ctpsv.f.html

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      SUBROUTINE <a name="CTPSV.1"></a><a href="ctpsv.f.html#CTPSV.1">CTPSV</a>(UPLO,TRANS,DIAG,N,AP,X,INCX)
<span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER INCX,N
      CHARACTER DIAG,TRANS,UPLO
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      COMPLEX AP(*),X(*)
<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="CTPSV.13"></a><a href="ctpsv.f.html#CTPSV.1">CTPSV</a>  solves one of the systems of equations
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     A*x = b,   or   A'*x = b,   or   conjg( A' )*x = b,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where b and x are n element vectors and A is an n by n unit, or
</span><span class="comment">*</span><span class="comment">  non-unit, upper or lower triangular matrix, supplied in packed form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  No test for singularity or near-singularity is included in this
</span><span class="comment">*</span><span class="comment">  routine. Such tests must be performed before calling this routine.
</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   - CHARACTER*1.
</span><span class="comment">*</span><span class="comment">           On entry, UPLO specifies whether the matrix is an upper or
</span><span class="comment">*</span><span class="comment">           lower triangular matrix as follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              UPLO = 'U' or 'u'   A is an upper triangular matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              UPLO = 'L' or 'l'   A is a lower triangular matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TRANS  - CHARACTER*1.
</span><span class="comment">*</span><span class="comment">           On entry, TRANS specifies the equations to be solved as
</span><span class="comment">*</span><span class="comment">           follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              TRANS = 'N' or 'n'   A*x = b.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              TRANS = 'T' or 't'   A'*x = b.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              TRANS = 'C' or 'c'   conjg( A' )*x = b.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIAG   - CHARACTER*1.
</span><span class="comment">*</span><span class="comment">           On entry, DIAG specifies whether or not A is unit
</span><span class="comment">*</span><span class="comment">           triangular as follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              DIAG = 'N' or 'n'   A is not assumed to be unit
</span><span class="comment">*</span><span class="comment">                                  triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N      - INTEGER.
</span><span class="comment">*</span><span class="comment">           On entry, N specifies the order of the matrix A.
</span><span class="comment">*</span><span class="comment">           N must be at least zero.
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP     - COMPLEX          array of DIMENSION at least
</span><span class="comment">*</span><span class="comment">           ( ( n*( n + 1 ) )/2 ).
</span><span class="comment">*</span><span class="comment">           Before entry with  UPLO = 'U' or 'u', the array AP must
</span><span class="comment">*</span><span class="comment">           contain the upper triangular matrix packed sequentially,
</span><span class="comment">*</span><span class="comment">           column by column, so that AP( 1 ) contains a( 1, 1 ),
</span><span class="comment">*</span><span class="comment">           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
</span><span class="comment">*</span><span class="comment">           respectively, and so on.
</span><span class="comment">*</span><span class="comment">           Before entry with UPLO = 'L' or 'l', the array AP must
</span><span class="comment">*</span><span class="comment">           contain the lower triangular matrix packed sequentially,
</span><span class="comment">*</span><span class="comment">           column by column, so that AP( 1 ) contains a( 1, 1 ),
</span><span class="comment">*</span><span class="comment">           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
</span><span class="comment">*</span><span class="comment">           respectively, and so on.
</span><span class="comment">*</span><span class="comment">           Note that when  DIAG = 'U' or 'u', the diagonal elements of
</span><span class="comment">*</span><span class="comment">           A are not referenced, but are assumed to be unity.
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  X      - COMPLEX          array of dimension at least
</span><span class="comment">*</span><span class="comment">           ( 1 + ( n - 1 )*abs( INCX ) ).
</span><span class="comment">*</span><span class="comment">           Before entry, the incremented array X must contain the n
</span><span class="comment">*</span><span class="comment">           element right-hand side vector b. On exit, X is overwritten
</span><span class="comment">*</span><span class="comment">           with the solution vector x.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INCX   - INTEGER.
</span><span class="comment">*</span><span class="comment">           On entry, INCX specifies the increment for the elements of
</span><span class="comment">*</span><span class="comment">           X. INCX must not be zero.
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Level 2 Blas routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- Written on 22-October-1986.
</span><span class="comment">*</span><span class="comment">     Jack Dongarra, Argonne National Lab.
</span><span class="comment">*</span><span class="comment">     Jeremy Du Croz, Nag Central Office.
</span><span class="comment">*</span><span class="comment">     Sven Hammarling, Nag Central Office.
</span><span class="comment">*</span><span class="comment">     Richard Hanson, Sandia National Labs.
</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 ZERO
      PARAMETER (ZERO= (0.0E+0,0.0E+0))
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      COMPLEX TEMP
      INTEGER I,INFO,IX,J,JX,K,KK,KX
      LOGICAL NOCONJ,NOUNIT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL <a name="LSAME.111"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL <a name="LSAME.112"></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.115"></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 CONJG
<span class="comment">*</span><span class="comment">     ..
</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
      IF (.NOT.<a name="LSAME.124"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(UPLO,<span class="string">'U'</span>) .AND. .NOT.<a name="LSAME.124"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(UPLO,<span class="string">'L'</span>)) THEN
          INFO = 1
      ELSE IF (.NOT.<a name="LSAME.126"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(TRANS,<span class="string">'N'</span>) .AND. .NOT.<a name="LSAME.126"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(TRANS,<span class="string">'T'</span>) .AND.
     +         .NOT.<a name="LSAME.127"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(TRANS,<span class="string">'C'</span>)) THEN
          INFO = 2
      ELSE IF (.NOT.<a name="LSAME.129"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(DIAG,<span class="string">'U'</span>) .AND. .NOT.<a name="LSAME.129"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(DIAG,<span class="string">'N'</span>)) THEN
          INFO = 3
      ELSE IF (N.LT.0) THEN
          INFO = 4
      ELSE IF (INCX.EQ.0) THEN
          INFO = 7
      END IF
      IF (INFO.NE.0) THEN
          CALL <a name="XERBLA.137"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>(<span class="string">'<a name="CTPSV.137"></a><a href="ctpsv.f.html#CTPSV.1">CTPSV</a> '</span>,INFO)
          RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible.
</span><span class="comment">*</span><span class="comment">
</span>      IF (N.EQ.0) RETURN
<span class="comment">*</span><span class="comment">
</span>      NOCONJ = <a name="LSAME.145"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(TRANS,<span class="string">'T'</span>)
      NOUNIT = <a name="LSAME.146"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(DIAG,<span class="string">'N'</span>)
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Set up the start point in X if the increment is not unity. This
</span><span class="comment">*</span><span class="comment">     will be  ( N - 1 )*INCX  too small for descending loops.
</span><span class="comment">*</span><span class="comment">
</span>      IF (INCX.LE.0) THEN
          KX = 1 - (N-1)*INCX
      ELSE IF (INCX.NE.1) THEN
          KX = 1
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Start the operations. In this version the elements of AP are
</span><span class="comment">*</span><span class="comment">     accessed sequentially with one pass through AP.
12

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