◆ WZposv2()

Solution to system of linear equations AX = B for a Hermitian positive definite matrix (complex numbers in pairs of cells)

Purpose: WZposv2 computes the solution to a complex system of linear equations
A * X = B,

where A is an N x N Hermitian positive definite matrix and X and B are N x Nrhs matrices.

The Cholesky decomposition is used to factor A as
A = U^H * U, if Uplo = "U", or

A = L * L^H, if Uplo = "L",

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

To represent complex numbers, a real part and an imaginary part are stored in a pair of adjacent cells (a real part in a left cell, and an imaginary part in a right cell). The computed results are stored in the same way.

Returns

N+1 x 2Nrhs

	Column 1	Column 2	. . .	Column 2Nrhs
Rows 1 to N	Solution matrix X (a real part and an imaginary part are stored in a pair of adjacent columns (a real part is left and an imaginary part is right))
Row N+1	Reciprocal condition number	Return code	. . .	0

Return code.
= 0: Successful exit.
= i > 0: The i-th diagonal element of the factor is zero. (Matrix A is singular)

Parameters

[in]	Uplo	= "U": Upper triangle of A is stored. = "L": Lower triangle of A is stored.
[in]	N	Number of linear equations, i.e., order of the matrix A. (N >= 1)
[in]	A	(N x 2N) N x N Hermitian positive definite matrix A. Upper or lower triangular part is to be referenced according to Uplo.
[in]	B	(N x 2Nrhs) N x Nrhs right hand side matrix B.
[in]	Nrhs	(Optional) Number of columns of right hand side matrix B. (Nrhs >= 1) (default = 1)

Example: Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where A is an Hermitian positive definite matrix and
( 2.20 -0.11+0.93i 0.81-0.37i )

A = ( -0.11-0.93i 2.32 -0.80+0.92i )

( 0.81+0.37i -0.80-0.92i 2.29 )

( 1.5980+1.4644i )

B = ( 1.3498+1.4398i )

( 2.0561-0.5441i )

WZposv2