From f40e284218890c17a48ff35227862c3e777e29b4 Mon Sep 17 00:00:00 2001
From: eneller <erikneller@gmx.de>
Date: Sun, 17 May 2026 16:09:04 +0200
Subject: [PATCH] hw4 functions

---
 hw4.Rmd | 42 ++++++++++++++++++++++++++++++++----------
 1 file changed, 32 insertions(+), 10 deletions(-)

diff --git a/hw4.Rmd b/hw4.Rmd
index ebd251c..ef02c45 100644
--- a/hw4.Rmd
+++ b/hw4.Rmd
@@ -149,11 +149,12 @@ $\lambda_I$ in radians, $t$ in seconds.
 where $0 \leq t \leq 86 400$. Therefore:
 If $t \geq 86 400$, subtract $86 400$. If $t < 0$, add $86 400$.
 ```{r klob-5}
-tGPS = 1 # TODO
-t = 43200 * lambda_I / pi + tGPS 
+t <- function(tGPS){
+  43200 * lambda_I / pi + tGPS
+}
 ```
 ```{r klob-5-demo}
-t
+t(1)
 ```
 
 ### 6. Compute the amplitude of ionospheric delay
@@ -188,10 +189,12 @@ P_I
 $$ X_I = \frac{2\pi ( t-50400)}{P_I}$$
 
 ```{r klob-8}
-X_I = (2 * pi * (t-50400))/P_I
+X_I <- function(tGPS){
+  (2 * pi * (t(tGPS)-50400))/P_I
+}
 ```
 ```{r klob-8-demo, echo=FALSE}
-X_I
+X_I(1)
 ```
 
 ### 9. Compute the slant factor (ionospheric mapping function)
@@ -214,15 +217,34 @@ I_1 = \begin{cases}
 $$
 
 ```{r klob-10}
-if (abs(X_I)< pi/2) {
-  I_1 = (5e-9 + A_I * cos(X_I)) * F
-}else{
-  I_1 = 5e-9 * F
+I_1 <- function(tGPS){
+  if (abs(X_I(tGPS))< pi/2) {
+    I_1 = (5e-9 + A_I * cos(X_I(tGPS))) * F
+  }else{
+    I_1 = 5e-9 * F
+  }
+I_1
 }
 ```
 
 ```{r klob-10-demo, echo=FALSE}
-I_1
+I_1(1)
 ```
 The delay $I_1$ is given in seconds and is referred to the GPS L1 or
 Beidou B1 frequencies.
+
+# 24-hour simulation
+```{r simulate}
+xs <- seq(from = 0, to = 24*60, by = 1)
+ys <- numeric(length(xs))
+for (x in xs){
+  y  <- I_1(x*60)
+  ys[x] <- y
+}
+```
+
+```{r simulate-demo, echo=FALSE}
+head(ys)
+plot(xs,ys,xlab="Time of Day [Minutes]",ylab="Delay [s]") 
+  
+```
\ No newline at end of file