Vectors

• veczero - Returns the zero vector, {0 0 0}

  Example:
  vmd > veczero
  0 0 0
  

• (C++) vecadd v1 v2 [v3 ... vn] - Returns the vector sum of all the terms.

  Examples:
  vmd > vecadd {1 2 3} {4 5 6} {7 8 9} {-11 -11 -11}
  1 4 7
  vmd > vecadd {0.1 0.2 0.4 0.8} {1 1 2 3} {3 1 4 1}
  4.1 2.2 6.4 4.8
  vmd > vecadd 4 5
  9
  

• vecmul v1 v2 - Returns the vector of a term-by-term multiply.

  Examples:
  vmd > vecmul {1 2 3} {4 5 6} 
  4 10 18
  vmd > vecmul {0.1 0.2 0.4 0.8} {1 1 2 3}
  0.1 0.2 0.8 2.4
  

• (C++) vecsub v1 v2 - Returns the vector subtraction of the second term from the first

  Examples:
  vmd > vecsub 6 3.2
  2.8
  vmd > vecsub {10 9.8 7} {0.1 0 -0.1}
  9.9 9.8 7.1
  vmd > vecsub {1 2 3 4 5} {6 7 8 9 10}
  -5 -5 -5 -5 -5
  

• (C++) vecsum v - Returns the sum of the elements in v

  Examples:
  vmd > vecsum { 1 2 3 }
  6.0
  

• (C++) vecmean v - Returns the mean of the elements in v

  Examples:
  vmd > vecmean { 1 2 3 }
  2.0
  

• (C++) vecstddev v - Returns the standard deviation of the elements in v

  Examples:
  vmd > vecstddev { 1 2 3 4 5 6 7 8 9 10 }
  2.87228131294
  

• (C++) vecscale c v -
• (C++) vecscale v c - Returns the vector of the scalar value c applied to each term of v

  Examples:
  vmd > vecscale .2 {1 2 3}
  0.2 0.4 0.6
  vmd > vecscale {-5 4 -3 2} -2
  10 -8 6 -4
  vmd > vecscale -2 3
  -6
  

• vecdot v1 v2 - Returns the scalar dot product of the two vectors

  Examples:
  vmd > vecdot {1 -2 3} {4 5 6}
  12
  vmd > vecdot {3 4} {3 4}
  25
  vmd > vecdot {1 2 3 4 5} {5 4 3 2 1}
  35
  vmd > vecdot 3 -2
  -6
  

• veccross v1 v2 - Returns the vector cross product of the two vectors.

  Examples:
  vmd > veccross {1 0 0} {0 1 0}
  0 0 1
  vmd > veccross {2 2 2} {-1 0 0}
  0 -2 2
  

• veclength v - Returns the scalar length of v ($\Vert v\Vert$ )

  Examples:
  vmd> veclength 5
  5.0
  vmd > veclength {5 12}
  13.0
  vmd > veclength {3 4 12}
  13.0
  vmd > veclength {1 -2 3 -4}
  5.47723
  

• veclength2 v - Returns the square of the scalar length of v ($\Vert v\Vert^2$ )

  Examples:
  vmd > veclength2 5
  25
  vmd > veclength2 {5 12}
  169
  vmd > veclength2 {3 4 12}
  169
  vmd > veclength2 {1 -2 3 -4}
  30
  

• vecnorm v - Returns the vector of length 1 directed along v

  Examples:
  vmd > vecnorm -10
  -1.0
  vmd > vecnorm {1 1 }
  0.707109 0.707109
  vmd > vecnorm {2 -3 1}
  0.534522 -0.801783 0.267261
  vmd > vecnorm {2 2 -2 2 -2 -2}
  0.408248 0.408248 -0.408248 0.408248 -0.408248 -0.408248
  

• vecdist v1 v2 - Returns the distance between the two vectors ( $\Vert v_2 - v_1 \Vert$ )

  Examples:
  vmd > vecdist -1.5 5.5
  7.0
  vmd > vecdist {0 0 0} {3 4 0}
  5.0
  vmd > vecdist {0 1 2 3 4 5 6} {-6 -5 -4 -3 -2 -1 0}
  15.8745
  

• vecinvert v - Returns the additive inverse of v ($-$ v).

  Examples:
  vmd > vecinvert -11.1
  11.1
  vmd > vecinvert {3 -4 5}
  -3 4 -5
  vmd > vecinvert {0 -1 2 -3}
  0 1 -2 3