◆ WZhesv()

Function WZhesv	(	Uplo As	String,
		N As	Long,
		A As	Variant,
		B As	Variant,
		Optional Nrhs As	Long = `1`
	)

Solution to system of linear equations AX = B for a Hermitian matrix (complex number representation in Excel format)

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

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

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

A = L * D * L^H, 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 in Excel cells, complex number format in Excel (e.g. 2.5+1i) is used. Worksheet function Complex can be used to input complex numbers into cells.

Returns

N+2 x Nrhs

	Column 1	Column 2	. . .	Column Nrhs
Rows 1 to N	Solution matrix X
Row N+1	Reciprocal condition number	0	. . .	0
Row N+2	Return code	0	. . .	0

Return code.
= 0: Successful exit.
= i > 0: The i-th element of D is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

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 N) N x N Hermitian matrix A. Upper or lower triangular part is to be referenced according to Uplo.
[in]	B	(N x Nrhs) N x Nrhs right hand side matrix B.
[in]	Nrhs	(Optional) Number of columns of right hand side matrix B. (Nrhs >= 1) (default = 1)

Reference: LAPACK

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 matrix and
( 0.20 -0.11+0.93i 0.81-0.37i )

A = ( -0.11-0.93i -0.32 -0.80+0.92i )

( 0.81+0.37i -0.80-0.92i -0.29 )

( -0.1220+0.1844i )

B = ( 0.0034-0.4346i )

( 0.5339-0.1571i )

WZhesv