Developer Reference for Intel® oneAPI Math Kernel Library for C
?sytri_3
Computes the inverse of a real or complex symmetric matrix.
Syntax
lapack_intLAPACKE_ssytri_3 ( intmatrix_layout , charuplo , lapack_intn , float*A , lapack_intlda , constfloat*e , constlapack_int*ipiv );
lapack_intLAPACKE_dsytri_3 ( intmatrix_layout , charuplo , lapack_intn , double*A , lapack_intlda , constdouble*e , constlapack_int*ipiv );
lapack_intLAPACKE_csytri_3 ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_float*A , lapack_intlda , constlapack_complex_float*e , constlapack_int*ipiv );
lapack_intLAPACKE_zsytri_3 ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_double*A , lapack_intlda , constlapack_complex_double*e , constlapack_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*(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
-
CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
- 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 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 :
- lda
-
INTEGER
The leading dimension of the array A .
- e
-
REAL for ssytri_3 DOUBLE PRECISION for dsytri_3 COMPLEX for csytri_3 COMPLEX*16 for zsytri_3
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.
- ipiv
-
INTEGER
Array of size 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 .
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 , \(D_{i,i}\) = 0; the matrix is singular and its inverse could not be computed.