◆ WZsysv2()

Solution to system of linear equations AX = B for a complex symmetric matrix

Purpose: WZsysv2 computes the solution to a complex system of linear equations
A * X = B

where A is an N x N symmetric matrix and X and B are N x Nrhs matrices.

The diagonal pivoting method is used to factor A as
A = U * D * U^T, if Uplo = "U", or

A = L * D * L^T, if Uplo = "L",

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1 x 1 and 2 x 2 diagonal blocks. 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 symmetric 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 symmetric and
( 0.20-0.11i -0.93-0.32i -0.80-0.92i )

A = ( -0.93-0.32i 0.81+0.37i -0.29+0.86i )

( -0.80-0.92i -0.29+0.86i 0.64+0.51i )

( 1.1120-1.0248i )

B = ( -1.5297-0.7781i )

( -0.4965-0.6057i )

WZsysv2