?sytri_3
?sytri_3
Computes the inverse of a real or complex symmetric matrix.
lapack_int
LAPACKE_ssytri_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float
*
A
,
lapack_int
lda
,
const
float
*
e
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_dsytri_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double
*
A
,
lapack_int
lda
,
const
double
*
e
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_csytri_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
A
,
lapack_int
lda
,
const
lapack_complex_float
*
e
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_zsytri_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
A
,
lapack_int
lda
,
const
lapack_complex_double
*
e
,
const
lapack_int
*
ipiv
);
Description
?sytri_3
computes the inverse of a real or complex symmetric matrix A using the factorization computed by ?sytrf_rk
: A = P*U*D*(UT
)*(PT
) or A = P*L*D*(LT
)*(PT
), where U (or L) is a unit upper (or lower) triangular matrix, UT
(or LT
) is the transpose of U (or L), P is a permutation matrix, PT
is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.?sytri_3
sets the leading dimension of the workspace before calling ?sytri_3x
, which actually computes the inverse. This is the blocked version of the algorithm, calling 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': The upper triangle of A is stored.
- ='L': The lower triangle of A is stored.
- n
- The order of the matrix A.n≥ 0.
- A
- Array of size max(1,On entry, diagonal of the block diagonal matrix D and factors U or L as computed bylda*n).?sytrf_rk:
- Onlydiagonal elements of the symmetric 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.—and—
- 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 symmetric 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 sizeDetails of the interchanges and the block structure of D as determined byn.?sytrf_rk.
Output Parameters
- A
- On exit, ifinfo= 0, the symmetric inverse of the original matrix. Ifuplo='U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced. Ifuplo='L', the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
Return Values
This function returns a value
info
.= 0: Successful exit.
< 0: If
info
= -
i
, the i
th
argument had an illegal value.> 0: If
info
= i
, D(i
,i
) = 0; the matrix is singular and its inverse could not be computed.