◆ Zpptri()

Inverse of a Hermitian positive definite matrix in packed form

Purpose: This routine computes the inverse of a Hermitian positive definite matrix A in packed form using the Cholesky factorization A = U^H*U or A = L*L^H computed by zpptrf.

Parameters

[in]	Uplo	= "U": Upper triangular factor U is stored in Ap(). = "L": Lower triangular factor L is stored in Ap().
[in]	N	Order of the matrix A. (N >= 0) (If N = 0, returns without computation)
[in]	Ap()	Array Ap(LAp - 1) (LAp >= N(N + 1)/2) [in] The triangular factor U or L in packed form from the Cholesky factorization A = U^HU or A = LL^H, as computed by Zpptrf. [out] If Info = 0, the upper or lower triangle of the (Hermitian) inverse of A, overwriting the input factor U or L.
[out]	Info	= 0: Successful exit. = -1: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -2: The argument N had an illegal value. (N < 0) = -3: The argument Ap() is invalid. = i > 0: The i-th diagonal element of the factor U or L is zero, and the inverse could not be computed.

Example Program: Compute the inverse matrix of A, where
( 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 )

Sub Ex_Zpptri()

Const N = 3

Dim Ap(N * (N + 1) / 2) As Complex, Info As Long

Ap(0) = Cmplx(2.2, 0)

Ap(1) = Cmplx(-0.11, -0.93): Ap(3) = Cmplx(2.32, 0)

Ap(2) = Cmplx(0.81, 0.37): Ap(4) = Cmplx(-0.8, -0.92): Ap(5) = Cmplx(2.29, 0)

Call Zpptrf("L", N, Ap(), Info)

If Info = 0 Then Call Zpptri("L", N, Ap(), Info)

Debug.Print "Inv(A) ="

Debug.Print Creal(Ap(0)), Cimag(Ap(0))

Debug.Print Creal(Ap(1)), Cimag(Ap(1)), Creal(Ap(3)), Cimag(Ap(3))

Debug.Print Creal(Ap(2)), Cimag(Ap(2)), Creal(Ap(4)), Cimag(Ap(4))

Debug.Print Creal(Ap(5)), Cimag(Ap(5))

Debug.Print "Info =", Info

End Sub

Example Results: Inv(A) =

0.96823675342099 0

-0.186364825657161 0.652567887151733 1.07415978942926 0

-0.669749382959094 -3.34014351483294E-03 0.335735031475792 0.692472480506973

1.06960504827267 0

Info = 0