Table of contents
CSPICE_VDOTG computes the dot product of two vectors of arbitrary
dimension.
Given:
v1,
v2 two arbitrary double precision n-dimensional vectors.
help, v1
DOUBLE = Array[N]
help, v2
DOUBLE = Array[N]
the call:
vdotg = cspice_vdotg( v1, v2 )
returns:
vdotg the value of the dot product (inner product)
of `v1' and `v2':
< v1, v2 >
help, vdotg
DOUBLE = Scalar
None.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Suppose that you have a set of double precision n-dimensional
vectors. Check if they are orthogonal to the Z-axis in
n-dimensional space.
Example code begins here.
PRO vdotg_ex1
;;
;; Local parameters.
;;
SETSIZ = 5L
;;
;; Define the vector set.
;;
v1 = [ [ 1.D0, 0.D0, 0.D0, 0.D0 ], $
[ 0.D0, 1.D0, 0.D0, 3.D0 ], $
[ 0.D0, 0.D0, -6.D0, 0.D0 ], $
[10.D0, 0.D0, -1.D0, 0.D0 ], $
[ 0.D0, 0.D0, 0.D0, 1.D0 ] ]
z = [ 0.D0, 0.D0, 1.D0, 0.D0 ]
;;
;; Check the orthogonality with respect to `z' of each
;; vector in `v1'.
;;
for i=0L, SETSIZ-1L do begin
print
print, format='(A,4F6.1)', 'Input vector (V1): ', v1[*,i]
if ( cspice_vdotg( v1[*,i], z ) eq 0.D0 ) then begin
print, format='(A)', 'V1 and Z are orthogonal.'
endif else begin
print, format='(A)', 'V1 and Z are NOT orthogonal.'
endelse
endfor
END
When this program was executed on a Mac/Intel/IDL8.x/64-bit
platform, the output was:
Input vector (V1): 1.0 0.0 0.0 0.0
V1 and Z are orthogonal.
Input vector (V1): 0.0 1.0 0.0 3.0
V1 and Z are orthogonal.
Input vector (V1): 0.0 0.0 -6.0 0.0
V1 and Z are NOT orthogonal.
Input vector (V1): 10.0 0.0 -1.0 0.0
V1 and Z are NOT orthogonal.
Input vector (V1): 0.0 0.0 0.0 1.0
V1 and Z are orthogonal.
cspice_vdotg calculates the dot product of `v1' and `v2' by a simple
application of the definition:
ndim-1
.------
\
cspice_vdotg = ) v1[i] * v2[i]
/
'------
i=0
No error checking is performed to prevent or recover from numeric
overflow.
Native IDL code to calculate the same scalar result:
vdotg = transpose(v1) # v2
vdotg = v2 ## transpose(v1)
The native IDL functions also accept arbitrary sized N vectors.
1) If any of the input arguments, `v1' or `v2', is undefined, an
error is signaled by the IDL error handling system.
2) If any of the input arguments, `v1' or `v2', is not of the
expected type, or it does not have the expected dimensions and
size, an error is signaled by the Icy interface.
3) If the input vector arguments `v1' and `v2' do not have the
same dimension (N), an error is signaled by the Icy interface.
None.
1) The user is responsible for determining that the vectors `v1'
and `v2' are not so large as to cause numeric overflow. In
most cases this will not present a problem.
ICY.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Icy Version 1.0.2, 10-AUG-2021 (JDR)
Edited the header to comply with NAIF standard. Added complete
code examples.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections, and
completed -Particulars section. Moved the contents of the existing
-Examples section to -Particulars.
Removed reference to the routine's corresponding CSPICE header from
-Abstract section.
Added arguments' type and size information in the -I/O section.
-Icy Version 1.0.1, 09-DEC-2005 (EDW)
Added -Examples section.
-Icy Version 1.0.0, 16-JUN-2003 (EDW)
dot product of n-dimensional vectors
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