stptri()

subroutine stptri	(	character	UPLO,
		character	DIAG,
		integer	N,
		real, dimension( * )	AP,
		integer	INFO
	)

STPTRI

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Purpose:

 STPTRI 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 REAL 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

December 2016

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 stptri.f.

*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, UPLO
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
      REAL               AP( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOUNIT, UPPER
      INTEGER            J, JC, JCLAST, JJ
      REAL               AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           sscal, stpmv, 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( 'STPTRI', -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 stpmv( 'Upper', 'No transpose', diag, j-1, ap,
     $                  ap( jc ), 1 )
            CALL sscal( 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 stpmv( 'Lower', 'No transpose', diag, n-j,
     $                     ap( jclast ), ap( jc+1 ), 1 )
               CALL sscal( n-j, ajj, ap( jc+1 ), 1 )
            END IF
            jclast = jc
            jc = jc - n + j - 2
   40    CONTINUE
      END IF
*
      RETURN
*
*     End of STPTRI
*

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