ztptri.f

          SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIAG, UPLO
          INTEGER            INFO, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX*16         AP( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZTPTRI computes the inverse of a complex upper or lower triangular
    *  matrix A stored in packed format.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  A is upper triangular;
    *          = 'L':  A is lower triangular.
    *
    *  DIAG    (input) CHARACTER*1
    *          = 'N':  A is non-unit triangular;
    *          = 'U':  A is unit triangular.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  AP      (input/output) COMPLEX*16 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.
    *
    *  INFO    (output) 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.
    *
    *  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
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX*16         ONE, ZERO
          PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
         $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            NOUNIT, UPPER
          INTEGER            J, JC, JCLAST, JJ
          COMPLEX*16         AJJ
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZSCAL, ZTPMV
    *     ..
    *     .. 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( 'ZTPTRI', -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 ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
         $                  AP( JC ), 1 )
                CALL ZSCAL( 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 ZTPMV( 'Lower', 'No transpose', DIAG, N-J,
         $                     AP( JCLAST ), AP( JC+1 ), 1 )
                   CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 )
                END IF
                JCLAST = JC
                JC = JC - N + J - 2
       40    CONTINUE
          END IF
    *
          RETURN
    *
    *     End of ZTPTRI
    *
          END