sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu 

INNER PRODUCT OF TWO VECTORS

FORMAT

  {S,D}DOT (n, x, incx, y, incy) DSDOT (n, x, incx, y, incy) {C,Z}DOT{C,U}
  (n, x, incx, y, incy)

Function Value

  dotpr: real*4 | real*8 | complex*8 | complex*16
  The dot product of the two vectors x and y.

       For real vectors, if n <= 0 , dotpr returns the value 0.0.
       For complex vectors, if n <= 0 , dotpr returns (0.0, 0.0).

Arguments

  n                   integer*4
                      On entry, the number of elements in the vectors x and
                      y.
                      On exit, n is unchanged.

  X                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array X of length at least
                      (1+(n-1)*|incx|), containing the elements of the vector
                      x.
                      On exit, x is unchanged.

  incx                integer*4
                      On entry, the increment for the array X.
                      If incx >= 0, vector x is stored forward in the array,
                      so that x(i) is stored in location X(1+(i-1)*incx).
                      If incx < 0, vector x is stored backward in the array,
                      so that x(i) is stored in location X(1+(n-i)*|incx|).
                      On exit, incx is unchanged.

  y                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array Y of length at least
                      (1+(n-1)*|incx|), containing the elements of the vector
                      y.
                      On exit, y is unchanged.

  incy                integer*4
                      On entry, the increment for the array Y.
                      If incy >= 0, vector y is stored forward in the array,
                      so that y(i) is stored in location Y(1+(i-1)*incy).
                      If incy < 0, vector y is stored backward in the array,
                      so that y(i) is stored in location Y(1+(n-i)*|incy|).
                      On exit, incy is unchanged.

Description

  SDOT, DDOT, and DSDOT compute the dot product of two real vectors.  CDOTC
  and ZDOTC compute the conjugated dot product of two complex vectors.  CDOTU
  and ZDOTU compute the unconjugated dot product of two complex vectors.

  SDOT, DDOT, DSDOT are functions that compute the dot product of two n-
  element real vectors, x and y:
  x dot y = SUM(i=1...n,x(i)y(i)) = x(1)y(1) + x(2)y(2) + ... + x(n)y(n)

  The order of operations is different from the order in a sequential
  evaluation of the dot product. The final result can differ from the result
  of a sequential evaluation. The DSDOT functions returns the value in
  double-precision.

  CDOTC and ZDOTC are functions that compute the conjugated dot product of
  two complex vectors, x and y, that is, the complex conjugate of the first
  vector is used to compute the dot product.

  Each element x(j) of the vector x is a complex number and each element y(j)
  of the vector y is a complex number.  The conjugated dot product of two
  complex vectors, x and y, is expressed as follows:
  conjugate(x) dot y = SUM(i=1...n,conjugate(x(i))y(i)) =
  = conjugate(x)(1)y(1) + conjugate(x)(2)y(2) + ... + conjugate(x)(n)y(n)

  For example, x and y each have two complex elements:
  x = (1 + i, 2 - i), y = (3 + i, 3 + 2i)
  The conjugate of vector x is
  conjugate(x) = (1 - i, 2 + i), and the dot product is
  conjugate(x) dot y = (1-i)(3+i) + (2+i)(3+2i) = (4-2i) + (4+7i) = (8+5i))

  CDOTU and ZDOTU compute the unconjugated dot product of two complex
  vectors. The unconjugated dot product of two complex vectors, x and y, is
  expressed as follows:
  x dot y = SUM(i=1...n,x(i)y(i)) = x(1)y(1) + x(2)y(2) + ... + x(n)y(n)

  For example, for the same complex vectors x and y:
  x dot y = (1+i)(2+i) + (2-i)(3+2i) = (1+3i) + (8+i) = 9+4i

Example

  INTEGER*4 INCX, INCY
  REAL*4 X(20), Y(20), DOTPR
  INCX = 1
  INCY = 1
  N = 20
  DOTPR = SDOT(N,X,INCX,Y,INCY)

  This FORTRAN code shows how to compute the dot product of two vectors, x
  and y, and return the result in dotpr.

  INTEGER*4 INCX, INCY
  COMPLEX*8 X(20), Y(20), DOTPR
  INCX = 1
  INCY = 1
  N = 20
  DOTPR = CDOTU(N,X,INCX,Y,INCY)

  This FORTRAN code shows how to compute the unconjugated dot product of two
  complex vectors, x and y, and return the result in dotpr.