Purpose
To compute an LU factorization of a complex n-by-n upper Hessenberg matrix H using partial pivoting with row interchanges.Specification
SUBROUTINE MB02SZ( N, H, LDH, IPIV, INFO ) C .. Scalar Arguments .. INTEGER INFO, LDH, N C .. Array Arguments .. INTEGER IPIV(*) COMPLEX*16 H(LDH,*)Arguments
Input/Output Parameters
N (input) INTEGER The order of the matrix H. N >= 0. H (input/output) COMPLEX*16 array, dimension (LDH,N) On entry, the n-by-n upper Hessenberg matrix to be factored. On exit, the factors L and U from the factorization H = P*L*U; the unit diagonal elements of L are not stored, and L is lower bidiagonal. LDH INTEGER The leading dimension of the array H. LDH >= max(1,N). IPIV (output) INTEGER array, dimension (N) The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).Error Indicator
INFO INTEGER = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.Method
The factorization has the form H = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (and one nonzero subdiagonal), and U is upper triangular. This is the right-looking Level 2 BLAS version of the algorithm (adapted after ZGETF2).References
-Numerical Aspects
2 The algorithm requires 0( N ) complex operations.Further Comments
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