◆ Ztptri()

Inverse of a complex triangular matrix in packed form

Purpose: This routine computes the inverse of a complex upper or lower triangular matrix A stored in packed form.

Parameters

[in]	Uplo	= "U": A is upper triangular. = "L": A is lower triangular.
[in]	Diag	= "N": A is non-unit triangular. = "U": A is unit triangular. (Diagonal elements of Ap() are not referenced and are assumed to be 1)
[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] N x N triangular matrix A in packed symmetric matrix form. Upper or lower part is to be stored in accordance with Uplo. [out] The (triangular) inverse of the original matrix, in the same packed form.
[out]	Info	= 0: Successful exit. = -1: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -2: The argument Diag had an illegal value. (Diag <> "N" nor "U") = -3: The argument N had an illegal value. (N < 0) = -4: The argument Ap() is invalid. = i > 0: The i-th diagonal element of A is exactly zero. The triangular matrix is singular and its inverse can not be computed.

Example Program: Compute the inverse matrix of A, where
( 0.20-0.11i 0 0 )

A = ( -0.93-0.32i 0.81+0.37i 0 )

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

Sub Ex_Ztptri()

Const N = 3

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

Ap(0) = Cmplx(0.2, -0.11)

Ap(1) = Cmplx(-0.93, -0.32): Ap(3) = Cmplx(0.81, 0.37)

Ap(2) = Cmplx(-0.8, -0.92): Ap(4) = Cmplx(-0.29, 0.86): Ap(5) = Cmplx(0.64, 0.51)

Call Ztptri("L", "N", 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

Cmplx
Function Cmplx(R As Double, Optional I As Double=0) As Complex
Building complex number

Cimag
Function Cimag(A As Complex) As Double
Imaginary part of complex number

Creal
Function Creal(A As Complex) As Double
Real part of complex number

Ztptri
Sub Ztptri(Uplo As String, Diag As String, N As Long, Ap() As Complex, Info As Long)
Inverse of a complex triangular matrix in packed form

Example Results: Inv(A) =

3.83877159309021 2.11132437619962

4.44578642778825 1.9098735819418 1.02143757881463 -0.466582597730139

5.36621770339369 -1.22742914259824 -0.87238813712865 -0.888792689354233

0.955651784381066 -0.761535015678662

Info = 0