1. Advanced Data Structure using C++

LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110)
AD and LA. Using the above convention for numbering the
diagonals, and given that sparse matrix A contains nd diagonals
having nonzero elements, arrays AD and LA are set up as follows:
• AD is defined as AD(lda,nd), where the leading dimension,
lda, must be greater than or equal to n. Each diagonal of
matrix A that has at least one nonzero element is stored in a
column of array AD. All of the elements of the diagonal,
including its zero elements, are stored in n contiguous
locations in the array, in the same order as they appear in
the diagonal. Padding with zeros is required as follows to fill
the n locations in each column of array AD:
o Each superdiagonal (k > 0), which has n‐k elements, is
padded with k trailing zeros.
o The main diagonal (k = 0), which has n elements, does
not require padding.
o Each subdiagonal (k < 0), which has n‐|k| elements, is
padded with |k| leading zeros.
• LA is a one‐dimensional integer array of length nd, containing
the diagonal numbers k for the diagonals stored in each
corresponding column in array AD.
3. Storage‐by‐Indices
For a sparse matrix A, storage‐by‐indices uses three one‐
dimensional arrays to define the sparse matrix storage, AR, IA, and
JA. Given the m by n sparse matrix A having ne nonzero elements,
the arrays are set up as follows:
• AR of (at least) length ne contains the ne nonzero elements of
the sparse matrix A, stored contiguously in any order.
• IA, an integer array of (at least) length ne contains the
Prepared By :­
Er. Harvinder Singh
Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 129 ‐