dtrti2.f.html

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      SUBROUTINE <a name="DTRTI2.1"></a><a href="dtrti2.f.html#DTRTI2.1">DTRTI2</a>( UPLO, DIAG, N, A, LDA, 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, LDA, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   A( LDA, * )
<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="DTRTI2.18"></a><a href="dtrti2.f.html#DTRTI2.1">DTRTI2</a> computes the inverse of a real upper or lower triangular
</span><span class="comment">*</span><span class="comment">  matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  This is the Level 2 BLAS version of the algorithm.
</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">          Specifies whether the matrix A is upper or lower triangular.
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangular
</span><span class="comment">*</span><span class="comment">          = 'L':  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">          Specifies whether or not the matrix A is unit triangular.
</span><span class="comment">*</span><span class="comment">          = 'N':  Non-unit triangular
</span><span class="comment">*</span><span class="comment">          = 'U':  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">  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the triangular matrix A.  If UPLO = 'U', the
</span><span class="comment">*</span><span class="comment">          leading n by n upper triangular part of the array A contains
</span><span class="comment">*</span><span class="comment">          the upper triangular matrix, and the strictly lower
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.  If UPLO = 'L', the
</span><span class="comment">*</span><span class="comment">          leading n by n lower triangular part of the array A contains
</span><span class="comment">*</span><span class="comment">          the lower triangular matrix, and the strictly upper
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.  If DIAG = 'U', the
</span><span class="comment">*</span><span class="comment">          diagonal elements of A are also not referenced and are
</span><span class="comment">*</span><span class="comment">          assumed to be 1.
</span><span class="comment">*</span><span class="comment">
</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 storage format.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</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 = -k, the k-th argument had an illegal value
</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>      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            NOUNIT, UPPER
      INTEGER            J
      DOUBLE PRECISION   AJJ
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.72"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.73"></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           DSCAL, DTRMV, <a name="XERBLA.76"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX
<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.86"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      NOUNIT = <a name="LSAME.87"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'N'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.88"></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.90"></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
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.98"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DTRTI2.98"></a><a href="dtrti2.f.html#DTRTI2.1">DTRTI2</a>'</span>, -INFO )
         RETURN
      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>         DO 10 J = 1, N
            IF( NOUNIT ) THEN
               A( J, J ) = ONE / A( J, J )
               AJJ = -A( J, J )
            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 DTRMV( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, DIAG, J-1, A, LDA,
     $                  A( 1, J ), 1 )
            CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
   10    CONTINUE
      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>         DO 20 J = N, 1, -1
            IF( NOUNIT ) THEN
               A( J, J ) = ONE / A( J, J )
               AJJ = -A( J, J )
            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 DTRMV( <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, DIAG, N-J,
     $                     A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
               CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
            END IF
   20    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="DTRTI2.144"></a><a href="dtrti2.f.html#DTRTI2.1">DTRTI2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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