Probit model in winbugs - winbugs

I conducted an analysis using a logit model and now want to do the same using a probit model. Can anyone please turn this winbugs logit model into a winbugs probit model?
model
{
for (i in 1:n) {
# Linear regression on logit
logit(p[i]) <- alpha + b.sex*sex[i] + b.age*age[i]
# Likelihood function for each data point
frac[i] ~ dbern(p[i])
}
alpha ~ dnorm(0.0,1.0E-4) # Prior for intercept
b.sex ~ dnorm(0.0,1.0E-4) # Prior for slope of sex
b.age ~ dnorm(0.0,1.0E-4) # Prior for slope of age
}
Data
list(sex=c(1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1,
1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0,
0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1,
0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1),
age= c(69, 57, 61, 60, 69, 74, 63, 68, 64, 53, 60, 58, 79, 56, 53, 74, 56, 76, 72,
56, 66, 52, 77, 70, 69, 76, 72, 53, 69, 59, 73, 77, 55, 77, 68, 62, 56, 68, 70, 60,
65, 55, 64, 75, 60, 67, 61, 69, 75, 68, 72, 71, 54, 52, 54, 50, 75, 59, 65, 60, 60,
57, 51, 51, 63, 57, 80, 52, 65, 72, 80, 73, 76, 79, 66, 51, 76, 75, 66, 75, 78, 70,
67, 51, 70, 71, 71, 74, 74, 60, 58, 55, 61, 65, 52, 68, 75, 52, 53, 70),
frac=c(1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0,
1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1,
1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 0, 0, 1, 0, 0, 1),
n=100)
Initial Values
list(alpha=0, b.sex=1, b.age=1)


WinBUGS accepts multiple types of link functions (see page 15 in the WinBUGS manual). For a probit model, change your linear regression equation to:
probit(p[i]) <- alpha + b.sex*sex[i] + b.age*age[i]
I would recommend you center the age variable, otherwise you may well run into some convergence problems, so something like:
probit(p[i]) <- alpha + b.sex*sex[i] + b.age*(age[i] - mean(age[]))
Alternatively, for a probit model (if the probit functions gives you some trap errors) you could use the phi standard normal cdf function:
p[i] <- phi(alpha + b.sex*sex[i] + b.age*(age[i] - mean(age[])))

Related

Seq sortWith function with strange behaviour

I was trying to sort elements of a Seq object with the sortWith function when I got an exception. I didn't use the sorted function because the code below is a simplification of the real code where the seq has tuples instead of ints.
See below that in the last two cases, when comparing with (v1 <= v2) an exception is thrown, but when comparing with (v1 < v2) no exception is thrown.
heitor#heitor-340XAA-350XAA-550XAA:~$ sbt console
[info] welcome to sbt 1.6.2 (Ubuntu Java 11.0.11)
[info] loading settings for project global-plugins from sbt-updates.sbt ...
[info] loading global plugins from /home/heitor/.sbt/1.0/plugins
[info] loading project definition from /home/heitor/project
[info] loading settings for project root from build.sbt ...
[info] set current project to example (in build file:/home/heitor/)
[info] Starting scala interpreter...
Welcome to Scala 2.13.8 (OpenJDK 64-Bit Server VM, Java 11.0.11).
Type in expressions for evaluation. Or try :help.
scala> val lst69 = List(1, 10, 4, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 4, 10, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1)
val lst69: List[Int] = List(1, 10, 4, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 4, 10, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1)
scala> lst69.size
val res0: Int = 69
scala> val lst68 = lst69.take(68)
val lst68: List[Int] = List(1, 10, 4, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 4, 10, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1)
scala> lst68.size
val res1: Int = 68
scala> lst68.sorted
val res2: List[Int] = List(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 10, 10)
scala> lst68.sortWith{ case (v1,v2) => (v1 <= v2) }
val res3: List[Int] = List(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 10, 10)
scala> lst69.sorted
val res4: List[Int] = List(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 10, 10)
scala> lst69.sortWith{ case (v1,v2) => (v1 <= v2) }
java.lang.IllegalArgumentException: Comparison method violates its general contract!
at java.base/java.util.TimSort.mergeHi(TimSort.java:903)
at java.base/java.util.TimSort.mergeAt(TimSort.java:520)
at java.base/java.util.TimSort.mergeForceCollapse(TimSort.java:461)
at java.base/java.util.TimSort.sort(TimSort.java:254)
at java.base/java.util.Arrays.sort(Arrays.java:1441)
at scala.collection.SeqOps.sorted(Seq.scala:700)
at scala.collection.SeqOps.sorted$(Seq.scala:692)
at scala.collection.immutable.List.scala$collection$immutable$StrictOptimizedSeqOps$$super$sorted(List.scala:79)
at scala.collection.immutable.StrictOptimizedSeqOps.sorted(StrictOptimizedSeqOps.scala:78)
at scala.collection.immutable.StrictOptimizedSeqOps.sorted$(StrictOptimizedSeqOps.scala:78)
at scala.collection.immutable.List.sorted(List.scala:79)
at scala.collection.SeqOps.sortWith(Seq.scala:727)
at scala.collection.SeqOps.sortWith$(Seq.scala:727)
at scala.collection.AbstractSeq.sortWith(Seq.scala:1161)
... 59 elided
scala> lst69.sortWith{ case (v1,v2) => (v1 < v2) }
val res6: List[Int] = List(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 10, 10)
scala> ```

You can try instead:
lst69.sortWith{ case (v1,v2) => (v1 < v2 || v1 == v2 ) }

why is this VRP problem taking so long to solve with the AUTOMATIC first solution strategy?

I've modified the data in https://developers.google.com/optimization/routing/vrptw to my specific problem - see below.
If I'm trying with FirstSolutionStrategy.PATH_CHEAPEST_ARC or FirstSolutionStrategy.AUTOMATIC, it takes 42 seconds to solve this tiny problem!
If I'm changing to FirstSolutionStrategy.PATH_MOST_CONSTRAINED_ARC it solves within 3ms.
Why is the solver so sensitive to this setting? Is there some mode in which the solver tries all strategies in parallel and selects the fastest or the best one?
def create_data_model():
"""Stores the data for the problem."""
data = {}
data['time_matrix'] = [
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1000, 99999, 99999, 99999, 99999, 99999, 73, 104, 113, 117, 99999],
[1000, 99999, 99999, 99999, 99999, 99999, 84, 99999, 122, 125, 99999],
[1000, 99999, 99999, 99999, 99999, 99999, 97, 75, 122, 125, 99999],
[1000, 99999, 99999, 99999, 99999, 99999, 99999, 61, 109, 114, 103],
[1000, 99999, 99999, 99999, 99999, 99999, 47, 99999, 83, 89, 77],
[1000, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99, 92],
[1000, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 88, 94],
[1000, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 42, 64],
[1000, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 51],
[1000, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999]]
data['time_windows'] = [(0, 10000), (435, 450), (450, 465), (450, 465), (475, 490), (480, 495), (540, 555), (540, 555), (600, 615), (720, 735), (810, 825)]
data['num_vehicles'] = 5
data['depot'] = 0
return data
also changed the time dimension:
routing.AddDimension(
transit_callback_index,
10000, # allow waiting time
10000, # maximum time per vehicle
True, # Don't force start cumul to zero.
time)

Numpy array: Conditional encoding

I have following numpy array:
array([1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 2, 3, 3, 3, 3, 1, 1, 1, 1,
1, 3, 1, 1, 3, 0, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 0, 1, 2, 0, 2,
2, 2, 1, 2, 2, 0, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 0, 2, 1, 1,
1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 0, 2, 3,
2, 1, 1, 1, 1, 3, 1, 0])
Question: How can I create another array that encodes the data, given condition: If value = 3 or 2, then "1", else "0".
I tried:
from sklearn.preprocessing import label_binarize
label_binarize(doc_topics, classes=[3,2])[:15]
array([[0, 0],
[0, 0],
[0, 0],
[1, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 1],
[0, 0],
[0, 0],
[0, 0],
[0, 1]])
However, this seems to return a 2-D array.

Use np.where and pass your condition to mask the elements of interest to set where the condition is met to 1, 0 otherwise:
In[18]:
a = np.where((a==3) | (a == 2),1,0)
a
Out[18]:
array([0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0,
0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1,
0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0])
Here we compare the array with the desired values, and use the unary | to or the conditions, due to operator precedence we have to use parentheses () around the conditions.
To do this using sklearn:
In[68]:
binarizer = preprocessing.Binarizer(threshold=1)
binarizer.transform(a.reshape(1,-1))
Out[68]:
array([[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0,
0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1,
0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]])
This treats values above 1 as 1 and 0 otherwise, this only works for this specific data set as you want 2 and 3 to be 1, it won't work if you have other values, so the numpy method is more general

Compare an element from a map with the rest of the map

I'm trying to select the last element from a map and compare it against the other last elements in the map to say if the selected element is higher or lower.
So far I can get it to select the element from user input but cannot work out how to loop through the map and get it to compare against the other elements:
def menu(f: (String) => (String, Int)) = {
print("Number > ")
val data = f(readLine)
println(s"${data._1}: ${data._2}")
}
Here is the map which the elements are coming from:
val mapdata = Map(
"A1" -> List(9, 7, 2, 0, 0, 2, 7, 9, 1, 2, 4, 1, 9, 6, 5, 3, 2, 3, 7, 2, 8, 5, 4, 5, 1, 6, 5, 2, 4, 1),
"B2" -> List(0, 7, 6, 3, 3, 3, 1, 2, 9, 2, 9, 7, 4, 7, 3, 6, 3, 9, 5, 2, 9, 7, 3, 4, 6, 3, 4, 3, 4, 1),
"C3" -> List(8, 7, 1, 8, 0, 5, 8, 0, 5, 9, 7, 5, 3, 7, 9, 8, 1, 4, 6, 5, 6, 6, 3, 6, 8, 8, 7, 4, 0, 6),
"D4" -> List(2, 9, 5, 7, 3, 8, 6, 9, 7, 9, 0, 1, 3, 1, 3, 0, 0, 1, 3, 8, 5, 4, 0, 9, 7, 1, 4, 5, 2, 9),
"E5" -> List(2, 6, 8, 0, 3, 5, 2, 1, 5, 9, 4, 5, 3, 5, 5, 8, 8, 2, 5, 9, 3, 8, 6, 7, 8, 7, 4, 1, 2, 3),
"F6" -> List(2, 7, 5, 9, 1, 9, 2, 4, 1, 6, 3, 7, 4, 3, 4, 5, 9, 2, 2, 4, 8, 7, 9, 2, 2, 7, 9, 1, 6, 9),
"G7" -> List(6, 9, 5, 0, 8, 0, 0, 5, 8, 5, 8, 7, 1, 6, 6, 1, 5, 2, 2, 7, 9, 5, 5, 9, 1, 4, 4, 0, 2, 0),
"H8" -> List(2, 8, 8, 3, 2, 1, 1, 8, 5, 9, 0, 2, 1, 6, 9, 7, 9, 6, 7, 7, 0, 9, 5, 2, 5, 0, 2, 1, 8, 6),
"I9" -> List(2, 1, 8, 2, 4, 4, 2, 4, 9, 4, 0, 6, 9, 5, 9, 4, 9, 1, 8, 6, 3, 4, 4, 3, 7, 9, 1, 2, 6, 6)
)
for example I select H8 and its last element is 6
I then want to compare it to all last elements and say if it is higher or lower than each of the last elements.
Thanks in advance

I'm not sure if I understand you correctly. You can access last element of the list by calling last.
object A extends App {
val mapdata: Map[String, List[Int]] = Map(
"A1" -> List(9, 7, 2, 0, 0, 2, 7, 9, 1, 2, 4, 1, 9, 6, 5, 3, 2, 3, 7, 2, 8, 5, 4, 5, 1, 6, 5, 2, 4, 1),
"B2" -> List(0, 7, 6, 3, 3, 3, 1, 2, 9, 2, 9, 7, 4, 7, 3, 6, 3, 9, 5, 2, 9, 7, 3, 4, 6, 3, 4, 3, 4, 1),
"C3" -> List(8, 7, 1, 8, 0, 5, 8, 0, 5, 9, 7, 5, 3, 7, 9, 8, 1, 4, 6, 5, 6, 6, 3, 6, 8, 8, 7, 4, 0, 6),
"D4" -> List(2, 9, 5, 7, 3, 8, 6, 9, 7, 9, 0, 1, 3, 1, 3, 0, 0, 1, 3, 8, 5, 4, 0, 9, 7, 1, 4, 5, 2, 9),
"E5" -> List(2, 6, 8, 0, 3, 5, 2, 1, 5, 9, 4, 5, 3, 5, 5, 8, 8, 2, 5, 9, 3, 8, 6, 7, 8, 7, 4, 1, 2, 3),
"F6" -> List(2, 7, 5, 9, 1, 9, 2, 4, 1, 6, 3, 7, 4, 3, 4, 5, 9, 2, 2, 4, 8, 7, 9, 2, 2, 7, 9, 1, 6, 9),
"G7" -> List(6, 9, 5, 0, 8, 0, 0, 5, 8, 5, 8, 7, 1, 6, 6, 1, 5, 2, 2, 7, 9, 5, 5, 9, 1, 4, 4, 0, 2, 0),
"H8" -> List(2, 8, 8, 3, 2, 1, 1, 8, 5, 9, 0, 2, 1, 6, 9, 7, 9, 6, 7, 7, 0, 9, 5, 2, 5, 0, 2, 1, 8, 6),
"I9" -> List(2, 1, 8, 2, 4, 4, 2, 4, 9, 4, 0, 6, 9, 5, 9, 4, 9, 1, 8, 6, 3, 4, 4, 3, 7, 9, 1, 2, 6, 6)
)
val choice = "H8"
val numberToBeCompared = mapdata.getOrElse(choice, throw new RuntimeException(s"couldn't find $choice")).last
mapdata.filter(_._1 != choice)
.values
.foreach(list => {
if (list.last > numberToBeCompared)
println(s"${list.last} > $numberToBeCompared")
else
println(s"${list.last} <= $numberToBeCompared")
})
}
Result:
1 <= 6
1 <= 6
0 <= 6
3 <= 6
9 > 6
9 > 6
6 <= 6
6 <= 6
Is this what you need ?
Note that I still learn Scala so there's probably better way of doing this.
I also don't know if any list in mapdata can be empty so use Option if necessary.
// EDIT
If you want the letters you may try sth like this:
val choice = "H8"
val numberToBeCompared = mapdata.getOrElse(choice, throw new RuntimeException(s"couldn't find $choice")).last
mapdata.filter(_._1 != choice)
.foreach(entry => {
if (entry._2.last > numberToBeCompared)
println(s"${choice} > ${entry._1}")
else
println(s"${choice} <= ${entry._1}")
})
H8 <= A1
H8 <= B2
H8 <= G7
H8 <= E5
H8 > D4
H8 > F6
H8 <= C3
H8 <= I9
You just need to remember that when you iterate through mapdata you get entry. entry._1 is the key (your string), entry._2 is the list.

easiest way to prototype a symbolic orthogonal matrix

I have 8 sins and cosines that I try to symbolically define as shown below using Matlab. My goal is to symbolically build a matrix H (accumulated Givens rotations matrix) of 8x8 using all these sins and cosines and end up seeing what the formula for this H orthogonal projection matrix is. I can do that using the code below conceptually G7*G6*...*G0*I where I is the Identity 8x8 and the Gi are the Givens rotation corresponding to elements (i:i+1,i:i+1).
c_0 = sym('c_0');
c_1 = sym('c_1');
c_2 = sym('c_2');
c_3 = sym('c_3');
c_4 = sym('c_4');
c_5 = sym('c_5');
c_6 = sym('c_6');
c_7 = sym('c_7');
s_0 = sym('s_0');
s_1 = sym('s_1');
s_2 = sym('s_2');
s_3 = sym('s_3');
s_4 = sym('s_4');
s_5 = sym('s_5');
s_6 = sym('s_6');
s_7 = sym('s_7');
% create H orthogonal matrix using the sin and cos symbols
% filling in the first rotation
I=eye(9,9)
H = I;
H(1:2,1:2) = [c_0 -s_0; s_0 c_0]
% build the 2nd rotation and update H
G = I;
G(2:3,2:3) = [c_1 -s_1; s_1 c_1]
H = G*H
% build the 3rd rotation and update H
G = I;
G(3:4,3:4) = [c_2 -s_2; s_2 c_2]
H = G*H
% build the 4rth rotation and update H
G = I;
G(4:5,4:5) = [c_3 -s_3; s_3 c_3]
H = G*H
% build the 5th rotation and update H
G = I;
G(5:6,5:6) = [c_4 -s_4; s_4 c_4]
H = G*H
% build the 6th rotation and update H
G = I;
G(6:7,6:7) = [c_5 -s_5; s_5 c_5]
H = G*H
% build the 7th rotation and update H
G = I;
G(7:8,7:8) = [c_6 -s_6; s_6 c_6]
H = G*H
% build the 8th rotation and update H
G = I;
G(8:9,8:9) = [c_7 -s_7; s_7 c_7]
H = G*H
The code fails with the following error and can't find how to fix this:
The following error occurred converting from sym to double:
Error using mupadmex
Error in MuPAD command: DOUBLE cannot convert the input expression into a double array.
If the input expression contains a symbolic variable, use the VPA function instead.
Error in build_rotH_test (line 26)
H(1:2,1:2) = [c_0 -s_0; s_0 c_0]

I solved it like this. Note I realized I need the transpose of each rotation so I can build and apply H'*x i.e. G7'*G6'*...*G0'*I that's why the sin signs are flipped in the solution.
clear all;
% defining 0 and 1 as symbols too, solves the problem
sym_0 = sym('0');
sym_1 = sym('1');
c0 = sym('c0');
c1 = sym('c1');
c2 = sym('c2');
c3 = sym('c3');
c4 = sym('c4');
c5 = sym('c5');
c6 = sym('c6');
c7 = sym('c7');
s0 = sym('s0');
s1 = sym('s1');
s2 = sym('s2');
s3 = sym('s3');
s4 = sym('s4');
s5 = sym('s5');
s6 = sym('s6');
s7 = sym('s7');
% create H orthogonal matrix using the sin and cos symbols
% filling in the first rotation
I = repmat(sym_0,9,9);
for i=1:9
I(i,i)=sym_1;
end
H = I
H(1:2,1:2) = [c0 s0; -s0 c0]
% build the 2nd rotation and update H
G = I;
G(2:3,2:3) = [c1 s1; -s1 c1]
H = G*H;
% build the 3rd rotation and update H
G = I;
G(3:4,3:4) = [c2 s2; -s2 c2]
H = G*H;
% build the 4rth rotation and update H
G = I;
G(4:5,4:5) = [c3 s3; -s3 c3]
H = G*H;
% build the 5th rotation and update H
G = I;
G(5:6,5:6) = [c4 s4; -s4 c4]
H = G*H;
% build the 6th rotation and update H
G = I;
G(6:7,6:7) = [c5 s5; -s5 c5]
H = G*H;
% build the 7th rotation and update H
G = I;
G(7:8,7:8) = [c6 s6; -s6 c6]
H = G*H;
% build the 8th rotation and update H
G = I;
G(8:9,8:9) = [c7 s7; -s7 c7]
H = G*H
and the output is:
H =
[ 1, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 1, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 1, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 1, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 1, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 1, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 1, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 1, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 1]
H =
[ c0, s0, 0, 0, 0, 0, 0, 0, 0]
[ -s0, c0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 1, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 1, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 1, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 1, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 1, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 1, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 1]
G =
[ 1, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, c1, s1, 0, 0, 0, 0, 0, 0]
[ 0, -s1, c1, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 1, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 1, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 1, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 1, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 1, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 1]
G =
[ 1, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 1, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, c2, s2, 0, 0, 0, 0, 0]
[ 0, 0, -s2, c2, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 1, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 1, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 1, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 1, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 1]
G =
[ 1, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 1, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 1, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, c3, s3, 0, 0, 0, 0]
[ 0, 0, 0, -s3, c3, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 1, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 1, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 1, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 1]
G =
[ 1, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 1, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 1, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 1, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, c4, s4, 0, 0, 0]
[ 0, 0, 0, 0, -s4, c4, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 1, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 1, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 1]
G =
[ 1, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 1, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 1, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 1, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 1, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, c5, s5, 0, 0]
[ 0, 0, 0, 0, 0, -s5, c5, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 1, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 1]
G =
[ 1, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 1, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 1, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 1, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 1, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 1, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, c6, s6, 0]
[ 0, 0, 0, 0, 0, 0, -s6, c6, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 1]
G =
[ 1, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 1, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 1, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 1, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 1, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 1, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 1, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, c7, s7]
[ 0, 0, 0, 0, 0, 0, 0, -s7, c7]
H =
[ c0, s0, 0, 0, 0, 0, 0, 0, 0]
[ -c1*s0, c0*c1, s1, 0, 0, 0, 0, 0, 0]
[ c2*s0*s1, -c0*c2*s1, c1*c2, s2, 0, 0, 0, 0, 0]
[ -c3*s0*s1*s2, c0*c3*s1*s2, -c1*c3*s2, c2*c3, s3, 0, 0, 0, 0]
[ c4*s0*s1*s2*s3, -c0*c4*s1*s2*s3, c1*c4*s2*s3, -c2*c4*s3, c3*c4, s4, 0, 0, 0]
[ -c5*s0*s1*s2*s3*s4, c0*c5*s1*s2*s3*s4, -c1*c5*s2*s3*s4, c2*c5*s3*s4, -c3*c5*s4, c4*c5, s5, 0, 0]
[ c6*s0*s1*s2*s3*s4*s5, -c0*c6*s1*s2*s3*s4*s5, c1*c6*s2*s3*s4*s5, -c2*c6*s3*s4*s5, c3*c6*s4*s5, -c4*c6*s5, c5*c6, s6, 0]
[ -c7*s0*s1*s2*s3*s4*s5*s6, c0*c7*s1*s2*s3*s4*s5*s6, -c1*c7*s2*s3*s4*s5*s6, c2*c7*s3*s4*s5*s6, -c3*c7*s4*s5*s6, c4*c7*s5*s6, -c5*c7*s6, c6*c7, s7]
[ s0*s1*s2*s3*s4*s5*s6*s7, -c0*s1*s2*s3*s4*s5*s6*s7, c1*s2*s3*s4*s5*s6*s7, -c2*s3*s4*s5*s6*s7, c3*s4*s5*s6*s7, -c4*s5*s6*s7, c5*s6*s7, -c6*s7, c7]