 |
LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
|
|
LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
|
| subroutine zhetrf_rook | ( | character | uplo, |
| integer | n, | ||
| complex*16, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| integer, dimension( * ) | ipiv, | ||
| complex*16, dimension( * ) | work, | ||
| integer | lwork, | ||
| integer | info ) |
ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
Download ZHETRF_ROOK + dependencies [TGZ] [ZIP] [TXT]
!> !> ZHETRF_ROOK computes the factorization of a complex Hermitian matrix A !> using the bounded Bunch-Kaufman () diagonal pivoting method. !> The form of the factorization is !> !> 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 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. !>
| [in] | UPLO | !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> |
| [in] | N | !> N is INTEGER !> The order of the matrix A. N >= 0. !> |
| [in,out] | A | !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the Hermitian 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. !> !> On exit, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L (see below for further details). !> |
| [in] | LDA | !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> |
| [out] | IPIV | !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D. !> !> If UPLO = 'U': !> Only the last KB elements of IPIV are set. !> !> 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) were interchanged and rows and !> columns k-1 and -IPIV(k-1) were inerchaged, !> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. !> !> If UPLO = 'L': !> Only the first KB elements of IPIV are set. !> !> 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) were interchanged and rows and !> columns k+1 and -IPIV(k+1) were inerchaged, !> D(k:k+1,k:k+1) is a 2-by-2 diagonal block. !> |
| [out] | WORK | !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> |
| [in] | LWORK | !> LWORK is INTEGER !> 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 by XERBLA. !> |
| [out] | INFO | !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero. 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. !> |
!> !> If UPLO = 'U', then A = U*D*U**T, where !> U = P(n)*U(n)* ... *P(k)U(k)* ..., !> i.e., U is a product of terms P(k)*U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k). !> !> If UPLO = 'L', then A = L*D*L**T, where !> L = P(1)*L(1)* ... *P(k)*L(k)* ..., !> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). !>
!> !> June 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !>
Definition at line 209 of file zhetrf_rook.f.
1.11.0