hetrf_rk#

chetrf_rk

Functions

void chetrf_rk(
    const char*          uplo,
    const INT            n,
          c64*  restrict A,
    const INT            lda,
          c64*  restrict E,
          INT*  restrict ipiv,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);

void chetrf_rk(const char *uplo, const INT n, c64 *restrict A, const INT lda, c64 *restrict E, INT *restrict ipiv, c64 *restrict work, const INT lwork, INT *info)#

CHETRF_RK computes the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (rook) diagonal pivoting method:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the blocked version of the algorithm, calling Level 3 BLAS.

If uplo='L':

If ipiv[k]>=0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.
If ipiv[k]<0 and ipiv[k+1]<0, then rows and columns k and -ipiv[k]-1 were interchanged and rows and columns k+1 and -ipiv[k+1]-1 were interchanged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

Parameters

out

work

Array of dimension max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in

lwork

The length of work. lwork>=1. For best performance lwork>=n*nb, where nb is the block size returned by ILAENV. 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.

out

info

info=0: successful exit
info<0: if info=-k, the k-th argument had an illegal value
info>0: if info=k, the matrix A is singular, because column k of the triangular part of A (upper or lower, per uplo) contains all zeros. D(k,k) is exactly zero, and superdiagonal (or subdiagonal) elements of column k of U (or L) are all zeros. 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. info only stores the first occurrence of a singularity; the factorization always completes.

in

uplo

'U': Upper triangular
'L': Lower triangular

in

n

The order of the matrix A. n>=0.

inout

A

Array of dimension (lda,n). On entry, the Hermitian matrix A. On exit, contains:

Only diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and
If uplo='U': factor U in the superdiagonal part of A. If uplo='L': factor L in the subdiagonal part of A.

in

lda

The leading dimension of the array A. lda>=max(1,n).

out

E

Array of dimension n. On exit, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where if uplo='U': E[i]=D(i-1,i), i=1:n-1, E[0] is set to 0; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] is set to 0. For a 1-by-1 diagonal block D(k), the element E[k] is set to 0 in both uplo='U' and uplo='L' cases.

out

ipiv

Array of dimension n. Pivot indices (0-based). If uplo='U':

If ipiv[k]>=0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.
If ipiv[k]<0 and ipiv[k-1]<0, then rows and columns k and -ipiv[k]-1 were interchanged and rows and columns k-1 and -ipiv[k-1]-1 were interchanged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

zhetrf_rk