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A square band matrix Dn,a is a n*n matrix in which all the non-zero terms lie in a band centered around the main diagonal. The band includes the main diagonal and (a - 1) diagonals below and above the main diagonal.
If the band matrix D4,3 is mapped on to a one dimensional array a(0, 1, ...., 13) by diagonals, starting with the lowest diagonal, then in which location is the element D0,2 stored?
Correct answer is '12'. Can you explain this answer?
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A square band matrix Dn,a is a n*n matrix in which all the non-zero te...
Explanation:
To understand the location of the element D0,2 in the one-dimensional array a(0, 1, ..., 13), we need to first understand how the band matrix D4,3 is mapped onto the array.
Mapping the Band Matrix:
The band matrix D4,3 has a size of 4*4 and a band width of 3. This means that all the non-zero elements are located within a band of width 3 centered around the main diagonal. The band includes the main diagonal and 3 diagonals below and above it.
To map this band matrix onto a one-dimensional array, we start with the lowest diagonal and move upwards. The elements in each diagonal are stored in consecutive positions in the array.
Mapping the Band Matrix D4,3:
The band matrix D4,3 can be represented as follows:
| d00 d01 d02 0 |
| d10 d11 d12 d13 |
| 0 d21 d22 d23 |
| 0 0 d32 d33 |
Here, dij represents the element in the ith row and jth column of the matrix.
Mapping this matrix onto the array a(0, 1, ..., 13) by diagonals, we get:
a(0) = d00
a(1) = d10
a(2) = d01
a(3) = d21
a(4) = d11
a(5) = d02
a(6) = d32
a(7) = d12
a(8) = d22
a(9) = d13
a(10) = d23
a(11) = d33
a(12) = 0
a(13) = 0
Locating the Element D0,2:
We are interested in finding the location of the element D0,2, which is the element in the 0th row and 2nd column of the matrix.
From the mapping above, we can see that D0,2 is mapped to the 5th position in the array, which is a(5). Therefore, the element D0,2 is stored in the location 5 of the one-dimensional array a(0, 1, ..., 13).
Conclusion:
The element D0,2 is stored in the location 5 of the one-dimensional array a(0, 1, ..., 13).
To understand the location of the element D0,2 in the one-dimensional array a(0, 1, ..., 13), we need to first understand how the band matrix D4,3 is mapped onto the array.
Mapping the Band Matrix:
The band matrix D4,3 has a size of 4*4 and a band width of 3. This means that all the non-zero elements are located within a band of width 3 centered around the main diagonal. The band includes the main diagonal and 3 diagonals below and above it.
To map this band matrix onto a one-dimensional array, we start with the lowest diagonal and move upwards. The elements in each diagonal are stored in consecutive positions in the array.
Mapping the Band Matrix D4,3:
The band matrix D4,3 can be represented as follows:
| d00 d01 d02 0 |
| d10 d11 d12 d13 |
| 0 d21 d22 d23 |
| 0 0 d32 d33 |
Here, dij represents the element in the ith row and jth column of the matrix.
Mapping this matrix onto the array a(0, 1, ..., 13) by diagonals, we get:
a(0) = d00
a(1) = d10
a(2) = d01
a(3) = d21
a(4) = d11
a(5) = d02
a(6) = d32
a(7) = d12
a(8) = d22
a(9) = d13
a(10) = d23
a(11) = d33
a(12) = 0
a(13) = 0
Locating the Element D0,2:
We are interested in finding the location of the element D0,2, which is the element in the 0th row and 2nd column of the matrix.
From the mapping above, we can see that D0,2 is mapped to the 5th position in the array, which is a(5). Therefore, the element D0,2 is stored in the location 5 of the one-dimensional array a(0, 1, ..., 13).
Conclusion:
The element D0,2 is stored in the location 5 of the one-dimensional array a(0, 1, ..., 13).
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A square band matrix Dn,a is a n*n matrix in which all the non-zero te...
D0,2 is stored at 12.
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A square band matrix Dn,a is a n*n matrix in which all the non-zero terms lie in a band centered around the main diagonal. The band includes the main diagonal and (a - 1) diagonals below and above the main diagonal.If the band matrix D4,3 is mapped on to a one dimensional array a(0, 1, ...., 13) by diagonals, starting with the lowest diagonal, then in which location is the element D0,2 stored?Correct answer is '12'. Can you explain this answer?
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