Computes the inverse of a complex triangular matrixs.

Required Arguments

A — Complex N by N matrix containing the triangular matrix to be inverted.   (Input)
For a lower triangular matrix, only the lower triangle of A is referenced. For an upper triangular matrix, only the upper triangle of A is referenced.

AINV — Complex N by N matrix containing the inverse of A.   (Output)
If A is lower triangular, AINV is also lower triangular. If A is upper triangular, AINV is also upper triangular. If A is not needed, A and AINV can share the same storage locations.

Optional Arguments

N — Number of equations.   (Input)
Default: N = size (A,2).

LDA — Leading dimension of A exactly as specified in the dimension statement of the calling program.   (Input)
Default: LDA = size (A,1).

IPATH — Path indicator.   (Input)
IPATH = 1 means A is lower triangular.
IPATH = 2 means A is upper triangular.
Default: IPATH = 1.

LDAINV — Leading dimension of AINV exactly as specified in the dimension statement of the calling program.   (Input)
Default: LDAINV = size (AINV,1).

FORTRAN 90 Interface

Generic:                              CALL LINCT (A, AINV [,…])

Specific:                             The specific interface names are S_LINCT and D_LINCT.

FORTRAN 77 Interface

Single:                                CALL LINCT (N, A, LDA, IPATH, AINV, LDAINV)

Double:                              The double precision name is DLINCT.

Description

Routine LINCT computes the inverse of a complex triangular matrix. It fails if A has a zero diagonal element.

Comments

Informational error

Type       Code

4                   1          The input triangular matrix is singular. Some of its diagonal elements are close to zero.

Example

The inverse is computed for a 3 × 3 lower triangular matrix.

 

      USE LINCT_INT
      USE WRCRN_INT

!                                 Declare variables

      INTEGER    LDA

      PARAMETER  (LDA=3)

      COMPLEX    A(LDA,LDA), AINV(LDA,LDA)

!                                Set values for A

!

!                                A = ( -3.0+2.0i                     )

!                                    ( -2.0-1.0i  0.0+6.0i           )

!                                    ( -1.0+3.0i  1.0-5.0i -4.0+0.0i )

!

      DATA A/(-3.0,2.0), (-2.0,-1.0), (-1.0, 3.0), (0.0,0.0), (0.0,6.0),&

            (1.0,-5.0), (0.0,0.0), (0.0,0.0), (-4.0,0.0)/

!

!                                 Compute the inverse of A

      CALL LINCT (A, AINV)

!                                 Print results

      CALL WRCRN ('AINV', AINV)

      END

Output

 

                           AINV
                   1                  2                  3
1  (-0.2308,-0.1538)  ( 0.0000, 0.0000)  ( 0.0000, 0.0000)
2  (-0.0897, 0.0513)  ( 0.0000,-0.1667)  ( 0.0000, 0.0000)
3  ( 0.2147,-0.0096)  (-0.2083,-0.0417)  (-0.2500, 0.0000)

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