2016 Update

Task/Vector-products/R/vector-products.r

@@ -1,10 +1,57 @@
-a <- c( 3.0,  4.0,  5.0)
-b <- c( 4.0,  3.0,  5.0)
+#===============================================================
+# Vector products
+# R implementation
+#===============================================================
 
-cross <- function(a, b)
-   c(a[2]*b[3] - a[3]*b[2],
-     a[3]*b[1] - a[1]*b[3],
-     a[1]*b[2] - a[2]*b[1])
+a <- c(3, 4, 5)
+b <- c(4, 3, 5)
+c <- c(-5, -12, -13)
 
-cross(a, b)
-# [1]  5  5 -7
+#---------------------------------------------------------------
+# Dot product
+#---------------------------------------------------------------
+
+dotp <- function(x, y) {
+  if (length(x) == length(y)) {
+    sum(x*y)
+  }
+}
+
+#---------------------------------------------------------------
+# Cross product
+#---------------------------------------------------------------
+
+crossp <- function(x, y) {
+  if (length(x) == 3 && length(y) == 3) {
+    c(x[2]*y[3] - x[3]*y[2], x[3]*y[1] - x[1]*y[3], x[1]*y[2] - x[2]*y[1])
+  }
+}
+
+#---------------------------------------------------------------
+# Scalar triple product
+#---------------------------------------------------------------
+
+scalartriplep <- function(x, y, z) {
+  if (length(x) == 3 && length(y) == 3 && length(z) == 3) {
+    dotp(x, crossp(y, z))
+  }
+}
+
+#---------------------------------------------------------------
+# Vector triple product
+#---------------------------------------------------------------
+
+vectortriplep <- function(x, y, z) {
+  if (length(x) == 3 && length(y) == 3 && length(z) == 3) {
+    crosssp(x, crossp(y, z))
+  }
+}
+
+#---------------------------------------------------------------
+# Compute and print
+#---------------------------------------------------------------
+
+cat("a . b =", dotp(a, b))
+cat("a x b =", crossp(a, b))
+cat("a . (b x c) =", scalartriplep(a, b, c))
+cat("a x (b x c) =", vectortriplep(a, b, c))