Developer Reference for Intel® oneAPI Math Kernel Library for C
?sysv_rook
Computes the solution to the system of linear equations with a real or complex symmetric coefficient matrix A and multiple right-hand sides.
Syntax
lapack_intLAPACKE_ssysv_rook ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , float*a , lapack_intlda , lapack_int*ipiv , float*b , lapack_intldb );
lapack_intLAPACKE_dsysv_rook ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , double*a , lapack_intlda , lapack_int*ipiv , double*b , lapack_intldb );
lapack_intLAPACKE_csysv_rook ( 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_rook ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , lapack_complex_double*a , lapack_intlda , lapack_int*ipiv , lapack_complex_double*b , lapack_intldb );
Include Files
mkl.h
Description
ssysv_rook dsysv_rook csysv_rook zsysv_rook sysv_rook
The routine solves for X the real or complex system of linear equations A*X = B , where A is an n -by- n symmetric matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.
The diagonal pivoting method is used to factor A as A = U*D*U^{T} or A = L*D*L^{T} , 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.
The ?sysv_rook routine is called to compute the factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.
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
Must be ‘U’ or ‘L’ .
Indicates whether the upper or lower triangular part of A is stored:
If uplo = 'U' , the upper triangle of A is stored.
If uplo = 'L' , the lower triangle of A is stored.
n
The order of matrix A ; n ≥ 0.
nrhs
The number of right-hand sides; the number of columns in B; nrhs≥ 0 .
a , b , work
Arrays: a (size max(1, lda * n )) , b of size max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout .
The array a contains the upper or the lower triangular part of the symmetric matrix A (see uplo ). The second dimension of a must be at least max(1, n) .
The array b contains the matrix B whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least max(1,nrhs) .
lda
The leading dimension of a ; lda≥ max(1, n) .
ldb
The leading dimension of b ; ldb≥ max(1, n)ldb ≥ max(1, n ) for column major layout and ldb ≥ nrhs ) for row major layout .
lwork
The size of the work array; lwork ≥ 1.
If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla . See Application Notes below for details and for the suggested value of lwork .
Output Parameters
a
If info = 0 , a is overwritten by the block-diagonal matrix D and the multipliers used to obtain the factor U (or L ) from the factorization of A .
b
If info = 0 , b is overwritten by the solution matrix X .
ipiv
Array, size at least max(1, n) . Contains details of the interchanges and the block structure of D .
If ipiv[k - 1] > 0 , then rows and columns k and ipiv [ k - 1] were interchanged and Dk, k is a 1-by-1 diagonal block.
If uplo = 'U' and ipiv[k - 1] < 0 and ipiv[k - 2] < 0 , then rows and columns k and - ipiv [ k - 1] were interchanged, rows and columns k - 1 and - ipiv [ k - 2] were interchanged, and D_{k-1:k, k-1:k} is a 2-by-2 diagonal block.
If uplo = 'L' and ipiv[k - 1] < 0 and ipiv[k] < 0 , then rows and columns k and -ipiv [ k - 1] were interchanged, rows and columns k + 1 and -ipiv [ k ] were interchanged, and D_{k:k+1, k:k+1} is a 2-by-2 diagonal block.
work(1)
If info = 0, on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.
Return Values
This function returns a value info .
If info = 0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.
If info = i , d_{ii} is 0. The factorization has been completed, but D is exactly singular, so the solution could not be computed.
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.