?spsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?spsv

Computes the solution to the system of linear equations with a real or complex symmetric coefficient matrix A stored in packed format, and multiple right-hand sides.

Syntax

call sspsv( uplo, n, nrhs, ap, ipiv, b, ldb, info )

call dspsv( uplo, n, nrhs, ap, ipiv, b, ldb, info )

call cspsv( uplo, n, nrhs, ap, ipiv, b, ldb, info )

call zspsv( uplo, n, nrhs, ap, ipiv, b, ldb, info )

call spsv( ap, b [,uplo] [,ipiv] [,info] )

Include Files

mkl.fi, lapack.f90

Description

The routine solves for X the real or complex system of linear equations A*X = B, where A is an n-by-n symmetric matrix stored in packed format, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.

The diagonal pivoting method is used to factor A as A = U*D*U^T or A = L*D*L^T, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

The factored form of A is then used to solve the system of equations A*X = B.

Input Parameters

uplo	CHARACTER*1. Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of `A` is stored: If `uplo = 'U'`, the upper triangle of `A` is stored. If `uplo = 'L'`, the lower triangle of `A` is stored.
n	INTEGER. The order of matrix `A`; `n`≥ 0.
nrhs	INTEGER. The number of right-hand sides, the number of columns in `B; nrhs≥ 0`.
ap, b	REAL for sspsv DOUBLE PRECISION for dspsv COMPLEX for cspsv DOUBLE COMPLEX for zspsv. Arrays: `ap`(size ), `b(size ldb by )`. The dimension of `ap` must be at least `max(1,n(n+1)/2)`. The array `ap` contains the factor `U` or `L`, as specified by `uplo`, in packed storage (see Matrix Storage Schemes). The array `b` contains the matrix `B` whose columns are the right-hand sides for the systems of equations. The second dimension of `b` must be at least `max(1,nrhs)`.
ldb	INTEGER. The leading dimension of `b`; `ldb≥ max(1, n)`.

Output Parameters

ap	The block-diagonal matrix `D` and the multipliers used to obtain the factor `U` (or `L`) from the factorization of `A` as computed by ?sptrf, stored as a packed triangular matrix in the same storage format as `A`.
b	If `info` = 0, `b` is overwritten by the solution matrix `X`.
ipiv	INTEGER. Array, size at least `max(1, n)`. Contains details of the interchanges and the block structure of `D`, as determined by ?sptrf. If `ipiv(i) = k > 0`, then `d_ii` is a 1-by-1 block, and the `i`-th row and column of `A` was interchanged with the `k`-th row and column. If `uplo = 'U'`and `ipiv`(`i`) =`ipiv`(`i`-1) = -`m` < 0, then `D` has a 2-by-2 block in rows/columns `i` and `i-1`, and (`i-1`)-th row and column of `A` was interchanged with the `m`-th row and column. If `uplo = 'L'`and `ipiv`(`i`) =`ipiv`(`i`+1) = -`m` < 0, then `D` has a 2-by-2 block in rows/columns `i` and `i+1`, and (`i+1`)-th row and column of `A` was interchanged with the `m`-th row and column.
info	INTEGER. If `info = 0`, the execution is successful. If `info = -i`, the `i`-th parameter had an illegal value. If `info = i`, `d_ii` is 0. The factorization has been completed, but `D` is exactly singular, so the solution could not be computed.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine spsv interface are as follows:

ap	Holds the array `A` of size (`n*(n+1)/2`).
b	Holds the matrix `B` of size (`n,nrhs`).
ipiv	Holds the vector with the number of elements `n`.
uplo	Must be 'U' or 'L'. The default value is 'U'.

Parent topic: LAPACK Linear Equation Driver Routines

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