subroutine ctptri	(	character	UPLO,
		character	DIAG,
		integer	N,
		complex, dimension( * )	AP,
		integer	INFO
	)

CTPTRI

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Purpose:

 CTPTRI computes the inverse of a complex upper or lower triangular
 matrix A stored in packed format.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.
[in]	DIAG	DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	AP	AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangular matrix A, stored columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the (triangular) inverse of the original matrix, in the same packed storage format.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

November 2011

Further Details:

  A triangular matrix A can be transferred to packed storage using one
  of the following program segments:

  UPLO = 'U':                      UPLO = 'L':

        JC = 1                           JC = 1
        DO 2 J = 1, N                    DO 2 J = 1, N
           DO 1 I = 1, J                    DO 1 I = J, N
              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
      1    CONTINUE                    1    CONTINUE
           JC = JC + J                      JC = JC + N - J + 1
      2 CONTINUE                       2 CONTINUE

Definition at line 119 of file ctptri.f.

*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          diag, uplo
      INTEGER            info, n
*     ..
*     .. Array Arguments ..
      COMPLEX            ap( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            one, zero
      parameter                ( one = ( 1.0e+0, 0.0e+0 ),
     $                   zero = ( 0.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            nounit, upper
      INTEGER            j, jc, jclast, jj
      COMPLEX            ajj
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           cscal, ctpmv, xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      nounit = lsame( diag, 'N' )
      IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = -1
      ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
         info = -2
      ELSE IF( n.LT.0 ) THEN
         info = -3
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CTPTRI', -info )
         RETURN
      END IF
*
*     Check for singularity if non-unit.
*
      IF( nounit ) THEN
         IF( upper ) THEN
            jj = 0
            DO 10 info = 1, n
               jj = jj + info
               IF( ap( jj ).EQ.zero )
     $            RETURN
   10       CONTINUE
         ELSE
            jj = 1
            DO 20 info = 1, n
               IF( ap( jj ).EQ.zero )
     $            RETURN
               jj = jj + n - info + 1
   20       CONTINUE
         END IF
         info = 0
      END IF
*
      IF( upper ) THEN
*
*        Compute inverse of upper triangular matrix.
*
         jc = 1
         DO 30 j = 1, n
            IF( nounit ) THEN
               ap( jc+j-1 ) = one / ap( jc+j-1 )
               ajj = -ap( jc+j-1 )
            ELSE
               ajj = -one
            END IF
*
*           Compute elements 1:j-1 of j-th column.
*
            CALL ctpmv( 'Upper', 'No transpose', diag, j-1, ap,
     $                  ap( jc ), 1 )
            CALL cscal( j-1, ajj, ap( jc ), 1 )
            jc = jc + j
   30    CONTINUE
*
      ELSE
*
*        Compute inverse of lower triangular matrix.
*
         jc = n*( n+1 ) / 2
         DO 40 j = n, 1, -1
            IF( nounit ) THEN
               ap( jc ) = one / ap( jc )
               ajj = -ap( jc )
            ELSE
               ajj = -one
            END IF
            IF( j.LT.n ) THEN
*
*              Compute elements j+1:n of j-th column.
*
               CALL ctpmv( 'Lower', 'No transpose', diag, n-j,
     $                     ap( jclast ), ap( jc+1 ), 1 )
               CALL cscal( n-j, ajj, ap( jc+1 ), 1 )
            END IF
            jclast = jc
            jc = jc - n + j - 2
   40    CONTINUE
      END IF
*
      RETURN
*
*     End of CTPTRI
*

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