Developer Reference for Intel® oneAPI Math Kernel Library for C
?sysv_aa
Computes the solution to a system of linear equations A * X = B for symmetric matrices.
Syntax
lapack_intLAPACKE_ssysv_aa ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , float*A , lapack_intlda , lapack_int*ipiv , float*B , lapack_intldb );
lapack_intLAPACKE_dsysv_aa ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , double*A , lapack_intlda , lapack_int*ipiv , double*B , lapack_intldb );
lapack_intLAPACKE_csysv_aa ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_float*A , lapack_intlda , lapack_int*ipiv , lapack_complex_float*B , lapack_intldb );
lapack_intLAPACKE_zsysv_aa ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_double*A , lapack_intlda , lapack_int*ipiv , lapack_complex_double*B , lapack_intldb );
Description
The ?sysv routine computes the solution to a complex system of linear equations A * X = B, where A is an n -by- n symmetric matrix and X and B are n -by- nrhs matrices.
Aasen’s algorithm is used to factor A as A = U * T * U T , if uplo = 'U' , or A = L * T * L T , if uplo = 'L' , where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tri-diagonal. The factored form of A is then used to solve the system of equations A * X= B.
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 number of linear equations; that is, the order of the matrix A. n ≥ 0.
- nrhs
-
INTEGER The number of right-hand sides; that is, the number of columns of the matrix B. nrhs ≥ 0.
- A
-
REAL for ssysv_aa DOUBLE PRECISION for dsysv_aa COMPLEX for csysv_aa COMPLEX*16 for zsysv_aa
Array of size max(1, 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 .
- B
-
REAL for ssysv_aa DOUBLE PRECISION for dsysv_aa COMPLEX for csysv_aa COMPLEX*16 for zsysv_aa
Array of size max(1, ldb * nrhs ) for column-major layout and max(1, ldb * n ) for row-major layout. On entry, the n -by- nrhs right-hand side matrix B.
- ldb
-
INTEGER
The leading dimension of the array B . ldb ≥ max(1, n ) for column-major layout and ldb ≥ nrhs for row-major layout.
- 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 ssysv_aa DOUBLE PRECISION for dsysv_aa COMPLEX for csysv_aa COMPLEX*16 for zsysv_aa On exit, if info = 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U*T*U T or A = L*T*L T as computed by ?sytrf .
- 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 ).
- B
-
REAL for ssysv_aa DOUBLE PRECISION for dsytrs_aa COMPLEX for csysv_aa COMPLEX*16 for zsysv_aa On exit, if info = 0, the n -by- nrhs solution matrix X.
- work
-
REAL for ssysv_aa DOUBLE PRECISION for dsytrs_aa COMPLEX for csysv_aa COMPLEX*16 for zsysv_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, so the solution could not be computed.