Developer Reference for Intel® oneAPI Math Kernel Library for C
?sytrf_aa
Computes the factorization of a symmetric matrix using Aasen’s algorithm.
Syntax
lapack_intLAPACKE_ssytrf_aa ( intmatrix_layout , charuplo , lapack_intn , float*A , lapack_intlda , lapack_int*ipiv );
lapack_intLAPACKE_dsytrf_aa ( intmatrix_layout , charuplo , lapack_intn , double*A , lapack_intlda , lapack_int*ipiv );
lapack_intLAPACKE_csytrf_aa ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_float*A , lapack_intlda , lapack_int*ipiv );
lapack_intLAPACKE_zsytrf_aa ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_double*A , lapack_intlda , lapack_int*ipiv );
Description
?sytrf_aa computes the factorization of a symmetric matrix A using Aasen’s algorithm. The form of the factorization is A = U*T*U T or A = L*T*L T where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a complex symmetric tridiagonal matrix.
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
-
CHARACTER*1
- n
-
INTEGER The order of the matrix A. n ≥ 0.
- A
-
REAL for ssytrf_aa DOUBLE PRECISION for dsytrf_aa COMPLEX for csytrf_aa COMPLEX*16 for zsytrf_aa 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. Array of size max(1, lda * n ). The array A contains either the upper or the lower triangular part of the matrix A (see uplo ).
- lda
-
INTEGER
The leading dimension of the array A .
- lwork
-
INTEGER The length of the array work . If lwork = -1 , a workspace query is assumed; the routine calculates only 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 ssytrf_aa DOUBLE PRECISION for dsytrf_aa COMPLEX for csytrf_aa COMPLEX*16 for zsytrf_aa On exit, the tridiagonal matrix is stored in the diagonals and the subdiagonals of A just below (or above) the diagonals, and L is stored below (or above) the subdiagonals, when uplo is 'L' (or 'U' ).
- ipiv
-
INTEGER
Array of size n . On exit, it contains the details of the interchanges; that is, the row and column k of A were interchanged with the row and column ipiv(k) .
- work
-
REAL for ssytrf_aa DOUBLE PRECISION for dsytrf_aa COMPLEX for csytrf_aa COMPLEX*16 for zsytrf_aa Array, dimension (max(1, lwork )). On exit, if info = 0, work (1) returns the optimal lwork .
Return Values
This function returns a value info .
If info = 0, the execution is successful.
If info = -i , the ith argument had an illegal value.
If info = i , \(D_{i,i}\) is exactly zero. The factorization has been 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.