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calc: Keypad Vectors Menu

 
 16.4 Vectors Menu
 =================
 
      |----+----+----+----+----+----4
      |SUM |PROD|MAX |MAP*|MAP^|MAP$|
      |----+----+----+----+----+----|
      |MINV|MDET|MTRN|IDNT|CRSS|"x" |
      |----+----+----+----+----+----|
      |PACK|UNPK|INDX|BLD |LEN |... |
      |----+----+----+----+----+----|
 
 The keys in this menu operate on vectors and matrices.
 
    <PACK> removes an integer N from the top of the stack; the next N
 stack elements are removed and packed into a vector, which is replaced
 onto the stack.  Thus the sequence ‘1 ENTER 3 ENTER 5 ENTER 3 PACK’
 enters the vector ‘[1, 3, 5]’ onto the stack.  To enter a matrix, build
 each row on the stack as a vector, then use a final <PACK> to collect
 the rows into a matrix.
 
    <UNPK> unpacks the vector on the stack, pushing each of its
 components separately.
 
    <INDX> removes an integer N, then builds a vector of integers from 1
 to N.  ‘INV INDX’ takes three numbers from the stack: The vector size N,
 the starting number, and the increment.  ‘BLD’ takes an integer N and
 any value X and builds a vector of N copies of X.
 
    <IDNT> removes an integer N, then builds an N-by-N identity matrix.
 
    <LEN> replaces a vector by its length, an integer.
 
    <...> turns on or off “abbreviated” display mode for large vectors.
 
    <MINV>, <MDET>, <MTRN>, and <CROSS> are the matrix inverse,
 determinant, and transpose, and vector cross product.
 
    <SUM> replaces a vector by the sum of its elements.  It is equivalent
 to ‘u +’ in normal Calc (Statistical Operations).  <PROD>
 computes the product of the elements of a vector, and <MAX> computes the
 maximum of all the elements of a vector.
 
    <INV SUM> computes the alternating sum of the first element minus the
 second, plus the third, minus the fourth, and so on.  <INV MAX> computes
 the minimum of the vector elements.
 
    <HYP SUM> computes the mean of the vector elements.  <HYP PROD>
 computes the sample standard deviation.  <HYP MAX> computes the median.
 
    <MAP*> multiplies two vectors elementwise.  It is equivalent to the
 ‘V M *’ command.  <MAP^> computes powers elementwise.  The arguments
 must be vectors of equal length, or one must be a vector and the other
 must be a plain number.  For example, ‘2 MAP^’ squares all the elements
 of a vector.
 
    <MAP$> maps the formula on the top of the stack across the vector in
 the second-to-top position.  If the formula contains several variables,
 Calc takes that many vectors starting at the second-to-top position and
 matches them to the variables in alphabetical order.  The result is a
 vector of the same size as the input vectors, whose elements are the
 formula evaluated with the variables set to the various sets of numbers
 in those vectors.  For example, you could simulate <MAP^> using <MAP$>
 with the formula ‘x^y’.
 
    The ‘"x"’ key pushes the variable name ‘x’ onto the stack.  To build
 the formula ‘x^2 + 6’, you would use the key sequence ‘"x" 2 y^x 6 +’.
 This formula would then be suitable for use with the <MAP$> key
 described above.  With <INV>, <HYP>, or <INV> and <HYP>, the ‘"x"’ key
 pushes the variable names ‘y’, ‘z’, and ‘t’, respectively.
 

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