cpttrf (l) - Linux Manuals

cpttrf: computes the L*D*Laq factorization of a complex Hermitian positive definite tridiagonal matrix A

NAME

CPTTRF - computes the L*D*Laq factorization of a complex Hermitian positive definite tridiagonal matrix A

SYNOPSIS

SUBROUTINE CPTTRF(
N, D, E, INFO )

    
INTEGER INFO, N

    
REAL D( * )

    
COMPLEX E( * )

PURPOSE

CPTTRF computes the L*D*Laq factorization of a complex Hermitian positive definite tridiagonal matrix A. The factorization may also be regarded as having the form A = Uaq*D*U.

ARGUMENTS

N (input) INTEGER
The order of the matrix A. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the L*D*Laq factorization of A.
E (input/output) COMPLEX array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*Laq factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the Uaq*D*U factorization of A.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, the leading minor of order k is not positive definite; if k < N, the factorization could not be completed, while if k = N, the factorization was completed, but D(N) <= 0.

Pages related to cpttrf

  • cpttrf (3)
  • cpttrs (l) - solves a tridiagonal system of the form A * X = B using the factorization A = Uaq*D*U or A = L*D*Laq computed by CPTTRF
  • cptts2 (l) - solves a tridiagonal system of the form A * X = B using the factorization A = Uaq*D*U or A = L*D*Laq computed by CPTTRF
  • cptcon (l) - computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF
  • cpteqr (l) - computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor
  • cptrfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
  • cptsv (l) - computes the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
  • cptsvx (l) - uses the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices