.TH "zhetf2_rook.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME zhetf2_rook.f \- .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBzhetf2_rook\fP (UPLO, N, A, LDA, IPIV, INFO)" .br .RI "\fI\fBZHETF2_ROOK\fP computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method (unblocked algorithm)\&. \fP" .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine zhetf2_rook (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, integerINFO)" .PP \fBZHETF2_ROOK\fP computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method (unblocked algorithm)\&. .PP \fBPurpose: \fP .RS 4 .PP .nf ZHETF2_ROOK computes the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method: A = U*D*U**H or A = L*D*L**H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U**H is the conjugate transpose of U, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the unblocked version of the algorithm, calling Level 2 BLAS. .fi .PP .RE .PP \fBParameters:\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A. N >= 0. .fi .PP .br \fIA\fP .PP .nf 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). .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D. 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) 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': 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. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value > 0: if INFO = k, D(k,k) 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. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 November 2013 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf If UPLO = 'U', then A = U*D*U**H, 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**H, 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). .fi .PP .RE .PP \fBContributors: \fP .RS 4 .PP .nf November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester 01-01-96 - Based on modifications by J. Lewis, Boeing Computer Services Company A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA .fi .PP .RE .PP .PP Definition at line 195 of file zhetf2_rook\&.f\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.