vvector.dat

basic linear algebra classes and applications (SVD,interpolation, multivariate optimization)

./vvector


-------------------------------------------------------------------------------
		Verify Operations on Vectors


---> Test allocation and compatibility check
The following vector have been allocated

Matrix 1:20x1:1  is not engaged

Matrix 1:20x1:1  is not engaged

Matrix 0:19x1:1  is not engaged

Matrix 1:20x1:1  is not engaged

Status information reported for vector v3:
  Lower bound ... 0
  Upper bound ... 19
  No. of elements 20
  Name 

Check vectors 1 & 2 for compatibility
Check vectors 1 & 4 for compatibility
v2 has to be compatible with v3 after resizing to v3
v1 has to be compatible with v5 after resizing to v5.upb

Matrix 1:25x1:1 Vector v5 is not engaged

Check that shrinking does not change remaining elements
Check that expansion expands by zeros

Done


---> Test operations that treat each element uniformly
Writing zeros to v...
Clearing v1 ...
Comparing v1 with 0 ...
Writing a pattern 3.14159 by assigning to v(i)...
Writing the pattern by assigning to v1 as a whole ...
Comparing v and v1 ...
Comparing (v=0) and v1 ...
Asigning the pattern via a LAStreamOut...

Clear v and add the pattern
   add the doubled pattern with the negative sign
Element (18,1) with value -3.14159 differs the most from what
was expected, -3.14159, though the deviation 2.38419e-07 is small
   subtract the trippled pattern with the negative sign

Verify comparison operations

Assign 2*pattern to v by repeating additions
Assign 2*pattern to v1 by multiplying by two 
Multiply v1 by one half returning it to the 1*pattern

Assign -pattern to v and v1
v = sqrt(sqr(v)); v1 = abs(v1); Now v and v1 have to be the same
Element (18,1) with value 9.86961 differs the most from what
was expected, 9.8696, though the deviation 9.53674e-07 is small

Check out to see that sin^2(x) + cos^2(x) = 1
Element (17,1) with value 1 differs the most from what
was expected, 1, though the deviation 2.38419e-07 is small

	do it again through LazyMatrix promise of a vector
Element (17,1) with value 1 differs the most from what
was expected, 1, though the deviation 2.38419e-07 is small
Element (17,1) with value 1 differs the most from what
was expected, 1, though the deviation 2.38419e-07 is small

Verify constructor with initialization

Done


---> Test Binary Vector operations

Verify assignment of a vector to the vector

Adding one vector to itself, uniform pattern 3.14159
  subtracting two vectors ...
  subtracting the vector from itself
  adding two vectors together

Arithmetic operations on vectors with not the same elements
   adding vp to the zero vector...

Testing element-by-element multiplications and divisions
   squaring each element with sqr() and via multiplication
   compare (v = pattern^2)/pattern with pattern


Comparison of two Matrices:
	Original vector and vector after squaring and dividing
Matrix 2:21x1:1  is not engaged

Matrix 2:21x1:1  is not engaged

Maximal discrepancy    		0
   occured at the point		(2,1)
 Matrix 1 element is    		3.14159
 Matrix 2 element is    		3.14159
 Absolute error v2[i]-v1[i]		0
 Relative error				0

||Matrix 1||   			62.8319
||Matrix 2||   			62.8319
||Matrix1-Matrix2||				0
||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||)	0

Done

---> Verify norm calculations

Assign 10.25 to all the elements and check norms
  1. norm should be pattern*no_elems
  Square of the 2. norm has got to be pattern^2 * no_elems
  Inf norm should be pattern itself
  Scalar product of vector by itself is the sqr(2. vector norm)

Assign the arithm progression with 1. term -10.25
and the difference 1
  1. norm should be 100.5
  Square of the 2. norm has got to be n*[ a0^2 + a0*q*(n-1) + q^2/6*(n-1)*(2n-1) ], or 676.25
  Inf norm should be max(abs(a0),abs(a0+(n-1)*q)), ie 10.25
  Scalar product of vector by itself is the sqr(2. vector norm)


Comparison of two Matrices:
	Compare the vector v with a zero vector
Matrix 1:20x1:1  is not engaged

Matrix 1:20x1:1  is not engaged

Maximal discrepancy    		10.25
   occured at the point		(1,1)
 Matrix 1 element is    		-10.25
 Matrix 2 element is    		0
 Absolute error v2[i]-v1[i]		10.25
 Relative error				2

||Matrix 1||   			100.5
||Matrix 2||   			0
||Matrix1-Matrix2||				100.5
||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||)	1.005e+09

Construct v1 to be orthogonal to v as v(n), -v(n-1), v(n-2)...
||v1|| has got to be equal ||v|| regardless of the norm def
But the scalar product has to be zero

Done


---> Test operations with vectors and matrix slices

Check modifying the matrix column-by-column

Check modifying the matrix row-by-row

Check modifying the matrix row-by-row, again

Check modifying the matrix diagonal

Check out to see that multiplying by diagonal is a column-wise
matrix multiplication

Done

All tests passed

Compilation finished at Fri Dec 25 23:17:14