generateTestBand¶
Generates test matrices of class and E(n, c). Returns in band or band symmetric format.
Synopsis¶
generateTestBand (n, c)
Required Arguments¶
- int
n(Input) - Number of rows in the matrix.
- int
c(Input) - Parameter used to alter structure, also the number of upper/lower codiagonals.
Return Value¶
A vector of type float. If no test was generated, then None is
returned.
Optional Arguments¶
symmetricStorage,- Return matrix stored in band symmetric format.
Description¶
The same nomenclature as Østerby and Zlatev (1982) is used. Test matrices of
class E(n, c), to which we will generally refer to as E-matrices,
are symmetric, positive definite matrices of order n with 4 in the
diagonal and -1 in the superdiagonal and subdiagonal. In addition there are
two bands with -1 at a distance c from the diagonal. More precisely:
| \(a_{i,i}=4\) | 0 ≤ i < n |
| \(a_i,_{i+1}=-1\) | 0 ≤ i < n -1 |
| \(a_{i+1,}i=-1\) | 0 ≤ i < n - 1 |
| \(a_{i,i+c}=-1\) | 0≤ i <n - c |
| \(a_{i+c,i}=-1\) | 0 ≤ i < n - c |
for any \(n\geq 3\) and \(2\leq c\leq n-1\).
E-matrices are similar to those obtained from the five-point formula in the discretization of elliptic partial differential equations.
By default, generateTestBand returns an E-matrix in band storage mode.
Option symmetricStorage returns a matrix in band symmetric storage mode.
Example¶
This example generates the matrix
and prints the result.
from pyimsl.math.generateTestBand import generateTestBand
from pyimsl.math.writeMatrix import writeMatrix
a = generateTestBand(5, 3)
writeMatrix("E(5, 3) in band storage: ", a)
Output¶
E(5, 3) in band storage:
1 2 3 4 5
1 0 0 0 -1 -1
2 0 0 0 0 0
3 0 -1 -1 -1 -1
4 4 4 4 4 4
5 -1 -1 -1 -1 0
6 0 0 0 0 0
7 -1 -1 0 0 0