ScaLAPACK Array Descriptors

Developer Reference for Intel® oneAPI Math Kernel Library for C

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Date 3/31/2023

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ScaLAPACK Array Descriptors

ScaLAPACK uses two-dimensional block-cyclic data distribution as a layout for dense matrix computations. This distribution provides good work balance between available processors, and also allows use of BLAS Level 3 routines for optimal local computations. Information about the data distribution that is required to establish the mapping between each global matrix and its corresponding process and memory location is contained in the array called the array descriptor associated with each global matrix. The size of the array descriptor is denoted as dlen_.

Let A be a two-dimensional block cyclicly distributed matrix with the array descriptor array desca. The meaning of each array descriptor element depends on the type of the matrix A. The tables "Array descriptor for dense matrices" and "Array descriptor for narrow-band and tridiagonal matrices" describe the meaning of each element for the different types of matrices.

Array descriptor for dense matrices (`dlen_`=9)
Element Name	Stored in	Description	Element Index Number
`dtype_a`	desca[`dtype_`]	Descriptor type ( =1 for dense matrices).	0
`ctxt_a`	desca[`ctxt_`]	BLACS context handle for the process grid.	1
`m_a`	desca[`m_`]	Number of rows in the global matrix `A`.	2
`n_a`	desca[`n_`]	Number of columns in the global matrix `A`.	3
`mb_a`	desca[`mb_`]	Row blocking factor.	4
`nb_a`	desca[`nb_`]	Column blocking factor.	5
`rsrc_a`	desca[`rsrc_`]	Process row over which the first row of the global matrix `A` is distributed.	6
`csrc_a`	desca[`csrc_`]	Process column over which the first column of the global matrix `A` is distributed.	7
`lld_a`	desca[`lld_`]	Leading dimension of the local matrix `A`.	8

Array descriptor for narrow-band and tridiagonal matrices (`dlen_`=7)
Element Name	Stored in	Description	Element Index Number
`dtype_a`	desca[`dtype_`]	Descriptor type `dtype_a`=501: 1-by-`P` grid, `dtype_a`=502: `P`-by-1 grid.	0
`ctxt_a`	desca[`ctxt_`]	BLACS context handle indicating the BLACS process grid over which the global matrix `A` is distributed. The context itself is global, but the handle (the integer value) can vary.	1
`n_a`	desca[`n_`]	The size of the matrix dimension being distributed.	2
`nb_a`	desca[`nb_`]	The blocking factor used to distribute the distributed dimension of the matrix `A`.	3
`src_a`	desca[`src_`]	The process row or column over which the first row or column of the matrix `A` is distributed.	4
`lld_a`	desca[`lld_`]	The leading dimension of the local matrix storing the local blocks of the distributed matrix `A`. The minimum value of `lld_a` depends on `dtype_a`. `dtype_a`=501: `lld_a`≥ max(size of undistributed dimension, 1), `dtype_a`=502: `lld_a`≥ max(`nb_a`, 1).	5
Not applicable		Reserved for future use.	6

Similar notations are used for different matrices. For example: lld_b is the leading dimension of the local matrix storing the local blocks of the distributed matrix B and dtype_z is the type of the global matrix Z.

The number of rows and columns of a global dense matrix that a particular process in a grid receives after data distributing is denoted by LOC_r() and LOC_c(), respectively. To compute these numbers, you can use the ScaLAPACK tool routine numroc.

After the block-cyclic distribution of global data is done, you may choose to perform an operation on a submatrix sub(A) of the global matrix A defined by the following 6 values (for dense matrices):

m: The number of rows of sub(A)
n: The number of columns of sub(A)
a: A pointer to the local matrix containing the entire global matrix A
ia: The row index of sub(A) in the global matrix A
ja: The column index of sub(A) in the global matrix A
desca: The array descriptor for the global matrix A

Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

Parent topic: ScaLAPACK Routines

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