ztptri.f.html

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      SUBROUTINE <a name="ZTPTRI.1"></a><a href="ztptri.f.html#ZTPTRI.1">ZTPTRI</a>( UPLO, DIAG, N, AP, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          DIAG, UPLO
      INTEGER            INFO, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      COMPLEX*16         AP( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZTPTRI.18"></a><a href="ztptri.f.html#ZTPTRI.1">ZTPTRI</a> computes the inverse of a complex upper or lower triangular
</span><span class="comment">*</span><span class="comment">  matrix A stored in packed format.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  A is upper triangular;
</span><span class="comment">*</span><span class="comment">          = 'L':  A is lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIAG    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  A is non-unit triangular;
</span><span class="comment">*</span><span class="comment">          = 'U':  A is unit triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangular matrix A, stored
</span><span class="comment">*</span><span class="comment">          columnwise in a linear array.  The j-th column of A is stored
</span><span class="comment">*</span><span class="comment">          in the array AP as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j&lt;=i&lt;=n.
</span><span class="comment">*</span><span class="comment">          See below for further details.
</span><span class="comment">*</span><span class="comment">          On exit, the (triangular) inverse of the original matrix, in
</span><span class="comment">*</span><span class="comment">          the same packed storage format.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  if INFO = i, A(i,i) is exactly zero.  The triangular
</span><span class="comment">*</span><span class="comment">                matrix is singular and its inverse can not be computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A triangular matrix A can be transferred to packed storage using one
</span><span class="comment">*</span><span class="comment">  of the following program segments:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO = 'U':                      UPLO = 'L':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        JC = 1                           JC = 1
</span><span class="comment">*</span><span class="comment">        DO 2 J = 1, N                    DO 2 J = 1, N
</span><span class="comment">*</span><span class="comment">           DO 1 I = 1, J                    DO 1 I = J, N
</span><span class="comment">*</span><span class="comment">              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
</span><span class="comment">*</span><span class="comment">      1    CONTINUE                    1    CONTINUE
</span><span class="comment">*</span><span class="comment">           JC = JC + J                      JC = JC + N - J + 1
</span><span class="comment">*</span><span class="comment">      2 CONTINUE                       2 CONTINUE
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      COMPLEX*16         ONE, ZERO
      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
     $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            NOUNIT, UPPER
      INTEGER            J, JC, JCLAST, JJ
      COMPLEX*16         AJJ
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.80"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.81"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.84"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, ZSCAL, ZTPMV
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      UPPER = <a name="LSAME.91"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      NOUNIT = <a name="LSAME.92"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'N'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.93"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.NOUNIT .AND. .NOT.<a name="LSAME.95"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'U'</span> ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.101"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZTPTRI.101"></a><a href="ztptri.f.html#ZTPTRI.1">ZTPTRI</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check for singularity if non-unit.
</span><span class="comment">*</span><span class="comment">
</span>      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
<span class="comment">*</span><span class="comment">
</span>      IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute inverse of upper triangular matrix.
</span><span class="comment">*</span><span class="comment">
</span>         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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute elements 1:j-1 of j-th column.
</span><span class="comment">*</span><span class="comment">
</span>            CALL ZTPMV( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, DIAG, J-1, AP,
     $                  AP( JC ), 1 )
            CALL ZSCAL( J-1, AJJ, AP( JC ), 1 )
            JC = JC + J
   30    CONTINUE
<span class="comment">*</span><span class="comment">
</span>      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute inverse of lower triangular matrix.
</span><span class="comment">*</span><span class="comment">
</span>         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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute elements j+1:n of j-th column.
</span><span class="comment">*</span><span class="comment">
</span>               CALL ZTPMV( <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, 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
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="ZTPTRI.174"></a><a href="ztptri.f.html#ZTPTRI.1">ZTPTRI</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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