mkl_?csrtrsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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mkl_?csrtrsv

Triangular solvers with simplified interface for a sparse matrix in the CSR format (3-array variation) with one-based indexing (deprecated).

Syntax

call mkl_scsrtrsv(uplo, transa, diag, m, a, ia, ja, x, y)

call mkl_dcsrtrsv(uplo, transa, diag, m, a, ia, ja, x, y)

call mkl_ccsrtrsv(uplo, transa, diag, m, a, ia, ja, x, y)

call mkl_zcsrtrsv(uplo, transa, diag, m, a, ia, ja, x, y)

Include Files

mkl.fi

Description

This routine is deprecated. Use mkl_sparse_?_trsvfrom the Intel® oneAPI Math Kernel Library Inspector-executor Sparse BLAS interface instead.

The mkl_?csrtrsv routine solves a system of linear equations with matrix-vector operations for a sparse matrix stored in the CSR format (3 array variation):

A*y = x

A^T*y = x,

where:

x and y are vectors,

A is a sparse upper or lower triangular matrix with unit or non-unit main diagonal, A^T is the transpose of A.

NOTE:

This routine supports only one-based indexing of the input arrays.

Input Parameters

Parameter descriptions are common for all implemented interfaces with the exception of data types that refer here to the FORTRAN 77 standard types. Data types specific to the different interfaces are described in the section "Interfaces" below.

uplo

CHARACTER*1. Specifies whether the upper or low triangle of the matrix A is used.

If uplo = 'U' or 'u', then the upper triangle of the matrix A is used.

If uplo = 'L' or 'l', then the low triangle of the matrix A is used.

transa

CHARACTER*1. Specifies the system of linear equations.

If transa = 'N' or 'n', then A*y = x

If transa = 'T' or 't' or 'C' or 'c', then A^T*y = x,

diag

CHARACTER*1. Specifies whether A is unit triangular.

If diag = 'U' or 'u', then A is a unit triangular.

If diag = 'N' or 'n', then A is not unit triangular.

m

INTEGER. Number of rows of the matrix A.

a

REAL for mkl_scsrtrmv.

DOUBLE PRECISION for mkl_dcsrtrmv.

COMPLEX for mkl_ccsrtrmv.

DOUBLE COMPLEX for mkl_zcsrtrmv.

Array containing non-zero elements of the matrix A. Its length is equal to the number of non-zero elements in the matrix A. Refer to values array description in Sparse Matrix Storage Formats for more details.

NOTE:

The non-zero elements of the given row of the matrix must be stored in the same order as they appear in the row (from left to right).

No diagonal element can be omitted from a sparse storage if the solver is called with the non-unit indicator.

ia

INTEGER. Array of length m + 1, containing indices of elements in the array a, such that ia(i) is the index in the array a of the first non-zero element from the row i. The value of the last element ia(m + 1) is equal to the number of non-zeros plus one. Refer to rowIndex array description in Sparse Matrix Storage Formats for more details.

ja

INTEGER. Array containing the column indices for each non-zero element of the matrix A.

Its length is equal to the length of the array a. Refer to columns array description in Sparse Matrix Storage Formats for more details.

NOTE:

Column indices must be sorted in increasing order for each row.

x

REAL for mkl_scsrtrmv.

DOUBLE PRECISION for mkl_dcsrtrmv.

COMPLEX for mkl_ccsrtrmv.

DOUBLE COMPLEX for mkl_zcsrtrmv.

Array, size is m.

On entry, the array x must contain the vector x.

Output Parameters

y

REAL for mkl_scsrtrmv.

DOUBLE PRECISION for mkl_dcsrtrmv.

COMPLEX for mkl_ccsrtrmv.

DOUBLE COMPLEX for mkl_zcsrtrmv.

Array, size at least m.

Contains the vector y.

Interfaces

FORTRAN 77:

SUBROUTINE mkl_scsrtrsv(uplo, transa, diag, m, a, ia, ja, x, y)

   CHARACTER*1  uplo, transa, diag

   INTEGER      m

   INTEGER      ia(*), ja(*)

   REAL          a(*), x(*), y(*)

SUBROUTINE mkl_dcsrtrsv(uplo, transa, diag, m, a, ia, ja, x, y)

   CHARACTER*1  uplo, transa, diag

   INTEGER      m

   INTEGER      ia(*), ja(*)

   DOUBLE PRECISION     a(*), x(*), y(*)

SUBROUTINE mkl_ccsrtrsv(uplo, transa, diag, m, a, ia, ja, x, y)

   CHARACTER*1  uplo, transa, diag

   INTEGER      m

   INTEGER      ia(*), ja(*)

   COMPLEX     a(*), x(*), y(*)

SUBROUTINE mkl_zcsrtrsv(uplo, transa, diag, m, a, ia, ja, x, y)

   CHARACTER*1  uplo, transa, diag

   INTEGER      m

   INTEGER      ia(*), ja(*)

   DOUBLE COMPLEX      a(*), x(*), y(*)

Parent topic: Sparse BLAS Level 2 and Level 3 Routines.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_?csrtrsv

FORTRAN 77: