?sysv_aa

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?sysv_aa

Computes the solution to a system of linear equations A * X = B for symmetric matrices.

call ssysv_aa(uplo, n, nrhs, A, lda, ipiv, B, ldb, work, lwork, info)

call csysv_aa(uplo, n, nrhs, A, lda, ipiv, B, ldb, work, lwork, info)

call dsysv_aa(uplo, n, nrhs, A, lda, ipiv, B, ldb, work, lwork, info)

call zsysv_aa(uplo, n, nrhs, A, lda, ipiv, B, ldb, work, lwork, info)

Description

The ?sysv routine computes the solution to a complex system of linear equations A * X = B, where A is an n-by-n symmetric matrix and X and B are n-by-nrhs matrices.

Aasen's algorithm is used to factor A as A = U * T * U^T, if uplo = 'U', or A = L * T * L^T, if uplo = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tri-diagonal. The factored form of A is then used to solve the system of equations A * X= B.

Input Parameters

uplo

CHARACTER*1

= 'U': The upper triangle of A is stored.
= 'L': The lower triangle of A is stored.

n

INTEGER

The number of linear equations; that is, the order of the matrix A. n ≥ 0.

nrhs

INTEGER

The number of right-hand sides; that is, the number of columns of the matrix B. nrhs ≥ 0.

A

REAL for ssysv_aa

DOUBLE PRECISION for dsysv_aa

COMPLEX for csysv_aa

COMPLEX*16 for zsysv_aa

Array, dimension (lda,n). On entry, the symmetric matrix A. If uplo = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

lda

INTEGER

The leading dimension of the array A.lda ≥ max(1, n).

B

REAL for ssysv_aa

DOUBLE PRECISION for dsysv_aa

COMPLEX for csysv_aa

COMPLEX*16 for zsysv_aa

Array, dimension (ldb,nrhs). On entry, the n-by-nrhs right-hand side matrix B.

ldb

INTEGER

The leading dimension of the array B. ldb ≥ max(1, n).

lwork

INTEGER

The length of the array work.

If lwork = -1, a workspace query is assumed; the routine calculates only the optimal size of the work array and returns this value as the first entry of the work array, and no error message related to lwork is issued by XERBLA.

Output Parameters

A

REAL for ssysv_aa

DOUBLE PRECISION for dsysv_aa

COMPLEX for csysv_aa

COMPLEX*16 for zsysv_aa

On exit, if info = 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U*T*U^T or A = L*T*L^T as computed by ?sytrf.

ipiv

INTEGER

Array, dimension (n). On exit, it contains the details of the interchanges; that is, the row and column k of A were interchanged with the row and column ipiv(k).

B

REAL for ssysv_aa

DOUBLE PRECISION for dsytrs_aa

COMPLEX for csysv_aa

COMPLEX*16 for zsysv_aa

On exit, if info = 0, the n-by-nrhs solution matrix X.

work

REAL for ssysv_aa

DOUBLE PRECISION for dsytrs_aa

COMPLEX for csysv_aa

COMPLEX*16 for zsysv_aa

Array, dimension (MAX(1,lwork)). On exit, if info = 0, work(1) returns the optimal lwork.

info

INTEGER

= 0: Successful exit.
< 0: If info = -i, the i^th argument had an illegal value.
> 0: If info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

Parent topic: LAPACK Linear Equation Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sysv_aa