + +%% Presets: + +% global preset +/SymGSet { % sradglo slinglo serrglo | - + /serrglo x def % plot error bars? 0=never, 1=always, 2=as_given_in_pset + /slinglo x def % symbol linewidth multiplier + /sradglo x def % symbol size multiplier + } def + +%% Retrieve presets from style array: + +/pstyle { pStyles setstyle } def +/cstyle { cStyles setstyle } def +/setstyle { % chosen_number array | - : set p or c as predefined in array. + dup length % i A n + 3 2 roll % A n i + dup 0 le { + pop pop pop ostyle % chosen_number<=0 means: don't plot + } { + 1 sub x % A i-1 n + mod get % A(i-1) + exec + } ifelse + } def + +%% Set plot symbol: + +/pset { % styp sfill serr srad slin | - + % arg -> symbol linewidth + /slin x slinglo mul def + % arg -> symbol size + /srad x fm 0.16 mul sradglo mul def + % arg -> plot error bar? + 2 serrglo ne { pop serrglo } if % if (serrglo=2) use serr else use serrglo + /plot_errorbar x 1 eq { { errorbar } } { { pop pop pop pop } } ifelse def + % arg -> fill the symbol? (0=open, 1=full, 2=colored_with_black_border) + /sfill x def + % adjust srad: it's the _outer_ radius + % TROUBLE sfill 1 ne {/srad srad slin fm pt sub def} if + % arg -> symbol type + /ps {ps_nil} def % default: don't plot (maybe we only want an error bar) + dup 1 eq {/ps {ps_square} def} if + dup 2 eq {/ps {ps_diamond} def} if + dup 3 eq {/ps {ps_circle} def} if + dup 4 eq {/ps {ps_triangle} def} if + dup 5 eq {/ps {ps_cedez} def} if + dup 6 eq {/ps {ps_eieruhr} def} if + dup 7 eq {/ps {ps_valve} def} if + dup 8 eq {/ps {ps_tfwd} def} if + dup 9 eq {/ps {ps_tbwd} def} if + dup 10 eq {/ps {ps_pentagram} def} if + dup 11 eq {/ps {ps_plus} def} if + dup 12 eq {/ps {ps_cross} def} if + dup 13 eq {/ps {ps_star} def} if + dup 14 eq {/ps {ps_pentagon} def} if + dup 15 eq {/ps {ps_horiz} def} if + dup 16 eq {/ps {ps_verti} def} if + pop + % + /t { % x y d[- d+] | - : plot a symbol and eventually an error bar. + err_asy not { dup } if + 4 copy pop pop plot_symbol + plot_errorbar + } bind def + /ti { t } bind def + /tf { t black } bind def + } def + +%% Set curve: + +/lset { % lwidth dashes | - + 0 setdash + dup 0 gt { + pt fm setlinewidth + % pop error bar and convert frame coord -> paper coord + /txy { err_asy { pop } if pop xym } def % x y d[- d+] | x' y' + % commands to plot points (can be overwritten by nopoints): + /ti { np txy mv } def % x y d[- d+] | - : start curve + /t { txy li } def % x y d[- d+] | - : continue curve + /tf { txy li st } def % x y d[- d+] | - : terminate and plot curve + } { + ostyle + } ifelse + } def + +%% Plot nothing: + +/ostyle { % - | - + /ti { nopoint } def + /t { nopoint } def + /tf { nopoint } def +} def +/nopoint { % x y d[- d+] | - + pop pop pop err_asy { pop } if +} def + +%% Plot an asymmetric vertical error bar: + +/errorbar { % x y d- d+ | - + gsave + slin setline + 3 copy pop pop + dup 0 gt x 10 lt and { + 4 copy + x pop add 10. 2 copy gt { x } if pop ym x xm x + 2 copy x .05 sub x np mv .1 0 rl st + np mv + pop sub 0. 2 copy lt { x } if pop ym x xm x + 2 copy lineto st + x .05 sub x np mv .1 0 rl st + } { + pop pop pop pop + } ifelse + grestore +} def + +%% Plot a data symbol: + +/plot_symbol { % x y | - + gsave + offset + srad dup scale + slin srad div setline % factor 1/srad compensates "scale" + ps % the actual plot symbol, defined by 'pset' + grestore + } def + +/fill_symbol { + sfill dup + 0 eq { + pop st + } { + 1 eq { + fill + } { + gsave fill grestore + gsave black st grestore + } ifelse + } ifelse + } def + +%% The different symbols, designed for unit area (no arguments): + +/ps_nil { + } bind def + +/ps_square { + .5 .5 np mv + 0 -1 rl + -1 0 rl + 0 1 rl cp fill_symbol + } bind def + +/ps_diamond { + gsave 45 rotate ps_square grestore + } bind def + +/ps_circle { + 0 0 np .564 0 360 arc cp fill_symbol + } bind def + +/ps_triangle { + .77 dup dup 90 pol2xy np mv + 210 pol2xy li + 330 pol2xy li cp fill_symbol + } bind def + +/ps_cedez { + gsave 180 rotate ps_triangle grestore + } bind def + +/ps_tfwd { + gsave 30 rotate ps_triangle grestore + } bind def + +/ps_tbwd { + gsave 210 rotate ps_triangle grestore + } bind def + +/ps_eieruhr { + -.7 -.7 np mv + .7 -.7 li + -.7 .7 li + .7 .7 li cp fill_symbol + } bind def + +/ps_valve { + gsave 90 rotate ps_eieruhr grestore + } bind def + +/ps_pentagram { + .8 dup dup dup dup + 90 pol2xy np mv + 234 pol2xy li + 18 pol2xy li + 162 pol2xy li + 306 pol2xy li cp fill_symbol + } bind def + +/ps_pentagon { + .8 dup dup dup dup + 18 pol2xy np mv + 90 pol2xy li + 162 pol2xy li + 234 pol2xy li + 306 pol2xy li cp fill_symbol + } bind def + +/ps_plus { + gsave 45 rotate ps_cross grestore + } bind def + +/ps_cross { + .5 .5 np mv + -1 -1 rl st + -.5 .5 np mv + 1 -1 rl st + } bind def + +/ps_star { + .7 dup 0 pol2xy np mv 180 pol2xy li st + .7 dup 120 pol2xy np mv 300 pol2xy li st + .7 dup 240 pol2xy np mv 60 pol2xy li st + } bind def + +/ps_horiz { + -.7 0 np mv + 1.4 0 rl st + } bind def + +/ps_verti { + 0 -.7 np mv + 0 1.4 rl st + } bind def + +%% Set column plotting (use this instead of pset) +/setcolumn{ % shift width exec | % + % usage: 0 .2 { gsave { .5 setgray fill } grestore cp } setcolumn + /colexec x def + /colwidth x xm def + /colshift x xm def + /t { + pop xym + np x colshift add colwidth 2 div sub dup 3 2 roll mv + colwidth 0 rl + colwidth add 0 li + colwidth neg 0 rl + cp colexec + } def + /ti { t } bind def + /tf { t black } bind def +} def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% 2D plots %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/t2d { + icCol rect fill + black +} def + +/ColorLegend { % - | - [plot color legend to rectangle hxlow hxhig 0 10] + /ncol 100 def + 1 1 ncol { + dup ncol div 10 mul icCol + dup ncol div 10 mul + x 1 sub ncol div 10 mul + hxlow hxhig 4 2 roll rect fill + } for + } def +/hColorLegend { % ditto, horizontally, to rectangle 0 10 hylow hyhig + /ncol 100 def + 1 1 ncol { + dup ncol div 10 mul icCol + dup ncol div 10 mul + x 1 sub ncol div 10 mul + hylow hyhig rect fill + } for + } def +% Usage: +% hColorLegend +% hylow hyhig 0 0 90 0 OneAxx Axx +% hylow hyhig 10 0 90 180 OneAxx Axx +% 0 10 0 hyhig 0 90 OneAxx Axx Tic Tac +% 0 10 0 0 0 90 OneAxx Axx Tic Tac xNumL +% {(intensity)} xCL + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Boxes +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/rect { % xl xh yl yh | - [path -> rectangle] + ym /qqyh x def + ym /qqyl x def + xm /qqxh x def + xm /qqxl x def + np + qqxl qqyl mv + qqxh qqyl li + qqxh qqyh li + qqxl qqyh li + cp + } def +/oval { % xl xh yl yh dr | - [path -> oval] + fm /qqdr x def + ym /qqyh x def + ym /qqyl x def + xm /qqxh x def + xm /qqxl x def + qqxl qqyl qqdr add np mv + qqxl qqyh qqdr sub li + qqxl qqdr add qqyh qqdr sub qqdr 180 90 arcn + qqxh qqdr sub qqyh li + qqxh qqdr sub qqyh qqdr sub qqdr 90 0 arcn + qqxh qqyl qqdr add li + qqxh qqdr sub qqyl qqdr add qqdr 0 -90 arcn + qqxl qqdr add qqyl li + qqxl qqdr add qqyl qqdr add qqdr -90 -180 arcn + cp + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Motifs %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/dot { % x y siz + 0 360 np arc cp fill +} def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% List %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/NewList { % xins yins size advance NewList - + /nl_advance x def setown /nl_yins x def /nl_xins x def + /nl_yorig nl_yins def + /nl_xshift fontsize xmm div .9 mul def + /nl_xrline 0.33 def + /nl_ystep fontheight ymm div nl_advance mul def + /newline { + /nl_yins nl_yins nl_ystep sub def + } def + /fracline { % frac | - + fontheight ymm div nl_advance mul mul /nl_yins x nl_yins x sub def + } def + } def +/newlist { 1.65 NewList } def +/nlbox { % width | xl xh yl yh + nl_xins add nl_xins fontwidth .4 mul sub x + nl_yins nl_ystep add fontheight 1.2 mul sub nl_yorig fontheight 1.2 mul add + } def +/TxLine { % text | - + nl_xins nl_yins 3 -1 roll textLM newline + } bind def +/TxCLine { % text | - + nl_xins nl_yins 3 -1 roll textCM newline + } bind def +/PtTxLine { % pstyle text | - + x pstyle + nl_xins nl_xshift .5 mul add nl_yins 0 t + black nl_xins nl_xshift 1.5 mul add nl_yins 3 2 roll textLM + newline + } bind def +/PttttTxLine { % pstyle text | - %% chain of very small symbols + x pstyle + nl_xins nl_xshift .10 mul add nl_yins 0 t + nl_xins nl_xshift .26 mul add nl_yins 0 t + nl_xins nl_xshift .42 mul add nl_yins 0 t + nl_xins nl_xshift .58 mul add nl_yins 0 t + nl_xins nl_xshift .74 mul add nl_yins 0 t + nl_xins nl_xshift .90 mul add nl_yins 0 t + black nl_xins nl_xshift 1.5 mul add nl_yins 3 2 roll textLM + newline + } bind def +/PtPtCvTxLine { % pstyle pstyle cstyle text | - + 4 3 roll pstyle nl_xins nl_yins 0 t + 3 2 roll pstyle nl_xins nl_xshift add nl_yins 0 t + x cstyle + nl_xins nl_xshift 2 mul add + dup dup nl_xshift nl_xrline mul sub nl_yins 0 ti + nl_xshift nl_xrline mul add nl_yins 0 tf + nl_xshift add nl_yins 3 2 roll black textLM + newline + } bind def +/PtCvTxLine { % pstyle cstyle text | - + 3 2 roll pstyle nl_xins nl_yins 0 t + x cstyle + nl_xins nl_xshift 1 mul add + dup dup nl_xshift -.33 mul add nl_yins 0 ti + nl_xshift 0.33 mul add nl_yins 0 tf + nl_xshift add nl_yins 3 2 roll black textLM + newline + } bind def +/PtPtTxLine { % pstyle pstyle text | - + 3 2 roll pstyle nl_xins nl_yins 0 t + x pstyle nl_xins nl_xshift add nl_yins 0 t + black nl_xins nl_xshift 2 mul add nl_yins 3 2 roll textLM + newline + } bind def +/CvTxLine { % cstyle text | - + x cstyle + nl_xins fontsize xmm div nl_xrline mul 0 mul sub nl_yins 0 ti + nl_xins fontsize xmm div nl_xrline mul 3 mul add nl_yins 0 tf + black nl_xins nl_xshift 1.5 mul add nl_yins 3 2 roll textLM + newline + } bind def +/Cv2TxLine { % cstyle text | - + x cstyle + nl_xins fontsize xmm div nl_xrline mul sub nl_yins 0 ti + nl_xins fontsize xmm div nl_xrline mul add nl_xshift add nl_yins 0 tf + black nl_xins nl_xshift 2 mul add nl_yins 3 2 roll textLM + newline + } bind def +/PCTxLine { % pstyle(with plset) text | - + x pstyle + nl_xins fontsize xmm div nl_xrline 2 mul mul sub nl_yins 0 ci + nl_xins fontsize xmm div nl_xrline 2 mul mul add nl_yins 0 cf + nl_xins yins 0 t + black nl_xins + fontsize xmm div 1.9 mul % instead of xshift + add nl_yins 3 2 roll textLM + newline + } bind def +/infSet { % oooinfo | - : set whether(1) or not(0) to plot info block + /oooinfo x def + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Arrows +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/pfeilangle 36.87 def +/pfeilspitze { % x[local] y[local] rot siz + % draw with current linestyle, as set e.g. by linsetAxx + x 4 2 roll % siz rot x y + gsave + xym translate 180 add rotate dup dup dup + [] 0 setdash + pfeilangle cos mul x pfeilangle sin mul np mv + 0 0 li pfeilangle cos mul x pfeilangle sin neg mul li st + grestore + } def +/pfeiL { % (arrow anchored at base) x y rot siz len + gsave + dup xm x ym mul sqrt % (scale len) + 5 3 roll + xym translate % (origin at base) rot siz len + 3 2 roll + rotate % (draw rightwards) siz len + dup 0 translate % (origin at head) siz len + x 0 0 0 4 3 roll pfeilspitze % len + 0 0 np mv neg 0 li st + grestore + } def +/Pfeil { % (arrow anchored at head) x y rot siz len + dup xm x ym mul sqrt 5 copy + pop pfeilspitze + x pop + x 4 2 roll % len rot x y + gsave + xym translate 180 add rotate + 0 0 np mv 0 li st + grestore + } def +/pfeil { % xi xf yi yf siz + gsave + 5 1 roll + 4 copy + 4 1 roll pop x pop x offset + sub 3 1 roll sub x 2 copy + x atan 180 add 3 1 roll + 0 0 np mv li st + x 0 0 4 2 roll pfeilspitze + grestore +} def + +/bemasz { % x y L ang text | - %% precede by '24 setown 1 [] lset /pfeilangle 90 def' + gsave + 5 3 roll offset % consumes x and y + x rotate % consumes ang | L text + dup textw .5 mul fontheight .4 mul add /bmszDT x def % => half text width + 0 0 3 2 roll textCM % L + .5 mul /bmszDX x def % => half bemasz length + bmszDX 0 0 fontheight .67 mul bmszDX bmszDT sub Pfeil + bmszDX neg 0 180 fontheight .67 mul bmszDX bmszDT sub Pfeil + grestore + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Text macros +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/Celsius { showif (\26x)g(C) showif } bind def +/hbar { + showif + (h) 1.2 .66 { + currentpoint fontheight .11 mul setline np mv + fontheight dup .8 mul x .3 mul rl + st () + } build + } bind def + +%% for neutron scattering: + +/hbarw { hbar () grec (w) endgr } bind def +/wbar { grec (w) endgr ( / 2) grec (p) endgr } bind def +/taumean { () (\341t\361) g } bind def +/Sqw { showif (S\(q,) grec (w) endgr (\)) showif } bind def +/Sqn { showif (S\(q,) grec (n) endgr (\)) showif } bind def +/SQw { showif (S\(Q,) grec (w) endgr (\)) showif } bind def +/Sttw { showif (S\(2) grec (q) endgr (,) grec (w) endgr (\)) showif } bind def +/Sttn { showif (S\(2) grec (q) endgr (,) grec (n) endgr (\)) showif } bind def +/Xqw { grec (c) endgr (''\(q,) grec (w) endgr (\)) showif } bind def +/Xqn { grec (c) endgr (''\(q,) grec (n) endgr (\)) showif } bind def +/ueV{ grec (m) endgr (eV) showif} bind def +/inueV { showif (\() grec (m) endgr (eV\)) showif } bind def +/inmeVr { showif (\(meV) supsc (-1) endsc (\)) showif } bind def +/inueVr { showif (\() grec (m) endgr (eV) + supsc (-1) endsc (\)) showif } bind def +/inGHzr { showif (\(GHz) (-1) sp (\)) showif } def +/inDeg { showif (\() (\260)g (\)) showif } def + +/Angstr { showif (\305) showif } bind def +/Angr { showif (\305) supsc (-1) endsc } bind def +/inAngr { showif (\() Angr (\)) showif } bind def +/Angrr { showif (\305) supsc (-2) endsc } bind def +/inAngrr { showif (\() Angrr (\)) showif } bind def +/wmin {grec (w) endgr () subsc (min) endsc} def +/winpi { grec (w) endgr ( / 2) grec (p) endgr } def + +end % WuGdict... + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Mark "ewu", the end of the wups.. macro definition file %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +WuGdict18a begin + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Customizable plot setup, copied from setup1D.ps +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +7 dup autolabel defsiz +1 dup geld stdred +2 -11 setnewpage newpage + +2 4 12.6 -12.6 setpagegrid +2 8 24 abcset % usage: {(text)} abc +/EndFrame { nextFrame end } def + +1 1 language +0 infSet % plot info block? +.8 1.2 2 SymGSet % srad slin serr(2=from pset) : graph symbols, global preset +% /setboxbackgroundcolor { 0.93 setgray } def % default is white +% setPalatino + +{ 9 aCol7 iColA } /ipCol x bind def % number of colours and colour style +/pStyles [ + { 11 0 0 1. 1. pset 0 ipCol } + { 12 1 0 1. 1. pset 1 ipCol } + { 13 1 0 1. 1. pset 2 ipCol } + { 1 0 0 .9 1. pset 3 ipCol } + { 1 1 0 .8 1. pset 4 ipCol } + { 3 0 0 .9 1. pset 5 ipCol } + { 3 1 0 .8 1. pset 6 ipCol } + { 4 0 0 .9 1. pset 7 ipCol } + { 4 1 0 .8 1. pset 8 ipCol } + { 5 0 0 .9 1. pset 0 ipCol } + { 5 1 0 .8 1. pset 1 ipCol } + { 2 0 0 .9 1. pset 2 ipCol } + { 2 1 0 .8 1. pset 3 ipCol } + { 11 0 0 1. 1. pset 4 ipCol } + { 12 1 0 1. 1. pset 5 ipCol } + { 13 1 0 1. 1. pset 6 ipCol } + ] def + +{ 7 aCol3 iColA } /icCol x bind def % number of colours and colour style +/cStyles [ + { 1. [] lset 0 icCol } + { 1. [] lset 1 icCol } + { 1. [] lset 2 icCol } + { 1. [] lset 3 icCol } + { 1. [] lset 4 icCol } + { 1. [] lset 5 icCol } + { 1. [] lset 6 icCol } + ] def + +Resets +BoxBackground + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Mark "ecu", end of the customization section +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% output created by Frida version post-2.4.4a + +1 0.02 20 xSetCoord +0 0 1.04 ySetCoord + +% x axis: +[ + 0.1 wx {(0.1)} + 1 wx {(1)} + 10 wx {(10)} + ] SetTacVec +0.01 wx 100 wx 5 9 SetTicVecLog + 0 10 0 0 0 90 OneAxx Axx Tic Tac xNumL %% low x axis + 0 10 0 10 0 270 OneAxx Axx Tic Tac %% top x axis +{()(k)g()(a)sb()(t)g()} xCL + +% y axis: +[ + 0 wy {(0)} + 0.25 wy {(0.25)} + 0.5 wy {(0.5)} + 0.75 wy {(0.75)} + 1 wy {(1)} + ] SetTacVec +-0.25 wy 1.25 wy 7 5 SetTicVecLin + 0 10 0 0 90 0 OneAxx Axx Tic Tac yNumL %% left y axis + 0 10 10 0 90 180 OneAxx Axx Tic Tac %% right y axis +{(reflectivity reduction factor)} yCL + +24 setown +7 5 -65 {()(k)g()( b)sb( / )(k)g()( a)sb( = 0.1)} rtextCM +2.5 5 -70 {()(k)g()( b)sb( / 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0.6109136 wx 0.03228932 wy + 4.95807 0.30374 0.00000 t % 0.6144017 wx 0.03158937 wy + 4.96627 0.29716 0.00000 t % 0.6178897 wx 0.03090459 wy + 4.97499 0.29027 0.00000 t % 0.6216223 wx 0.03018824 wy + 4.98328 0.28383 0.00000 t % 0.6251918 wx 0.02951871 wy + 4.99152 0.27754 0.00000 t % 0.6287613 wx 0.02886403 wy + 5.00010 0.27110 0.00000 t % 0.6324977 wx 0.0281943 wy + 5.00843 0.26495 0.00000 t % 0.6361507 wx 0.02755455 wy + 5.01672 0.25894 0.00000 t % 0.6398037 wx 0.02692931 wy + 5.02496 0.25306 0.00000 t % 0.6434566 wx 0.02631826 wy + 5.03316 0.24732 0.00000 t % 0.6471096 wx 0.02572108 wy + 5.04188 0.24132 0.00000 t % 0.6510187 wx 0.02509702 wy + 5.05017 0.23572 0.00000 t % 0.654757 wx 0.0245144 wy + 5.05841 0.23024 0.00000 t % 0.6584954 wx 0.0239453 wy + 5.06699 0.22465 0.00000 t % 0.6624084 wx 0.02336374 wy + 5.07532 0.21932 0.00000 t % 0.6662342 wx 0.02280883 wy + 5.08361 0.21411 0.00000 t % 0.6700599 wx 0.02226709 wy + 5.09185 0.20902 0.00000 t % 0.6738856 wx 0.02173823 wy + 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wy + 5.46832 0.05943 0.00000 t % 0.8740317 wx 0.006181229 wy + 5.48495 0.05578 0.00000 t % 0.8841276 wx 0.005801305 wy + 5.50139 0.05235 0.00000 t % 0.8942235 wx 0.005444733 wy + 5.51839 0.04899 0.00000 t % 0.9047912 wx 0.005094947 wy + 5.53521 0.04584 0.00000 t % 0.9153645 wx 0.004767468 wy + 5.55184 0.04289 0.00000 t % 0.9259378 wx 0.004461037 wy + 5.56828 0.04014 0.00000 t % 0.9365111 wx 0.004174303 wy + 5.58528 0.03744 0.00000 t % 0.9475787 wx 0.003893887 wy + 5.60210 0.03492 0.00000 t % 0.958652 wx 0.003632177 wy + 5.61873 0.03258 0.00000 t % 0.9697253 wx 0.003388057 wy + 5.63517 0.03039 0.00000 t % 0.9807986 wx 0.003160344 wy + 5.65217 0.02825 0.00000 t % 0.9923895 wx 0.002938364 wy + 5.66899 0.02627 0.00000 t % 1.003986 wx 0.002731872 wy + 5.68562 0.02442 0.00000 t % 1.015583 wx 0.002539892 wy + 5.70206 0.02271 0.00000 t % 1.02718 wx 0.002361402 wy + 5.71906 0.02104 0.00000 t % 1.039319 wx 0.002187991 wy + 5.73588 0.01949 0.00000 t % 1.051465 wx 0.002027233 wy + 5.75251 0.01806 0.00000 t % 1.06361 wx 0.001878287 wy + 5.76895 0.01673 0.00000 t % 1.075756 wx 0.001740284 wy + 5.78595 0.01545 0.00000 t % 1.088469 wx 0.00160668 wy + 5.80277 0.01426 0.00000 t % 1.101188 wx 0.00148327 wy + 5.81940 0.01317 0.00000 t % 1.113908 wx 0.00136934 wy + 5.83584 0.01216 0.00000 t % 1.126628 wx 0.001264161 wy + 5.85284 0.01118 0.00000 t % 1.139942 wx 0.001162708 wy + 5.86966 0.01028 0.00000 t % 1.153263 wx 0.001069351 wy + 5.90272 0.00870 0.00000 t % 1.179906 wx 0.0009045231 wy + 5.91973 0.00797 0.00000 t % 1.19385 wx 0.000828648 wy + 5.95318 0.00669 0.00000 t % 1.221752 wx 0.0006953946 wy + 5.98662 0.00559 0.00000 t % 1.250307 wx 0.0005811831 wy + 6.02007 0.00465 0.00000 t % 1.279529 wx 0.0004836972 wy + 6.05351 0.00385 0.00000 t % 1.309434 wx 0.0004008395 wy + 6.08696 0.00318 0.00000 t % 1.340038 wx 0.0003307199 wy + 6.12040 0.00261 0.00000 t % 1.371357 wx 0.0002716428 wy + 6.15385 0.00214 0.00000 t % 1.403408 wx 0.000222095 wy + 6.18729 0.00174 0.00000 t % 1.436208 wx 0.0001807321 wy + 6.22074 0.00141 0.00000 t % 1.469775 wx 0.0001463659 wy + 6.28763 0.00091 0.00000 t % 1.53928 wx 9.457511e-05 wy + 6.35452 0.00058 0.00000 t % 1.612072 wx 5.986109e-05 wy + 6.42140 0.00036 0.00000 t % 1.688307 wx 3.707825e-05 wy + 6.55518 0.00013 0.00000 t % 1.851762 wx 1.327671e-05 wy + 6.82274 0.00001 0.00000 t % 2.22768 wx 1.251136e-06 wy +10.00000 0.00000 0.00000 tf % 20 wx 3.99059e-55 wy + +{ black 0 -3 13 1.65 NewList + {(fit_grid1x19)} TxLine + {( cc sinh(pi*t*(1-z0))/sinh(pi*t*(1+z0))/((1-z0)/(1+z0)) # z from grid1x19)} TxLine + {( oz0 j==17?2:z0)} TxLine + {( oz0 j==18?5:z0)} TxLine + {( sinh(pi*t*(1-z0))/sinh(pi*t*(1+z0))/((1-z0)/(1+z0)))} TxLine + {( data file: 9, weighing: constant)} TxLine + {( j z0 oc chi^2 1-R^2)} TxLine + 1 {( 0.1 0 0 1 )} CvTxLine + 2 {( 0.2 0 0 1 )} CvTxLine + 3 {( 0.4 0 0 1 )} CvTxLine + 4 {( 0.9 0 0 1 )} CvTxLine + 5 {( 1.1 0 0 1 )} CvTxLine + 6 {( 2 0 0 1 )} CvTxLine + 7 {( 5 0 0 1 )} CvTxLine + {(plot -> /home/jwu/gnew/L1.ps)} TxLine +} oooinfo 1 eq { exec } { pop } ifelse + +EndFrame diff --git a/Doc/DevRef/fig/funcplot/tanhc.ps b/Doc/DevRef/fig/funcplot/tanhc.ps new file mode 100644 index 00000000000..70c14e68ffc --- /dev/null +++ b/Doc/DevRef/fig/funcplot/tanhc.ps @@ -0,0 +1,1913 @@ +%!PS-Adobe-1.0 EPSF-1.0 +%%BoundingBox: 14 604 258 788 +%%Comment: Bounding box extracted by bboxx +%%+: A program by Dov Grobgeld 2003 +%%Comment: Bounding box extracted by bboxx +%%+: A program by Dov Grobgeld 2003 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FRIDA: fast reliable interactive data analysis %% +%% wups18a.ps: graphic macros %% +%% (C) Joachim Wuttke 1990-2018 %% +%% http://www.messen-und-deuten.de/frida %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/WuGdict18a 400 dict def +WuGdict18a begin + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Generic and math operators +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Shortcuts: + +/np { newpath } bind def +/mv { moveto } bind def +/rm { rmoveto } bind def +/rl { rlineto } bind def +/li { lineto } bind def +/cp { closepath } bind def +/st { stroke } bind def +/x { exch } bind def +/gs { gsave } bind def +/gr { grestore } bind def +/G { gsave exec grestore } bind def + +%% Math operators: + +/twopi { 6.2831853072 } def + +/rnd { rand cvr 1 30 bitshift div 2 div 0 max 1 min } def % -> between 0 and 1 + +/min { 2 copy gt { x } if pop } def +/max { 2 copy lt { x } if pop } def + +/tan { dup sin x cos div } def +/cot { dup cos x sin div } def +/pol2xy{ 2 copy cos mul 3 1 roll sin mul } def % r phi | x y + +/eexp { 2.71828 x exp } def % "exp" is x^y, eexp is e^x +/tanh { 2.71828 x 2 copy exp 3 1 roll neg exp 2 copy sub 3 1 roll add div } def + +%% Loop: + +/iterate { % xi yi what dx dy num_repeats | - %% after each repeat, translates by (dx,dy) + gsave + 6 4 roll xym translate % what x_mv y_mv num_repeats + { % what x_mv y_mv + 3 copy + 3 2 roll + exec + xym translate + } repeat + pop pop pop + grestore +} def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Incremental path construction with persistent direction +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/NP { % x y [new path] + gsave translate np 0 0 mv } bind def +/EP { % [end path] + grestore } bind def +/L { % len rel_dir [line] + 90 mul rotate 0 2 copy rl translate } bind def +/A { % radius angle [arc segment] + /IPCa x 90 mul def /IPCr x def + IPCa 0 lt + { + 0 IPCr neg IPCr 90 90 IPCa add arcn + 0 IPCr neg translate IPCa rotate 0 IPCr translate + } { + 0 IPCr IPCr -90 -90 IPCa add arc + 0 IPCr translate IPCa rotate 0 IPCr neg translate + } ifelse + } def +/V { % size [simple arrow] - + gsave /IPCr x def np -.8 IPCr mul .6 IPCr mul mv + 0 0 li -.8 IPCr mul -.6 IPCr mul li st grestore + } def % size [arrow] +/Vc { % size [triangular unfilled arrow] - + gsave /IPCr x def np -.8 IPCr mul .6 IPCr mul mv + 0 0 li -.8 IPCr mul -.6 IPCr mul li cp { white fill } G st grestore + } def % + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Page coordinates +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/pt { .018567 mul} bind def % for line widths and font sizes, reason unclear +/cm {28.346456 mul} bind def % typographic_point -> cm + +/cmtranslate { % x y [] - + cm x cm x translate } bind def + +% Move origin from lower left (PostScript default) to upper left +/setnewpage { % xoff yoff + /yoffnewpage x def + /xoffnewpage x def +} def +/originUpperLeft_A4{ .7 28.3 cmtranslate } bind def +/goffsetA4 { ungscale originUpperLeft_A4 gscale } def +/newpage { + goffsetA4 + xoffnewpage yoffnewpage offset +} def + +% Set absolute global scale and relative symbol size +/defsiz { % size(cm) symbolsize(rel) | - + /ftot x def + /gsiz x cm 10 div def + gscale % within 'size', coordinates run from 0 to 10 + } def +/gscale { + gsiz dup scale + } def +/ungscale { + 1 gsiz div dup scale + } def + +% Symbol (and label?) size as sublinear function of figure size +/autolabel { % size(cm) | symbolsize(rel) + dup 7 div 2 add 4 mul % the simplest sublinear increase + x div % anticipate overall rescaling + } def + +% Aspect ratios +/gyld {0.447214 mul} bind def /Gyld {0.447214 div} bind def % sqrt(5) +/guld {0.547723 mul} bind def /Guld {0.547723 div} bind def % sqrt(3) +/gold {0.618034 mul} bind def /Gold {0.618034 div} bind def % goldener Schnitt +/gild {0.707107 mul} bind def /Gild {0.707107 div} bind def % sqrt(2) : DIN +/geld {0.759836 mul} bind def /Geld {0.759836 div} bind def % sqrt(sqrt(3)) +/gald {0.817765 mul} bind def /Gald {0.817765 div} bind def % sqrt sqrt sqrt 5 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Several frames per page +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/setpagegrid { % ncol nrow xoffnewframe yoffnewframe + /yoffnewframe x def + /xoffnewframe x def + /nrowpage x def + /ncolpage x def +} def +/iFrame 0 def +/nextFrame { + /iFrame iFrame 1 add def + iFrame nrowpage ncolpage mul mod 0 eq { + showpage gscale newpage + } { + iFrame ncolpage mod 0 eq { + xoffnewframe ncolpage 1 sub neg mul yoffnewframe offset + } { + xoffnewframe 0 offset + } ifelse + } ifelse + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Frame coordinates +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/defred { % x_reduction y_reduction label_reduction | - + /fmm x ftot mul def + /ymm x def + /xmm x def + + % conversion frame_coordinate -> global_coord + /xm {xmm mul} bind def + /ym {ymm mul} bind def + /fm {fmm mul} bind def + /xym {ym x xm x} bind def + + % prefer rescaling over explicit conversion (make more use of this !) + /mmscale { xmm ymm scale } bind def + /mmunscale { 1 xmm div 1 ymm div scale } bind def + + % graphic commands in frame coordinates + /offset { xym translate } bind def + /currentxy { currentpoint ymm div x xmm div x } bind def + /setline { pt fm setlinewidth [] 0 setdash } bind def + } def + +/stdred { % x_reduction y_reduction | - + 2 copy mul sqrt defred + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% World (= user application) coordinates +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/xSetCoord { % log min max | - + /wxmax x def + /wxmin x def + /wxlog x 0 eq not def + /wxdel wxmax wxmin wxlog { div log } { sub } ifelse def + /wxd { % dx(world) | dx(frame) + wxlog { log } if wxdel div 10 mul + } bind def + /wx { % x(world) | x(frame) + wxmin wxlog { div } { sub } ifelse + wxd + } bind def + } def +/ySetCoord { % log min max | - + /wymax x def + /wymin x def + /wylog x 0 eq not def + /wydel wymax wymin wylog { div log } { sub } ifelse def + /wyd { % dy(world) | dy(frame) + wylog { log } if wydel div 10 mul + } bind def + /wy { % y(world) | y(frame) + wymin wylog { div } { sub } ifelse + wyd + } bind def + } def +/hSetCoord { % log min max | - % for use in 2D plot + /whmax x def + /whmin x def + /whlog x 0 eq not def + /wH { % h(world) | h(col) + dup whmin lt { + pop -1 + } { + dup whmax gt { + pop 11 + } { + wh + } ifelse + } ifelse + } bind def + whlog { + /whdel whmax whmin div log def + /wh { whmin div log whdel div 10 mul } bind def % h(world) | h(col) + } { + /whdel whmax whmin sub def + /wh { whmin sub whdel div 10 mul } bind def % h(world) | h(col) + } ifelse + } def + +% pair conversion +/wxy { % x,y(world) -> x,y(frame) + wy x wx x + } def + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Colors %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Color operators: + +/setRGBcolor { + 3 { 255 div 3 1 roll } repeat setrgbcolor + } def + +/colormix { % weight(0..1) col1(R|G|B) col2(R|G|B) | col(R|G|B) + 7 -1 roll dup /weightA x def /weightB x 1 x sub def + 4 -1 roll weightA mul x weightB mul add 5 1 roll + 3 -1 roll weightA mul x weightB mul add 4 1 roll + 2 -1 roll weightA mul x weightB mul add 3 1 roll + } def + +/relcol { % i_col n_col | rel(0..1) : for one-dimensional choices + 1 sub div 0 max 1 min + } def + +%% Named colors: + +/black { 0 setgray } bind def +/white { 1 setgray } bind def + +/red { 255 0 0 setRGBcolor } bind def + +/siemensorange { 255 153 0 setRGBcolor } bind def +/siemensblue { 0 102 153 setRGBcolor } bind def +/siemenstext { 0 51 102 setRGBcolor } bind def +/siemensred { 165 0 33 setRGBcolor } bind def +/siemenspink { 221 102 102 setRGBcolor } bind def +/siemensgrey { 221 221 221 setRGBcolor } bind def +/siemensdark { 102 102 102 setRGBcolor } bind def +/siemensgreen { 33 153 102 setRGBcolor } bind def +/siemensyellow { 255 221 0 setRGBcolor } bind def + + +%% One-dimensional linear color choices: + +/iCol1 { % i i_max | - : default -2010, round the circle, RGBR + relcol dup 1 x % rel 1 rel + 360 mul 255 add cos 1 add dup mul neg .053 mul 1 add % modulate saturation + sethsbcolor + } def +/iCol2 { % i i_max | - : cyan - yellow - magenta + relcol 3 mul + dup 1 le { + dup 1 sub neg 0 3 2 roll } { + dup 2 le { + 1 sub dup 1 sub neg 0 3 1 roll } { + 2 sub dup 1 sub neg 0 3 0 roll } ifelse + } ifelse + 0 setcmykcolor + } def +/iCol3 { % i i_max | - : siemens + div /icnow x def + 165 1 icnow sub mul + 102 icnow mul + 33 120 icnow mul add setRGBcolor + } def +/iCol4 { % i i_max | - : red to blue (subsequence of old scheme iCol1) + relcol + 3 x sub 3 div 1 iCol1 + } def + + +%% One-dimensional color choice from given array: + +/iColA { % i i_max arr | - + /aCol x def + relcol + aCol length 1 sub mul % position within array + dup cvi dup 3 1 roll % idx pos idx + sub x % offset idx + 0 max aCol length 1 sub min % offset safe_idx + dup 1 add aCol length 1 sub min % offset i i+1 + aCol x get exec + 4 3 roll aCol x get exec colormix setRGBcolor + } def + +%% ditto with discontinuous values for h<0 and h>1 + +/iColAA { % i i_max arr {low_col} {hig_col} | - + 5 3 roll + div + dup 0 lt { + pop pop x pop exec + } { + dup 1 gt { + pop 3 1 roll pop pop exec + } { + 1 % arr {l} {h} i i_max + 5 2 roll pop pop + x 1 add x % ad-hoc correction for legacy definition of relcol + iColA + } ifelse + } ifelse + } def + +%% Color arrays for non-linear one-dimensional choices: + +/aCol1 [ % red-blue + { 255 0 0 } % 1 + { 240 10 10 } % 2 + { 220 40 40 } % 3 + { 205 65 90 } % 4 + { 195 80 130 } % 5 + { 180 110 180 } % 6 + { 165 120 185 } % 7 + { 150 130 190 } % 8 + { 130 150 210 } % 9 + { 110 125 220 } % 10 + { 85 105 230 } % 11 + { 70 90 255 } % 12 + { 0 0 255 } % 13 + ] def +/aCol2 [ % orange-red-blue-darkblue + { 255 180 0 } + { 255 160 0 } + { 255 120 0 } + { 255 70 0 } + { 255 0 0 } + { 220 30 30 } + { 220 70 60 } + { 220 100 110 } + { 200 130 130 } + { 200 130 160 } + { 180 110 180 } + { 165 110 185 } + { 150 130 190 } + { 130 150 210 } + { 100 120 220 } + { 85 105 230 } + { 70 90 255 } + { 0 0 255 } + { 0 0 180 } + { 10 10 150 } + { 30 30 130 } + ] def +/aCol3 [ % [fixed size: max_i=8] siemenscolors + { 165 0 33 } % siemensred + { 33 153 102 } % siemensgreen + { 0 102 153 } % siemensblue + { 0 51 102 } % siemenstext + { 255 153 0 } % siemensorange + { 102 102 102 } % siemensdark + { 255 221 0 } % siemensyellow + { 221 221 221 } % siemensgrey + { 221 102 102 } % siemenspink + ] def +/aCol4 [ % green-blue-brown + { 120 160 60 } + { 90 185 40 } + { 50 215 20 } + { 0 245 0 } + { 10 235 112 } + { 20 235 143 } + { 30 230 173 } + { 40 225 194 } + { 50 205 215 } + { 40 153 204 } + { 40 102 153 } + { 40 82 122 } + { 90 74 101 } + { 140 68 80 } + { 170 59 60 } + { 190 50 40 } + { 180 65 40 } + { 160 80 40 } + { 140 100 40 } + { 120 80 30 } + { 100 60 20 } + ] def +/aCol5 [ % [fixed size: max_i=7] old gnuplot default (see man gnuplot and rgb.txt) + { 255 0 0 } % red + { 0 255 0 } % green + { 0 0 255 } % blue + { 255 0 255 } % magenta + { 0 255 255 } % cyan + { 160 82 45 } % sienna + { 255 165 0 } % orange + { 255 127 80 } % coral + ] def +/aCol6 [ % heat plot + { 100 0 100 } % violet + { 60 30 130 } % dark blue + { 30 50 220 } % blue + { 50 150 100 } % green + { 150 200 100 } % green + { 215 255 50 } % green/yellow + { 255 255 0 } % yellow + { 255 125 0 } % orange + { 255 0 0 } % red + ] def +/aCol7 [ % [fixed size: max_i=8] default colors, modified from old gnuplot + { 80 80 255 } % blue + { 255 0 0 } % red + { 0 160 0 } % dark green + { 255 0 255 } % magenta + { 0 160 192 } % dark cyan + { 160 82 45 } % sienna + { 255 165 0 } % orange + { 255 127 80 } % coral + { 64 224 32 } % light greenish + ] def +/aCol8 [ % matplotlib's viridis: blue - green -yellow + { 64 0 79 } + { 72 36 117 } + { 65 68 135 } + { 53 95 141 } + { 42 120 142 } + { 33 145 140 } + { 34 168 132 } + { 68 191 112 } + { 122 209 81 } + { 189 223 38 } + { 239 218 34 } + ] def +/aCol9 [ % matplotlib's inferno: black - violet - red - orange - yellow + { 0 0 0 } + { 27 12 65 } + { 74 12 107 } + { 120 28 109 } + { 165 44 96 } + { 207 68 70 } + { 237 105 37 } + { 251 155 6 } + { 247 209 61 } + { 252 255 164 } + ] def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Fonts +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% extend font encoding +/ReEncode { % OldFont NewFont Encoding | - + /MyEncoding x def + x findfont % select OldFont + dup length dict begin + {def} forall + /Encoding MyEncoding def + currentdict + end + definefont pop % define as NewFont + } def + +% we assume that image scripts are Latin1 encoded +/Helvetica /MyFont ISOLatin1Encoding ReEncode +/Helvetica-Oblique /MyFont-Oblique ISOLatin1Encoding ReEncode +/Helvetica-Bold /MyFont-Bold ISOLatin1Encoding ReEncode +/Helvetica-BoldOblique /MyFont-BoldOblique ISOLatin1Encoding ReEncode + +/setPalatino { + /Palatino /MyFont ISOLatin1Encoding ReEncode + /Palatino-Italic /MyFont-Oblique ISOLatin1Encoding ReEncode + /Palatino-Bold /MyFont-Bold ISOLatin1Encoding ReEncode + /Palatino-BoldItalic /MyFont-BoldOblique ISOLatin1Encoding ReEncode + } def + +%% Preset standard styles: + +% scale and set font; define fontsize, fontheight +/setfontandsize { % font size | - + dup 0 le { pop 100 } if % fontsize <= 0 not allowed ! + /fontnonnil true def + pt fm dup /fontsize x def + x findfont + x scalefont + setfont + gsave % determine fontheight - from the cookbook : + np 0 0 mv (W) true charpath flattenpath + pathbbox % low_left_x, low_left_y, up_right_x, up_right_y + /fontheight x def + /fontwidth x def + pop pop + grestore + } def + +% standard settings for labelling axes +/numlabcol { black } def +/setnum { /MyFont 24 setfontandsize numlabcol } def +/setlab { /MyFont 24 setfontandsize numlabcol } def + +% user commands (free choice of fontsize, but fixed font family) +/setown { /MyFont x setfontandsize } def +/setbol { /MyFont-Bold x setfontandsize } def +/setboq { /MyFont-BoldOblique x setfontandsize } def +/setobl { /MyFont-Oblique x setfontandsize } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Text blocks +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/showif { % string | - : increment xwidth or plot string + prepare + { stringwidth pop xwidth add /xwidth x def } + { show } + ifelse + } def +/script { % matrix relpos_y | - + /yoffset x fontheight mul def + currentfont x makefont setfont + 0 yoffset rm + } def +/scred .71 def +/subsc { + showif + [scred 0 0 scred 0 0] -.2 script + } def +/supsc { + showif + [scred 0 0 scred 0 0] .6 script + } def +/endsc { + showif + regularfont setfont + 0 yoffset neg rm + } def +/grec { + showif + /Symbol findfont fontsize scalefont setfont + } def +/endgr { + showif + regularfont setfont + } def +/endall { + showif + regularfont setfont + } def +/build { % string xrel yrel obj | - : plot obj above/below string + /obj x def /yrelbui x def /xrelbui x def + dup showif + prepare + { pop } + { stringwidth pop xrelbui neg mul fontheight yrelbui mul % relpos for obj + currentpoint 4 2 roll % save position after string + rm obj pop % obj must end with () that will be pop'ed + mv % back to saved position + } + ifelse + } def +/gbuild { % string xrel yrel obj | - : plot obj above/below string + /obj x def /yrelbui x def /xrelbui x def + /Symbol findfont fontsize scalefont setfont + dup showif + prepare + { pop regularfont setfont } + { stringwidth pop xrelbui neg mul fontheight yrelbui mul % relpos for obj + currentpoint 4 2 roll % save position after string + regularfont setfont + rm obj pop % obj must end with () that will be pop'ed + mv % back to saved position + } + ifelse + } def +/hut { % ..) (<Char>) hut (.. %%% MISERABEL PROGRAMMIERT + x showif + 1.4 .6 {(\136) show ()} build + } def +/ghut { % ..) (<grec-Char>) ghut (.. %%% BREITE PASST NUR FUER Phi(t) + x showif + .8 .65 {(\136) show ()} gbuild + } def +/tilde { + x showif + 1. .6 {(~) show ()} build + } def +/gtilde { + x showif + 1. .6 {(~) show ()} gbuild + } def +/spce { % string n spce - ; insert n times ( ) + {showif ( )} repeat + } def + +% the following macros use the symbol/curve plotting mechanism +/pins { % string symins - ; symbol must be selected by pset + showif + ( ) showif ( ) .5 .5 { currentxy 0 p black ()} build ( ) showif + } def +/clenins { % string len clenins - ; curve must be selected by cset + x showif % I suppose that pins is preceeded by 8 spaces + dup ( ) stringwidth pop mul 2 add /xstrich x xmm div def + % length of inserted curve : + % -1 space : curve begins and ends in middle of ( ) + % +3 spaces: pins requires 3 times ( ) + ( ) 0 .5 { currentxy currentxy 0 ci x xstrich add x 0 cf () } build + 2 add {( ) showif} repeat + } def +/cins { % string symins - ; curve must be selected by cset + showif 8 % I suppose that pins is preceeded by 8 spaces + dup ( ) stringwidth pop mul 2 add /xstrich x xmm div 10 div def + % nov03, ohne zu verstehen, "10 div" eingefuegt + % length of inserted curve : + % -1 space : curve begins and ends in middle of ( ) + % +3 spaces: pins requires 3 times ( ) + ( ) 0 .5 { currentxy currentxy 0 ci x xstrich add x 0 cf () } build + 2 add {( ) showif} repeat + } def + +/block { % x y ob xrel yrel | - + /yrel x def /xrel x def /blabla x def + /ypos x ym def /xpos x xm def + /regularfont currentfont def /yoffset 0 def % initialize for security + /prepare true def /xwidth 0 def 0 0 mv % to prevent empty-path-error + blabla endall % first pass : determine xwidth + boxif { /boxwidth xwidth (M) stringwidth pop boxxr mul 2 mul add def + /boxheight fontheight 1 boxyr 2 mul add mul def + np xpos xwidth xrel mul sub boxwidth xwidth sub 2 div sub + ypos fontheight .5 boxyr add mul sub mv + boxwidth 0 rl 0 boxheight rl boxwidth neg 0 rl cp + boxproc + } if + xpos xwidth xrel mul sub ypos fontheight yrel mul sub mv + /prepare false def + blabla endall % second pass : plot + /boxif false def + } def +/rblock { % x y ang ob proc rblock - + 5 3 roll + gsave + xym translate + 3 2 roll rotate + 0 0 4 2 roll exec + grestore + } def + +/Box { % x y {exe} + /boxif true def + /boxproc x def /boxyr x def /boxxr x def + } def +/nBox { .6 .6 3 2 roll Box } def +/boxif false def +/textW { % obj | length : calculate only length. + /blabla x def + /regularfont currentfont def /yoffset 0 def % initialize for security + /prepare true def /xwidth 0 def 0 0 mv % to prevent empty-path-error + blabla endall + xwidth % has been determined + } def +/textw { % obj | y : dito, in 0..10-units + textW xmm div + } def + +% horizontal text: x y ob | - +/textLB { 0. 0. block } bind def +/textCB { .5 0. block } bind def +/textRB { 1. 0. block } bind def +/textLM { 0. .5 block } bind def +/textCM { .5 .5 block } bind def +/textRM { 1. .5 block } bind def +/textLT { 0. 1. block } bind def +/textCT { .5 1. block } bind def +/textRT { 1. 1. block } bind def + +% rotated text: x y ang ob | - +/rtextLB { {textLB} rblock } bind def +/rtextLM { {textLM} rblock } bind def +/rtextRB { {textRB} rblock } bind def +/rtextRM { {textRM} rblock } bind def +/rtextCM { {textCM} rblock } bind def + +%% Language selection: + +% preset +/language { % choose_this of_so_many | - % select current language + /langMax x def + /langChc x def + } def +1 1 language % default +% choose text from sequence +/langSel { % text_1 .. text_M | text_C : choose text, M=langMax, C=langChc + langMax dup langChc sub 1 add roll + langMax 1 sub { pop } repeat + } def + +%% Text composition shortcuts: + +/g { x grec endgr} bind def +/sb { x subsc endsc} bind def +/sp { x supsc endsc} bind def +/sbgr { x grec () subsc endsc () endgr} bind def +/spgr { x grec () supsc endsc () endgr} bind def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Coordinate Frame %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Layout presets: + +/xyTicLen {0.10 fm} def +/xyTacLen {0.20 fm} def +/txllen {0.20 fm} def +/tyllen {0.20 fm} def +/linsetAxx {black 0.7 setline} def +/linsetTic {black 0.7 setline} def +/linsetTac {black 0.7 setline} def +/linsetGri {black 0.4 setline} def + +%% Start-up commands: + +/Resets { + /yNumLengthL 0 def /yNumLengthH 0 def + /xNumHeightL .3 def /xNumHeightH 0 def + /xNumHeightRel 2.4 def + /aMean 5 def + black + } def +/BoxBackground { + 0 10 0 10 rect gsave setboxbackgroundcolor fill grestore +} def +/setboxbackgroundcolor { white } def + +/zValues { pop pop } def +/whiteframe { 1 0 0 10 10 graybox } def + +/abc {abclab setown abcx abcy 3 2 roll textCM} def % usage ((a)) abc +/abcset { % x y siz abcset - : preset for abc + /abclab x def /abcy x def /abcx x def + } def + +%% Ticks: + +% set tick array - internal macros +/tiputs { % rel_pos_of_tick | pos_of_tick : innermost routine for /taproc + tastep mul taloop add + } def +/taproclin { % (#tick/tack) | - : define /taproc for use in SetVec + 1 x div /tistep x def + /taproc { 0 tistep .999 { tiputs } for } def + } def +/taproclog { % (#ticks/tacks) | - : define /taproc for use in SetVec + dup 3 gt { pop /taproc { 1 1 9 { log tiputs } for } def + }{ dup 1 gt { pop /taproc { 0 tiputs 2 log tiputs 5 log tiputs } def + }{ dup 0 gt { pop /taproc { 0 tiputs } def + }{ neg taproclin + } ifelse } ifelse } ifelse + } def +/SetVec { % tafro tatoo nta /vector | - : set /vector + 4 1 roll + /nta x def /tatoo x def /tafro x def + /tastep tatoo tafro sub nta 1 sub div def + [ + 0 1 nta { + tastep mul tafro add /taloop x def + taproc exec + } for + ] def + } def +% set tick array - user commands +/SetTicVecLin { taproclin /TicVec SetVec } def +/SetTicVecLog { taproclog /TicVec SetVec } def + +% set tack-and-number array +/SetTacVec { % [ pos {label} pos {label} ... ] | - + /TacVec x def + } def + +% define axes + % note on angles : 0 = x-axis, 90 = y-axis +/OneAxx { % fro to xpos ypos aang tang | - : presets for Axx, Tic, Tac, Num + % store arguments + /tAng x def /aAng x def + /yPos x def /xPos x def + /aTo x def /aFro x def + % set constants + /xTicLen tAng cos xyTicLen mul def /yTicLen tAng sin xyTicLen mul def + /xTacLen tAng cos xyTacLen mul def /yTacLen tAng sin xyTacLen mul def + /xAng aAng cos def /yAng aAng sin def + /aMean aFro aTo add 2 div def + } def + +% draw axis (with parameters preset by OneAxx or ArrAxx) +/Axx { % - | - + linsetAxx + gsave + xPos yPos offset + mmscale + aAng rotate + % draw a line + aFro 0 np mv + aTo 0 li st + grestore + } def + +% draw ticks (positions given by SetTicVec, parameters preset by OneAxx/..) +/Tic { % - | - : draw tick as defined in TicProc + linsetTic + TicVec { + dup dup aFro lt x aTo gt or {pop} {TicProc} ifelse + } forall + } def +/TicProc { % aPos | - : default procedure to plot one tick + np + xPos yPos xym mv + dup xAng mul x yAng mul xym rm % eat argument, go to start pos. + xTicLen yTicLen rl st + } def +/xGric { % yFro yTo | - : draw a grid line (instead of an x tick) + linsetGri + TicVec { + 3 copy dup 5 -1 roll aFro lt x aTo gt or {pop pop pop} { + dup % y1 y2 x x + 4 -1 roll xym np mv % y2 x + x xym li st + } ifelse + } forall + pop pop + } def +/yGric { % xFro xTo | - : draw a grid line (instead of an y tick) + linsetGri + TicVec { + 3 copy dup 5 -1 roll aFro lt x aTo gt or {pop pop pop} { + dup % x1 x2 y y + 4 -1 roll x xym np mv % x2 y + xym li st + } ifelse + } forall + pop pop + } def + +% draw tacks (positions given by SetTacVec, parameters preset by OneAxx/..) +/TacExe { % Proc | - % Execute Proc for all pairs of elements of TacVec + % (but only if inside aFro..aTo) + /TacProc x def + /ispair true def % toggle: take pos, take label, take pos, take label ... + TacVec { + ispair + { + /aPos x def + /ispair false def + } { + aPos dup aFro lt x aTo gt or + {pop} {TacProc} ifelse + /ispair true def + } ifelse + } forall + } def +/Tac { + linsetTac + { pop xPos yPos xym mv + aPos dup xAng mul x yAng mul xym rm + xTacLen yTacLen rl st + } TacExe + } def +% special tack routines, only for rectangular axes +/xTacC { % : centered tack on x axis + linsetTac + { pop aPos xm yPos ym txllen 2 div sub np mv 0 txllen rl st } TacExe + } def +/xGrid { % : rule instead of tack on x axis + linsetTac + { pop aPos xm np yPos ym mv 0 10 xym rl st } TacExe + } def +/yTacC { % : centered tack on y axis + linsetTac + { pop xPos xm tyllen 2 div sub aPos ym np mv tyllen 0 rl st } TacExe + } def +/yGrid { % : rule instead of tack on low y axis + linsetTac + { pop aPos ym np xPos xm x mv 10 0 xym rl st } TacExe + } def + +% draw numbers (pos-txt pairs given by SetTacVec) +/Num { % Generic but useless. Adjust for your application. + setnum + fontheight ymm div yDisRel mul tAng sin mul /yDist x def + { dup textW xDisRel mul tAng cos mul /xDist x def + xPos aPos xAng mul add xDist sub + yPos aPos yAng mul add yDist sub 3 2 roll textCM + } TacExe + } def +/setnumDisRel { % xDisRel yDisRel | - : adjust just a little bit + /yDisRel x def /xDisRel x def + } def +1.2 1.2 setnumDisRel % default setting +% explicit Num routines for rectangular case +/xNumL { % : numbers on low x axis + setnum + { fontheight ymm div % conversion -> user_scale + dup /xNumHeightL x def + -.6 mul yPos add aPos x 3 2 roll textCT + } TacExe + } def +/xNumH { % : numbers on high x axis + setnum + { fontheight ymm div % conversion -> user_scale + dup /xNumHeightH x def + .6 mul yPos add aPos x 3 2 roll textCB + } TacExe + } def +/yNumL { % : numbers on low y axis + setnum + { fontsize -.3 mul xmm div xPos add aPos 3 2 roll textRM + xwidth dup yNumLengthL gt {/yNumLengthL x def} {pop} ifelse + } TacExe + } def +/yNumLD { % : calculate only yNumLength (used for adjustement) + setnum + { textW dup yNumLengthL gt {/yNumLengthL x def} {pop} ifelse + } TacExe + } def +/yDumL { % {(..)} yDumL : compare yNumLength with one arg (used for adjustement) + setnum + textW dup yNumLengthL gt {/yNumLengthL x def} {pop} ifelse + } def +/yNumH { % : numbers on high y axis + setnum + { fontsize .3 mul xmm div xPos add aPos 3 2 roll textLM + xwidth dup yNumLengthH gt {/yNumLengthH x def} {pop} ifelse + } TacExe + } def +/yNumHD { % : calculate only yNumLength (used for adjustement) + setnum + {textW dup yNumLengthH gt {/yNumLengthH x def} {pop} ifelse + } TacExe + } def +/yDumH { % {(..)} yDumH : compare yNumLength with one arg (used for adjustement) + setnum + textW dup yNumLengthH gt {/yNumLengthH x def} {pop} ifelse + } def + +% draw labels +/xCL { % xlabel | - ; plots coordinate name below the x-axis. + setlab + aMean xNumHeightL xNumHeightRel neg mul + 3 -1 roll textCT + } def +/xCH { % xlabel | - ; plots coordinate name above the x-axis. + setlab + aMean xNumHeightH xNumHeightRel mul 10 add + 3 -1 roll textCB + } def +/yCL { % ylabel | - ; plots coordinate name to the left of the y-axis. + gsave + setlab + yNumLengthL neg fontsize -.85 mul add % yNumLengthL calculated in yN + aMean ym translate + 0 0 mv + 90 rotate + 0 x 0 x textCB + grestore + } def +/YCH { % ylabel xpos | - ; plots coordinate name to the right of a vertical axis + gsave + setlab + yNumLengthH fontsize .85 mul add x xm add + aMean ym translate + 0 0 mv + 90 rotate + 0 x 0 x textCT + grestore + } def +/yCH { 10 YCH } def % ylabel | - ; plots coordinate name to the right of the y-axis. +/yCF { % ylabel | - ; plots coordinate name *falling* right of the y-axis. + gsave + setlab + yNumLengthH fontsize .85 mul add 10 xm add + aMEan ym translate + 0 0 mv + -90 rotate + 0 x 0 x textCB + grestore + } def + +/knautschy { % x0 y0 y_knau y_tot knautschy - : insert an S in dived y-axis + % the total height of the generated object is y_tot + % of which y_knau(.le. y_tot) is for the real knautsch, + % the remainder is for vertical prolongations. + x ym 4 div dup /tmpy x def 5 sqrt mul /tmpx x def + /tmpa x ym tmpy 4 mul sub 2 div def + np ym x xm x mv 0 tmpa rl tmpx tmpy rl tmpx -2 mul tmpy 2 mul rl + tmpx tmpy rl 0 tmpa rl st + } def +/separy { % x0 y0 sep lng ang lin - : insert an // in dived y-axis + setline + /spang x def + /splng x def + /spsep x def + 2 copy spsep sub gsave offset spang rotate + splng -.5 mul fm 0 np mv splng fm 0 rl st grestore + spsep add gsave offset spang rotate + splng -.5 mul fm 0 np mv splng fm 0 rl st grestore + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Data Plotting (Symbols and Curves) %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Initializations: + +% asymmetric error bars? +/err_asy false def % overwrite this if data are quadruples x y d- d+ + +%% Presets: + +% global preset +/SymGSet { % sradglo slinglo serrglo | - + /serrglo x def % plot error bars? 0=never, 1=always, 2=as_given_in_pset + /slinglo x def % symbol linewidth multiplier + /sradglo x def % symbol size multiplier + } def + +%% Retrieve presets from style array: + +/pstyle { pStyles setstyle } def +/cstyle { cStyles setstyle } def +/setstyle { % chosen_number array | - : set p or c as predefined in array. + dup length % i A n + 3 2 roll % A n i + dup 0 le { + pop pop pop ostyle % chosen_number<=0 means: don't plot + } { + 1 sub x % A i-1 n + mod get % A(i-1) + exec + } ifelse + } def + +%% Set plot symbol: + +/pset { % styp sfill serr srad slin | - + % arg -> symbol linewidth + /slin x slinglo mul def + % arg -> symbol size + /srad x fm 0.16 mul sradglo mul def + % arg -> plot error bar? + 2 serrglo ne { pop serrglo } if % if (serrglo=2) use serr else use serrglo + /plot_errorbar x 1 eq { { errorbar } } { { pop pop pop pop } } ifelse def + % arg -> fill the symbol? (0=open, 1=full, 2=colored_with_black_border) + /sfill x def + % adjust srad: it's the _outer_ radius + % TROUBLE sfill 1 ne {/srad srad slin fm pt sub def} if + % arg -> symbol type + /ps {ps_nil} def % default: don't plot (maybe we only want an error bar) + dup 1 eq {/ps {ps_square} def} if + dup 2 eq {/ps {ps_diamond} def} if + dup 3 eq {/ps {ps_circle} def} if + dup 4 eq {/ps {ps_triangle} def} if + dup 5 eq {/ps {ps_cedez} def} if + dup 6 eq {/ps {ps_eieruhr} def} if + dup 7 eq {/ps {ps_valve} def} if + dup 8 eq {/ps {ps_tfwd} def} if + dup 9 eq {/ps {ps_tbwd} def} if + dup 10 eq {/ps {ps_pentagram} def} if + dup 11 eq {/ps {ps_plus} def} if + dup 12 eq {/ps {ps_cross} def} if + dup 13 eq {/ps {ps_star} def} if + dup 14 eq {/ps {ps_pentagon} def} if + dup 15 eq {/ps {ps_horiz} def} if + dup 16 eq {/ps {ps_verti} def} if + pop + % + /t { % x y d[- d+] | - : plot a symbol and eventually an error bar. + err_asy not { dup } if + 4 copy pop pop plot_symbol + plot_errorbar + } bind def + /ti { t } bind def + /tf { t black } bind def + } def + +%% Set curve: + +/lset { % lwidth dashes | - + 0 setdash + dup 0 gt { + pt fm setlinewidth + % pop error bar and convert frame coord -> paper coord + /txy { err_asy { pop } if pop xym } def % x y d[- d+] | x' y' + % commands to plot points (can be overwritten by nopoints): + /ti { np txy mv } def % x y d[- d+] | - : start curve + /t { txy li } def % x y d[- d+] | - : continue curve + /tf { txy li st } def % x y d[- d+] | - : terminate and plot curve + } { + ostyle + } ifelse + } def + +%% Plot nothing: + +/ostyle { % - | - + /ti { nopoint } def + /t { nopoint } def + /tf { nopoint } def +} def +/nopoint { % x y d[- d+] | - + pop pop pop err_asy { pop } if +} def + +%% Plot an asymmetric vertical error bar: + +/errorbar { % x y d- d+ | - + gsave + slin setline + 3 copy pop pop + dup 0 gt x 10 lt and { + 4 copy + x pop add 10. 2 copy gt { x } if pop ym x xm x + 2 copy x .05 sub x np mv .1 0 rl st + np mv + pop sub 0. 2 copy lt { x } if pop ym x xm x + 2 copy lineto st + x .05 sub x np mv .1 0 rl st + } { + pop pop pop pop + } ifelse + grestore +} def + +%% Plot a data symbol: + +/plot_symbol { % x y | - + gsave + offset + srad dup scale + slin srad div setline % factor 1/srad compensates "scale" + ps % the actual plot symbol, defined by 'pset' + grestore + } def + +/fill_symbol { + sfill dup + 0 eq { + pop st + } { + 1 eq { + fill + } { + gsave fill grestore + gsave black st grestore + } ifelse + } ifelse + } def + +%% The different symbols, designed for unit area (no arguments): + +/ps_nil { + } bind def + +/ps_square { + .5 .5 np mv + 0 -1 rl + -1 0 rl + 0 1 rl cp fill_symbol + } bind def + +/ps_diamond { + gsave 45 rotate ps_square grestore + } bind def + +/ps_circle { + 0 0 np .564 0 360 arc cp fill_symbol + } bind def + +/ps_triangle { + .77 dup dup 90 pol2xy np mv + 210 pol2xy li + 330 pol2xy li cp fill_symbol + } bind def + +/ps_cedez { + gsave 180 rotate ps_triangle grestore + } bind def + +/ps_tfwd { + gsave 30 rotate ps_triangle grestore + } bind def + +/ps_tbwd { + gsave 210 rotate ps_triangle grestore + } bind def + +/ps_eieruhr { + -.7 -.7 np mv + .7 -.7 li + -.7 .7 li + .7 .7 li cp fill_symbol + } bind def + +/ps_valve { + gsave 90 rotate ps_eieruhr grestore + } bind def + +/ps_pentagram { + .8 dup dup dup dup + 90 pol2xy np mv + 234 pol2xy li + 18 pol2xy li + 162 pol2xy li + 306 pol2xy li cp fill_symbol + } bind def + +/ps_pentagon { + .8 dup dup dup dup + 18 pol2xy np mv + 90 pol2xy li + 162 pol2xy li + 234 pol2xy li + 306 pol2xy li cp fill_symbol + } bind def + +/ps_plus { + gsave 45 rotate ps_cross grestore + } bind def + +/ps_cross { + .5 .5 np mv + -1 -1 rl st + -.5 .5 np mv + 1 -1 rl st + } bind def + +/ps_star { + .7 dup 0 pol2xy np mv 180 pol2xy li st + .7 dup 120 pol2xy np mv 300 pol2xy li st + .7 dup 240 pol2xy np mv 60 pol2xy li st + } bind def + +/ps_horiz { + -.7 0 np mv + 1.4 0 rl st + } bind def + +/ps_verti { + 0 -.7 np mv + 0 1.4 rl st + } bind def + +%% Set column plotting (use this instead of pset) +/setcolumn{ % shift width exec | % + % usage: 0 .2 { gsave { .5 setgray fill } grestore cp } setcolumn + /colexec x def + /colwidth x xm def + /colshift x xm def + /t { + pop xym + np x colshift add colwidth 2 div sub dup 3 2 roll mv + colwidth 0 rl + colwidth add 0 li + colwidth neg 0 rl + cp colexec + } def + /ti { t } bind def + /tf { t black } bind def +} def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% 2D plots %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/t2d { + icCol rect fill + black +} def + +/ColorLegend { % - | - [plot color legend to rectangle hxlow hxhig 0 10] + /ncol 100 def + 1 1 ncol { + dup ncol div 10 mul icCol + dup ncol div 10 mul + x 1 sub ncol div 10 mul + hxlow hxhig 4 2 roll rect fill + } for + } def +/hColorLegend { % ditto, horizontally, to rectangle 0 10 hylow hyhig + /ncol 100 def + 1 1 ncol { + dup ncol div 10 mul icCol + dup ncol div 10 mul + x 1 sub ncol div 10 mul + hylow hyhig rect fill + } for + } def +% Usage: +% hColorLegend +% hylow hyhig 0 0 90 0 OneAxx Axx +% hylow hyhig 10 0 90 180 OneAxx Axx +% 0 10 0 hyhig 0 90 OneAxx Axx Tic Tac +% 0 10 0 0 0 90 OneAxx Axx Tic Tac xNumL +% {(intensity)} xCL + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Boxes +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/rect { % xl xh yl yh | - [path -> rectangle] + ym /qqyh x def + ym /qqyl x def + xm /qqxh x def + xm /qqxl x def + np + qqxl qqyl mv + qqxh qqyl li + qqxh qqyh li + qqxl qqyh li + cp + } def +/oval { % xl xh yl yh dr | - [path -> oval] + fm /qqdr x def + ym /qqyh x def + ym /qqyl x def + xm /qqxh x def + xm /qqxl x def + qqxl qqyl qqdr add np mv + qqxl qqyh qqdr sub li + qqxl qqdr add qqyh qqdr sub qqdr 180 90 arcn + qqxh qqdr sub qqyh li + qqxh qqdr sub qqyh qqdr sub qqdr 90 0 arcn + qqxh qqyl qqdr add li + qqxh qqdr sub qqyl qqdr add qqdr 0 -90 arcn + qqxl qqdr add qqyl li + qqxl qqdr add qqyl qqdr add qqdr -90 -180 arcn + cp + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Motifs %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/dot { % x y siz + 0 360 np arc cp fill +} def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% List %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/NewList { % xins yins size advance NewList - + /nl_advance x def setown /nl_yins x def /nl_xins x def + /nl_yorig nl_yins def + /nl_xshift fontsize xmm div .9 mul def + /nl_xrline 0.33 def + /nl_ystep fontheight ymm div nl_advance mul def + /newline { + /nl_yins nl_yins nl_ystep sub def + } def + /fracline { % frac | - + fontheight ymm div nl_advance mul mul /nl_yins x nl_yins x sub def + } def + } def +/newlist { 1.65 NewList } def +/nlbox { % width | xl xh yl yh + nl_xins add nl_xins fontwidth .4 mul sub x + nl_yins nl_ystep add fontheight 1.2 mul sub nl_yorig fontheight 1.2 mul add + } def +/TxLine { % text | - + nl_xins nl_yins 3 -1 roll textLM newline + } bind def +/TxCLine { % text | - + nl_xins nl_yins 3 -1 roll textCM newline + } bind def +/PtTxLine { % pstyle text | - + x pstyle + nl_xins nl_xshift .5 mul add nl_yins 0 t + black nl_xins nl_xshift 1.5 mul add nl_yins 3 2 roll textLM + newline + } bind def +/PttttTxLine { % pstyle text | - %% chain of very small symbols + x pstyle + nl_xins nl_xshift .10 mul add nl_yins 0 t + nl_xins nl_xshift .26 mul add nl_yins 0 t + nl_xins nl_xshift .42 mul add nl_yins 0 t + nl_xins nl_xshift .58 mul add nl_yins 0 t + nl_xins nl_xshift .74 mul add nl_yins 0 t + nl_xins nl_xshift .90 mul add nl_yins 0 t + black nl_xins nl_xshift 1.5 mul add nl_yins 3 2 roll textLM + newline + } bind def +/PtPtCvTxLine { % pstyle pstyle cstyle text | - + 4 3 roll pstyle nl_xins nl_yins 0 t + 3 2 roll pstyle nl_xins nl_xshift add nl_yins 0 t + x cstyle + nl_xins nl_xshift 2 mul add + dup dup nl_xshift nl_xrline mul sub nl_yins 0 ti + nl_xshift nl_xrline mul add nl_yins 0 tf + nl_xshift add nl_yins 3 2 roll black textLM + newline + } bind def +/PtCvTxLine { % pstyle cstyle text | - + 3 2 roll pstyle nl_xins nl_yins 0 t + x cstyle + nl_xins nl_xshift 1 mul add + dup dup nl_xshift -.33 mul add nl_yins 0 ti + nl_xshift 0.33 mul add nl_yins 0 tf + nl_xshift add nl_yins 3 2 roll black textLM + newline + } bind def +/PtPtTxLine { % pstyle pstyle text | - + 3 2 roll pstyle nl_xins nl_yins 0 t + x pstyle nl_xins nl_xshift add nl_yins 0 t + black nl_xins nl_xshift 2 mul add nl_yins 3 2 roll textLM + newline + } bind def +/CvTxLine { % cstyle text | - + x cstyle + nl_xins fontsize xmm div nl_xrline mul 0 mul sub nl_yins 0 ti + nl_xins fontsize xmm div nl_xrline mul 3 mul add nl_yins 0 tf + black nl_xins nl_xshift 1.5 mul add nl_yins 3 2 roll textLM + newline + } bind def +/Cv2TxLine { % cstyle text | - + x cstyle + nl_xins fontsize xmm div nl_xrline mul sub nl_yins 0 ti + nl_xins fontsize xmm div nl_xrline mul add nl_xshift add nl_yins 0 tf + black nl_xins nl_xshift 2 mul add nl_yins 3 2 roll textLM + newline + } bind def +/PCTxLine { % pstyle(with plset) text | - + x pstyle + nl_xins fontsize xmm div nl_xrline 2 mul mul sub nl_yins 0 ci + nl_xins fontsize xmm div nl_xrline 2 mul mul add nl_yins 0 cf + nl_xins yins 0 t + black nl_xins + fontsize xmm div 1.9 mul % instead of xshift + add nl_yins 3 2 roll textLM + newline + } bind def +/infSet { % oooinfo | - : set whether(1) or not(0) to plot info block + /oooinfo x def + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Arrows +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/pfeilangle 36.87 def +/pfeilspitze { % x[local] y[local] rot siz + % draw with current linestyle, as set e.g. by linsetAxx + x 4 2 roll % siz rot x y + gsave + xym translate 180 add rotate dup dup dup + [] 0 setdash + pfeilangle cos mul x pfeilangle sin mul np mv + 0 0 li pfeilangle cos mul x pfeilangle sin neg mul li st + grestore + } def +/pfeiL { % (arrow anchored at base) x y rot siz len + gsave + dup xm x ym mul sqrt % (scale len) + 5 3 roll + xym translate % (origin at base) rot siz len + 3 2 roll + rotate % (draw rightwards) siz len + dup 0 translate % (origin at head) siz len + x 0 0 0 4 3 roll pfeilspitze % len + 0 0 np mv neg 0 li st + grestore + } def +/Pfeil { % (arrow anchored at head) x y rot siz len + dup xm x ym mul sqrt 5 copy + pop pfeilspitze + x pop + x 4 2 roll % len rot x y + gsave + xym translate 180 add rotate + 0 0 np mv 0 li st + grestore + } def +/pfeil { % xi xf yi yf siz + gsave + 5 1 roll + 4 copy + 4 1 roll pop x pop x offset + sub 3 1 roll sub x 2 copy + x atan 180 add 3 1 roll + 0 0 np mv li st + x 0 0 4 2 roll pfeilspitze + grestore +} def + +/bemasz { % x y L ang text | - %% precede by '24 setown 1 [] lset /pfeilangle 90 def' + gsave + 5 3 roll offset % consumes x and y + x rotate % consumes ang | L text + dup textw .5 mul fontheight .4 mul add /bmszDT x def % => half text width + 0 0 3 2 roll textCM % L + .5 mul /bmszDX x def % => half bemasz length + bmszDX 0 0 fontheight .67 mul bmszDX bmszDT sub Pfeil + bmszDX neg 0 180 fontheight .67 mul bmszDX bmszDT sub Pfeil + grestore + } def + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Text macros +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +/Celsius { showif (\26x)g(C) showif } bind def +/hbar { + showif + (h) 1.2 .66 { + currentpoint fontheight .11 mul setline np mv + fontheight dup .8 mul x .3 mul rl + st () + } build + } bind def + +%% for neutron scattering: + +/hbarw { hbar () grec (w) endgr } bind def +/wbar { grec (w) endgr ( / 2) grec (p) endgr } bind def +/taumean { () (\341t\361) g } bind def +/Sqw { showif (S\(q,) grec (w) endgr (\)) showif } bind def +/Sqn { showif (S\(q,) grec (n) endgr (\)) showif } bind def +/SQw { showif (S\(Q,) grec (w) endgr (\)) showif } bind def +/Sttw { showif (S\(2) grec (q) endgr (,) grec (w) endgr (\)) showif } bind def +/Sttn { showif (S\(2) grec (q) endgr (,) grec (n) endgr (\)) showif } bind def +/Xqw { grec (c) endgr (''\(q,) grec (w) endgr (\)) showif } bind def +/Xqn { grec (c) endgr (''\(q,) grec (n) endgr (\)) showif } bind def +/ueV{ grec (m) endgr (eV) showif} bind def +/inueV { showif (\() grec (m) endgr (eV\)) showif } bind def +/inmeVr { showif (\(meV) supsc (-1) endsc (\)) showif } bind def +/inueVr { showif (\() grec (m) endgr (eV) + supsc (-1) endsc (\)) showif } bind def +/inGHzr { showif (\(GHz) (-1) sp (\)) showif } def +/inDeg { showif (\() (\260)g (\)) showif } def + +/Angstr { showif (\305) showif } bind def +/Angr { showif (\305) supsc (-1) endsc } bind def +/inAngr { showif (\() Angr (\)) showif } bind def +/Angrr { showif (\305) supsc (-2) endsc } bind def +/inAngrr { showif (\() Angrr (\)) showif } bind def +/wmin {grec (w) endgr () subsc (min) endsc} def +/winpi { grec (w) endgr ( / 2) grec (p) endgr } def + +end % WuGdict... + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Mark "ewu", the end of the wups.. macro definition file %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +WuGdict18a begin + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Customizable plot setup, copied from setup1D.ps +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +7 dup autolabel defsiz +1 dup geld stdred +2 -11 setnewpage newpage + +2 4 12.6 -12.6 setpagegrid +2 8 24 abcset % usage: {(text)} abc +/EndFrame { nextFrame end } def + +1 1 language +0 infSet % plot info block? +.8 1.2 2 SymGSet % srad slin serr(2=from pset) : graph symbols, global preset +% /setboxbackgroundcolor { 0.93 setgray } def % default is white +% setPalatino + +{ 9 aCol7 iColA } /ipCol x bind def % number of colours and colour style +/pStyles [ + { 11 0 0 1. 1. pset 0 ipCol } + { 12 1 0 1. 1. pset 1 ipCol } + { 13 1 0 1. 1. pset 2 ipCol } + { 1 0 0 .9 1. pset 3 ipCol } + { 1 1 0 .8 1. pset 4 ipCol } + { 3 0 0 .9 1. pset 5 ipCol } + { 3 1 0 .8 1. pset 6 ipCol } + { 4 0 0 .9 1. pset 7 ipCol } + { 4 1 0 .8 1. pset 8 ipCol } + { 5 0 0 .9 1. pset 0 ipCol } + { 5 1 0 .8 1. pset 1 ipCol } + { 2 0 0 .9 1. pset 2 ipCol } + { 2 1 0 .8 1. pset 3 ipCol } + { 11 0 0 1. 1. pset 4 ipCol } + { 12 1 0 1. 1. pset 5 ipCol } + { 13 1 0 1. 1. pset 6 ipCol } + ] def + +{ 3 aCol1 iColA } /icCol x bind def % number of colours and colour style +/cStyles [ + { 1. [] lset 0 icCol } + { 1. [] lset 1 icCol } + { 1. [] lset 2 icCol } + ] def + +Resets +BoxBackground + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Mark "ecu", end of the customization section +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% output created by Frida version post-2.4.4a + +1 0.03 30 xSetCoord +1 0.02 2 ySetCoord + +% x axis: +[ + 0.1 wx {(0.1)} + 1 wx {(1)} + 10 wx {(10)} + ] SetTacVec +0.01 wx 100 wx 5 9 SetTicVecLog + 0 10 0 0 0 90 OneAxx Axx Tic Tac xNumL %% low x axis + 0 10 0 10 0 270 OneAxx Axx Tic Tac %% top x axis +{(x)} xCL + +% y axis: +[ + 0.1 wy {(0.1)} + 1 wy {(1)} + ] SetTacVec +0.01 wy 10 wy 4 9 SetTicVecLog + 0 10 0 0 90 0 OneAxx Axx Tic Tac yNumL %% left y axis + 0 10 10 0 90 180 OneAxx Axx Tic Tac %% right y axis +{(tanhc x)} yCL + + + 1 [ 0.100000 ] zValues + 1 cstyle % (x () -> y ()) + 0.00000 8.49420 0.00000 ti % 0.03 wx 0.9997001 wy + 0.26756 8.49391 0.00000 t % 0.03609016 wx 0.9995661 wy + 0.53512 8.49349 0.00000 t % 0.04341666 wx 0.9993721 wy + 0.80268 8.49288 0.00000 t % 0.05223047 wx 0.9990917 wy + 0.93645 8.49248 0.00000 t % 0.05728721 wx 0.9989075 wy + 1.07023 8.49199 0.00000 t % 0.06283353 wx 0.9986861 wy + 1.20401 8.49142 0.00000 t % 0.06891683 wx 0.9984198 wy + 1.33779 8.49072 0.00000 t % 0.07558908 wx 0.9980998 wy + 1.47157 8.48988 0.00000 t % 0.08290731 wx 0.9977151 wy + 1.60535 8.48888 0.00000 t % 0.09093407 wx 0.9972528 wy + 1.73913 8.48767 0.00000 t % 0.09973794 wx 0.9966973 wy + 1.80602 8.48697 0.00000 t % 0.1044545 wx 0.9963789 wy + 1.87291 8.48621 0.00000 t % 0.1093942 wx 0.99603 wy + 1.93980 8.48538 0.00000 t % 0.1145674 wx 0.9956476 wy + 2.00669 8.48446 0.00000 t % 0.1199853 wx 0.9952287 wy + 2.07358 8.48346 0.00000 t % 0.1256594 wx 0.9947696 wy + 2.14047 8.48236 0.00000 t % 0.1316018 wx 0.9942667 wy + 2.20736 8.48116 0.00000 t % 0.1378252 wx 0.9937158 wy + 2.27425 8.47984 0.00000 t % 0.1443429 wx 0.9931124 wy + 2.34114 8.47840 0.00000 t % 0.1511689 wx 0.9924516 wy + 2.40803 8.47681 0.00000 t % 0.1583176 wx 0.9917281 wy + 2.47492 8.47508 0.00000 t % 0.1658044 wx 0.990936 wy + 2.54181 8.47318 0.00000 t % 0.1736453 wx 0.9900689 wy + 2.60870 8.47109 0.00000 t % 0.181857 wx 0.9891199 wy + 2.67559 8.46881 0.00000 t % 0.190457 wx 0.9880816 wy + 2.74247 8.46632 0.00000 t % 0.1994636 wx 0.9869458 wy + 2.80936 8.46358 0.00000 t % 0.2088962 wx 0.9857036 wy + 2.84281 8.46212 0.00000 t % 0.2137785 wx 0.9850397 wy + 2.87625 8.46059 0.00000 t % 0.2187749 wx 0.9843455 wy + 2.90970 8.45899 0.00000 t % 0.2238881 wx 0.9836197 wy + 2.94314 8.45731 0.00000 t % 0.2291207 wx 0.982861 wy + 2.97659 8.45556 0.00000 t % 0.2344757 wx 0.982068 wy + 3.01003 8.45372 0.00000 t % 0.2399558 wx 0.981239 wy + 3.04348 8.45181 0.00000 t % 0.245564 wx 0.9803727 wy + 3.07692 8.44980 0.00000 t % 0.2513033 wx 0.9794674 wy + 3.11037 8.44770 0.00000 t % 0.2571767 wx 0.9785214 wy + 3.14381 8.44551 0.00000 t % 0.2631874 wx 0.9775331 wy + 3.17726 8.44321 0.00000 t % 0.2693385 wx 0.9765006 wy + 3.21070 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