dtptri()

subroutine dtptri	(	character	uplo,
		character	diag,
		integer	n,
		double precision, dimension( * )	ap,
		integer	info
	)

DTPTRI

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Purpose:

 DTPTRI computes the inverse of a real 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 DOUBLE PRECISION 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.

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 116 of file dtptri.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, UPLO
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AP( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOUNIT, UPPER
      INTEGER            J, JC, JCLAST, JJ
      DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dscal, dtpmv, 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( 'DTPTRI', -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 dtpmv( 'Upper', 'No transpose', diag, j-1, ap,
     $                  ap( jc ), 1 )
            CALL dscal( 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 dtpmv( 'Lower', 'No transpose', diag, n-j,
     $                     ap( jclast ), ap( jc+1 ), 1 )
               CALL dscal( n-j, ajj, ap( jc+1 ), 1 )
            END IF
            jclast = jc
            jc = jc - n + j - 2
   40    CONTINUE
      END IF
*
      RETURN
*
*     End of DTPTRI
*

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