NAG Library Function Document
nag_complex_cholesky (f01bnc) computes a Cholesky factorization of a complex positive definite Hermitian matrix.
||nag_complex_cholesky (Integer n,
nag_complex_cholesky (f01bnc) computes the Cholesky factorization of a complex positive definite Hermitian matrix , where is a complex upper triangular matrix with real diagonal elements.
Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag
n – IntegerInput
On entry: , the order of the matrix .
a – ComplexInput/Output
On entry: the lower triangle of the by positive definite Hermitian matrix . The elements of the array above the diagonal need not be set.
On exit: the off-diagonal elements of the upper triangular matrix . The lower triangle of is unchanged.
tda – IntegerInput
: the stride separating matrix column elements in the array a
p[n] – doubleOutput
On exit: the reciprocals of the real diagonal elements of .
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, while . These arguments must satisfy .
Matrix diagonal element has nonzero imaginary part.
On entry, .
The matrix is not positive definite, possibly due to rounding errors.
The Cholesky factorization of a positive definite matrix is known for its remarkable numerical stability. The computed matrix
satisfies the relation
where the 2-norms of
are related by
is a modest function of
is the machine precision
8 Parallelism and Performance
The time taken by nag_complex_cholesky (f01bnc) is approximately proportional to .
To compute the Cholesky factorization of the well-conditioned positive definite Hermitian matrix
10.1 Program Text
Program Text (f01bnce.c)
10.2 Program Data
Program Data (f01bnce.d)
10.3 Program Results
Program Results (f01bnce.r)