Visible to Intel only — GUID: GUID-02BB87DC-3293-468B-91BC-567BC2B42380
Visible to Intel only — GUID: GUID-02BB87DC-3293-468B-91BC-567BC2B42380
?sytf2_rook
Computes the factorization of a real/complex symmetric indefinite matrix, using the bounded Bunch-Kaufman diagonal pivoting method (unblocked algorithm).
Syntax
call ssytf2_rook( uplo, n, a, lda, ipiv, info )
call dsytf2_rook( uplo, n, a, lda, ipiv, info )
call csytf2_rook( uplo, n, a, lda, ipiv, info )
call zsytf2_rook( uplo, n, a, lda, ipiv, info )
Include Files
- mkl.fi
Description
The routine ?sytf2_rook computes the factorization of a real/complex symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:
A = U*D*UT, or A = L*D*LT,
where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
This is the unblocked version of the algorithm, calling BLAS Level 2 Routines.
Input Parameters
- uplo
-
CHARACTER*1.
Specifies whether the upper or lower triangular part of the symmetric matrix A is stored
= 'U': upper triangular
= 'L': lower triangular
- n
-
INTEGER. The order of the matrix A. n≥ 0.
- a
-
REAL for ssytf2_rook
DOUBLE PRECISION for dsytf2_rook
COMPLEX for csytf2_rook
DOUBLE COMPLEX for zsytf2_rook.
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).
Output Parameters
- a
-
On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L.
- ipiv
-
INTEGER.
Array, DIMENSION (n).
Details of the interchanges and the block structure of D
If ipiv(k) > 0, then rows and columns k and ipiv(k) were interchanged and Dk, k is a 1-by-1 diagonal block.
If uplo = 'U' and ipiv(k) < 0 and ipiv(k - 1) < 0, then rows and columns k and -ipiv(k) were interchanged, rows and columns k - 1 and -ipiv(k - 1) were interchanged, and Dk-1:k, k-1:k is a 2-by-2 diagonal block.
If uplo = 'L' and ipiv(k) < 0 and ipiv(k + 1) < 0, then rows and columns k and -ipiv(k) were interchanged, rows and columns k + 1 and -ipiv(k + 1) were interchanged, and Dk:k+1, k:k+1 is a 2-by-2 diagonal block.
- info
-
INTEGER.
= 0: successful exit
< 0: if info = -k, the k-th argument has an illegal value
> 0: if info = k, D(k,k) is exactly zero. The factorization are completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.