/*************************************************
 *            BEGIN RVL UNIT TEST 4              *
 * Purpose: exercise StdProductSpace, Components *
 *************************************************/

1. construct 5, 10-diml RnSpace<float>s

2. build StdProductSpace with these two spaces as components

3. construct Vector in the StdProductSpace

4. initialize with val = 2.0 via RVLAssignConst FO eval

5. construct RVLAssignConst with val = 3.0

6. within a new scope, construct Components from Vector in 
   product space (step 3)

7. write out components:
Components of a Vector
  number = 2
***component 0:
Vector Object
member of space:
RnSpace: simple dense vector space
dimension = 5
data container:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 2
data[1] = 2
data[2] = 2
data[3] = 2
data[4] = 2
***component 1:
Vector Object
member of space:
RnSpace: simple dense vector space
dimension = 10
data container:
RnArray Local Data Container object
length = 10
samples: 
data[0] = 2
data[1] = 2
data[2] = 2
data[3] = 2
data[4] = 2
data[5] = 2
data[6] = 2
data[7] = 2
data[8] = 2
data[9] = 2

8. evaluate FO constructed in 5 on 2nd component, setting
   its coordinates all to 3

9. exit scope, which destroys Components object

10. write product vector - first component should still be 2's,
    second component should now be 3's
Vector Object
member of space:
Product Space
size = 2
***factor 0:
RnSpace: simple dense vector space
dimension = 5
***factor 1:
RnSpace: simple dense vector space
dimension = 10
data container:
Product Data Container
***factor 0:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 2
data[1] = 2
data[2] = 2
data[3] = 2
data[4] = 2
***factor 1:
RnArray Local Data Container object
length = 10
samples: 
data[0] = 3
data[1] = 3
data[2] = 3
data[3] = 3
data[4] = 3
data[5] = 3
data[6] = 3
data[7] = 3
data[8] = 3
data[9] = 3

11. construct another vector in same product space

12. initialize all coords to 3

13. write it out
Vector Object
member of space:
Product Space
size = 2
***factor 0:
RnSpace: simple dense vector space
dimension = 5
***factor 1:
RnSpace: simple dense vector space
dimension = 10
data container:
Product Data Container
***factor 0:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 3
data[1] = 3
data[2] = 3
data[3] = 3
data[4] = 3
***factor 1:
RnArray Local Data Container object
length = 10
samples: 
data[0] = 3
data[1] = 3
data[2] = 3
data[3] = 3
data[4] = 3
data[5] = 3
data[6] = 3
data[7] = 3
data[8] = 3
data[9] = 3

14. compute L2 inner product = 120, value should = 120
14a. compute L2 inner product of pv with itself - should be 110.
15. build another product space, all components having dim 5,
    by default-constructing a StdProductSpace and pushing the 
    5D RnSpace constructed in step 1 onto it 3 times

16. construct a Vector in this 3-component space, construct its
    Components object, initialize the first component to 1, second
    to 2, third to 3, using appropriate FOs

18. write out the Vector
Vector Object
member of space:
Product Space
size = 3
***factor 0:
RnSpace: simple dense vector space
dimension = 5
***factor 1:
RnSpace: simple dense vector space
dimension = 5
***factor 2:
RnSpace: simple dense vector space
dimension = 5
data container:
Product Data Container
***factor 0:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 1
data[1] = 1
data[2] = 1
data[3] = 1
data[4] = 1
***factor 1:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 2
data[1] = 2
data[2] = 2
data[3] = 2
data[4] = 2
***factor 2:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 3
data[1] = 3
data[2] = 3
data[3] = 3
data[4] = 3

18.5 write out the Components
Components of a Vector
  number = 3
***component 0:
Vector Object
member of space:
RnSpace: simple dense vector space
dimension = 5
data container:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 1
data[1] = 1
data[2] = 1
data[3] = 1
data[4] = 1
***component 1:
Vector Object
member of space:
RnSpace: simple dense vector space
dimension = 5
data container:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 2
data[1] = 2
data[2] = 2
data[3] = 2
data[4] = 2
***component 2:
Vector Object
member of space:
RnSpace: simple dense vector space
dimension = 5
data container:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 3
data[1] = 3
data[2] = 3
data[3] = 3
data[4] = 3

19. construct a vector in the first component space (5D RnSpace)

20. overwrite the sum of the three components of the Vector
    constructed in steps 16 and 17 on the Vector construced in 
    step 19, using two applications of RVL::Vector::linComb

21. write out the sum
Vector Object
member of space:
RnSpace: simple dense vector space
dimension = 5
data container:
RnArray Local Data Container object
length = 5
samples: 
data[0] = 6
data[1] = 6
data[2] = 6
data[3] = 6
data[4] = 6

/*************************************************
 *              END RVL UNIT TEST 4              *
 *************************************************/