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## Array Descriptor for Narrow Band and Tridiagonal Matrices

The array descriptor DESC_ whose type is defined as DESC_(DTYPE_)=501 , is an integer array of length 7. This descriptor type is used in the ScaLAPACK narrow band routines and tridiagonal routines to specify a block-column distribution of a global array over a one-dimensional process grid. In the general and symmetric positive definite banded and tridiagonal routines, a one-dimensional block-column distribution is specified for the coefficient matrix . The matrix of right-hand-side vectors must be distributed over a one-dimensional process grid using a block-row data distribution. Refer to section 4.4.1 for further details on block data distribution.

Let us assume, for example, that we have an array descriptor DESCA for a block-column distributed array A. For readability of the code, we have associated symbolic names with the descriptor entries. As previously mentioned, the notations x_ used in the entries of the array descriptor denote the attributes of a global array. For readability of the code, we have associated symbolic names for the descriptor entries. For example, N_ denotes the number of columns and N_A specifically denotes the number of columns in global array A.

Table 4.11: Content of the array descriptor for in-core narrow band and tridiagonal coefficient matrices

When A is non-symmetric and factorized without pivoting, LLD_A must be at least BWL+1+BWU. When A is non-symmetric and factorized with partial pivoting, LLD_A must be at least 2(BWL+BWU)+1. When A is symmetric positive definite, LLD_A must be at least BW+1. Finally, when A is tridiagonal, LLD_A is not referenced.