?hesv_rkcomputes the solution to a system of linear equations A * X = B for Hermitian matrices.
?hesv_rkcomputes the solution to a complex system of linear equations A * X = B, where A is an
nHermitian matrix and X and B are
The bounded Bunch-Kaufman (rook) diagonal pivoting method is used to factor A as A = P*U*D*(U
'U', or A = P*L*D*(L
'L', where U (or L) is unit upper (or lower) triangular matrix, U
H) is the conjugate of U (or L), P is a permutation matrix, P
Tis the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
?hetrf_rkis called to compute the factorization of a complex Hermitian matrix. The factored form of A is then used to solve the system of equations A * X = B by calling BLAS3 routine
- CHARACTER*1Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:
- ='U': The upper triangle of A is stored.
- ='L': The lower triangle of A is stored.
- INTEGERThe number of linear equations; that is, the order of the matrix A.n≥ 0.
- INTEGERThe number of right-hand sides; that is, the number of columns of the matrix B.nrhs≥ 0.
- COMPLEXforchesv_rkCOMPLEX*16forzhesv_rkArray, dimension (On entry, the Hermitian matrix A. Iflda,n).uplo='U': the leadingn-by-nupper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. Ifuplo='L': the leadingn-by-nlower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
- INTEGERThe leading dimension of the arrayA.lda≥ max(1,n).
- COMPLEXforchesv_rkCOMPLEX*16forzhesv_rkOn entry, then-by-nrhsright-hand side matrix B.The second dimension ofBmust be at least max(1,nrhs).
- INTEGERThe leading dimension of the arrayB.ldb≥ max(1,n).
- INTEGERThe length of the arraywork.Iflwork=-1, a workspace query is assumed; the routine calculates only the optimal size of theworkarray for the factorization stage and returns this value as the first entry of theworkarray, and no error message related tolworkis issued by XERBLA.
- COMPLEXforchesv_rkCOMPLEX*16forzhesv_rkOn exit, ifinfo= 0, diagonal of the block diagonal matrix D and factors U or L as computed by?hetrf_rk:
For more information, see the description of the?hetrf_rkroutine.
- Onlydiagonal elements of the Hermitian block diagonal matrix D on the diagonal of A; that is, D(k,k) =A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in arraye).—and—
- Ifuplo='U', factor U in the superdiagonal part of A. Ifuplo='L', factor L in the subdiagonal part of A.