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--- gibson:teaching:spring-2016:math445:lecture:forloop [2016/02/16 11:02]
gibson [functions]
+++ gibson:teaching:spring-2016:math445:lecture:forloop [2016/02/17 07:38] (current)
gibson
@@ Line 24: / Line 24: @@
   * ''%d'' decimal (integer), e.g. 5
   * ''%f'' floating-point, e.g. 2.75
+  * ''%e'' floating-point in scientific (exponential) notation, e.g. 2.75e+00 for 2.75
   * ''%s'' string (a sequence of characters), e.g. '' 'banana'''.
   * ''%c'' character, e.g. '' 'q' ''
+The decimal and floating-point slots can be specialized to print numbers in particular ways, for example,
+<code matlab>
+>> fprintf('The value of pi is %8.3f\n', pi)
+The value of pi is    3.142
+</code>
+This prints $\pi$ with 3 digits after the decimal in a fixed-width field of 8 characters.
+You can put as many slots in a format string as you like. Just provide as many variables as slots, and make sure the types of the slots match the variables.
 ===== for loops: repeating sequences of commands=====
@@ Line 74: / Line 87: @@
 </code>
-===== example function: my sum =====
+===== example functions =====
+==== sum the components of a vector ====
+This ''mysum'' function computes the sum of the components in the input vector $x$. There are a
+number of extraneous print statements which show how the calculation works, step-by-step.
 <file matlab mysum.m>
 function s = mysum(x);
@@ Line 83: / Line 99: @@
   n = length(x);   % get length of vector x
-  fprintf('Will need to do %d additions.\n', n);
+  fprintf('Will need to do %d additions.\n\n', n);
   for i=1:n
-    fprintf('The current value of s is %f.\n', s);
+    fprintf('The current partial sum is s = %f.\n\n', s);
     pause
-    fprintf('Add %f to s.\n', x(i));
+    fprintf('Add %f.\n', x(i));
     s = s + x(i);
   end
-  fprintf('The current value of s is %f.\n', s);
+  fprintf('The total sum is s = %f.\n', s);
   pause
 end
 </file>
-===== example function: myfactorial =====
+You can execute this function with on the input vector ''[4 2 9 1]]'' like this
+<code>
+>> mysum([4 2 9 1])
+Will need to do 4 additions.
+The current partial sum is s = 0.000000.
+Add 4.000000.
+The current partial sum is s = 4.000000.
+Add 2.000000.
+The current partial sum is s = 6.000000.
+Add 9.000000.
+The current partial sum is s = 15.000000.
+Add 1.000000.
+The total sum is s = 16.000000.
+ans =
+
+>>
+</code>
+The function is a lot easier to read if you take out the print statements
+<file matlab mysum.m>
+function s = mysum(x);
+% compute the sum of the components of vector x
+  s = 0;           % variable to hold partial sum
+  n = length(x);   % get length of vector x
+  for i=1:n        % for each number i from 1 to n
+    s = s + x(i);  %    add x(i) to the partial sum
+  end
+end
+</file>
+==== compute the factorial ====
+This function computes $n!$, the factorial of $n$, according to the formula
+\begin{eqnarray*}
+n! = \prod_{i=1}^n i = 1\cdot 2 \cdot 3 \cdot \ldots \cdot (n-2) \cdot (n-1) \cdot n
+\end{eqnarray*}
 <file matlab myfactorial.m>
@@ Line 104: / Line 164: @@
   p = 1;   % variable to store partial products
-  fprintf('Will need to do %d products.\n', n);
   % each step through the loop does one more multiplication
   % in the sequence of products 1, 1*2, 1*2*3, etc.
   for i=1:n
-    fprintf('The current value of p is %f.\n', p);
-    pause
-    fprintf('Multiply p by %f.\n', i);
     p = p * i;
   end
-  fprintf('The current value of p is %f.\n', p);
-  pause
 end
 </file>

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