?hetrs_3
?hetrs_3
Solves a system of linear equations A * X = B with a complex Hermitian matrix using the factorization computed by
?hetrf_rk
.lapack_int
LAPACKE_chetrs_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_float
*
A
,
lapack_int
lda
,
const
lapack_complex_float
*
e
,
const
lapack_int
*
ipiv
,
lapack_complex_float
*
B
,
lapack_int
ldb
);
lapack_int
LAPACKE_zhetrs_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_double
*
A
,
lapack_int
lda
,
const
lapack_complex_double
*
e
,
const
lapack_int
*
ipiv
,
lapack_complex_double
*
B
,
lapack_int
ldb
);
Description
?hetrs_3
solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by ?hetrf_rk
: A = P*U*D*(UH
)*(PT
) or A = P*L*D*(LH
)*(PT
), where U (or L) is unit upper (or lower) triangular matrix, UH
(or LH
) is the conjugate of U (or L), P is a permutation matrix, PT
is the transpose of P, and D is a Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.This algorithm uses Level 3 BLAS.
Input Parameters
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- uplo
- Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
- ='U': Upper triangular; form is A = P*U*D*(UH)*(PT).
- ='L': Lower triangular; form is A = P*L*D*(LH)*(PT).
- n
- The order of the matrix A.n≥ 0.
- nrhs
- The number of right-hand sides; that is, the number of columns in the matrix B.nrhs≥ 0.
- A
- Array of size max(1,Diagonal of the block diagonal matrix D and factor U or L as computed bylda*n).?hetrf_rk:
- Onlydiagonal elements of the Hermitian block diagonal matrix D on the diagonal of A; that is, D(k,k) = A(k,k). Superdiagonal (or subdiagonal) elements of D should be provided on entry in arraye.
- Ifuplo='U', factor U in the superdiagonal part of A. Ifuplo='L', factor L in the subdiagonal part of A.
- lda
- The leading dimension of the arrayA.
- e
- Array of sizeOn entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. Ifn.uplo='U', e(i) = D(i-1,i),i=2:N, and e(1) is not referenced. Ifuplo='L', e(i) = D(i+1,i),i=1:N-1, and e(n) is not referenced.For 1-by-1 diagonal block D(k), where 1 ≤k≤n, the elemente[k-1] is not referenced in both theuplo='U'anduplo='L'cases.
- ipiv
- Array of size (Details of the interchanges and the block structure of D as determined byn.?hetrf_rk.
- B
- On entry, the right-hand side matrix B.The size ofBis at least max(1,ldb*nrhs) for column-major layout and max(1,ldb*n) for row-major layout.
- ldb
- The leading dimension of the arrayB.ldb≥ max(1,n) for column-major layout andldb≥nrhsfor row-major layout.
Output Parameters
- B
- On exit, the solution matrix X.
Return Values
This function returns a value
info
.= 0: Successful exit.
< 0: If , the
info
= -i
i
th
argument had an illegal value.