Visible to Intel only — GUID: GUID-B7C7995B-E1B7-4F55-9A90-F44E856A1E5C
Visible to Intel only — GUID: GUID-B7C7995B-E1B7-4F55-9A90-F44E856A1E5C
?sytri_3
Computes the inverse of a real or complex symmetric matrix.
call ssytri_3(uplo, n, A, lda, e, ipiv, work, lwork, info)
call dsytri_3(uplo, n, A, lda, e, ipiv, work, lwork, info)
call csytri_3(uplo, n, A, lda, e, ipiv, work, lwork, info)
call zsytri_3(uplo, n, A, lda, e, ipiv, work, lwork, info)
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
- uplo
-
CHARACTER*1
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
-
INTEGER
The order of the matrix A. n ≥ 0.
- A
-
REAL for ssytri_3
DOUBLE PRECISION for dsytri_3
COMPLEX for csytri_3
COMPLEX*16 for zsytri_3
Array, dimension (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
-
INTEGER
The leading dimension of the array A.lda ≥ max(1, n).
- e
-
REAL for ssytri_3
DOUBLE PRECISION for dsytri_3
COMPLEX for csytri_3
COMPLEX*16 for zsytri_3
Array, dimension (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.
NOTE:For 1-by-1 diagonal block D(k), where 1 ≤ k ≤ n, the element e(k) is not referenced in both the uplo = 'U' and uplo = 'L' cases. - ipiv
-
INTEGER
Array, dimension (n). Details of the interchanges and the block structure of D as determined by ?sytrf_rk.
- lwork
-
INTEGER
The length of the array work.
If LDWORK = -1, a workspace query is assumed; the routine calculates only the optimal size of 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 ssytri_3
DOUBLE PRECISION for dsytri_3
COMPLEX for csytri_3
COMPLEX*16 for zsytri_3
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.
- work
-
REAL for ssytri_3
DOUBLE PRECISION for dsytri_3
COMPLEX for csytri_3
COMPLEX*16 for zsytri_3
Array, dimension (n+NB+1)*(NB+3). On exit, if info = 0, work(1) returns the optimal lwork.
- info
-
INTEGER
- = 0: successful exit.
- < 0: If info = -i, the ith argument had an illegal value.
- > 0: If info = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.