Contents

# ?sytri_3

Computes the inverse of a real or complex symmetric matrix.
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*(U
T
)*(P
T
) or A = P*L*D*(L
T
)*(P
T
), where U (or L) is a unit upper (or lower) triangular matrix, U
T
(or L
T
) is the transpose of U (or L), P is a permutation matrix, P
T
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,
lda
*
n
).
On entry, diagonal of the block diagonal matrix D and factors U or L as computed by
?sytrf_rk
:
• Only
diagonal 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 array
e
.
—and—
• If
uplo
=
'U'
, factor U in the superdiagonal part of A. If
uplo
=
'L'
, factor L in the subdiagonal part of A.
lda
The leading dimension of the array
A
.
e
Array of size
n
.
On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If
uplo
=
'U'
, e(
i
) = D(
i
-
1,
i
),
i
=2:N, and e(1) is not referenced. If
uplo
=
'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 element
e
[
k
-
1] is not referenced in both the
uplo
=
'U'
and
uplo
=
'L'
cases.
ipiv
Array of size
n
.
Details of the interchanges and the block structure of D as determined by
?sytrf_rk
.
Output Parameters
A
On exit, if
info
= 0, the symmetric inverse of the original matrix. If
uplo
=
'U'
, the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced. If
uplo
=
'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.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.