dtrsv.f.html

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      SUBROUTINE <a name="DTRSV.1"></a><a href="dtrsv.f.html#DTRSV.1">DTRSV</a>(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
<span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER INCX,LDA,N
      CHARACTER DIAG,TRANS,UPLO
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION A(LDA,*),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="DTRSV.13"></a><a href="dtrsv.f.html#DTRSV.1">DTRSV</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,
</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.
</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'   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">  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
</span><span class="comment">*</span><span class="comment">           Before entry with  UPLO = 'U' or 'u', the leading n by n
</span><span class="comment">*</span><span class="comment">           upper triangular part of the array A must contain the upper
</span><span class="comment">*</span><span class="comment">           triangular matrix and the strictly lower triangular part of
</span><span class="comment">*</span><span class="comment">           A is not referenced.
</span><span class="comment">*</span><span class="comment">           Before entry with UPLO = 'L' or 'l', the leading n by n
</span><span class="comment">*</span><span class="comment">           lower triangular part of the array A must contain the lower
</span><span class="comment">*</span><span class="comment">           triangular matrix and the strictly upper triangular part of
</span><span class="comment">*</span><span class="comment">           A is not referenced.
</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 either, 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">  LDA    - INTEGER.
</span><span class="comment">*</span><span class="comment">           On entry, LDA specifies the first dimension of A as declared
</span><span class="comment">*</span><span class="comment">           in the calling (sub) program. LDA must be at least
</span><span class="comment">*</span><span class="comment">           max( 1, n ).
</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      - DOUBLE PRECISION 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>      DOUBLE PRECISION ZERO
      PARAMETER (ZERO=0.0D+0)
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      DOUBLE PRECISION TEMP
      INTEGER I,INFO,IX,J,JX,KX
      LOGICAL NOUNIT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL <a name="LSAME.114"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL <a name="LSAME.115"></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.118"></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">
</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.127"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(UPLO,<span class="string">'U'</span>) .AND. .NOT.<a name="LSAME.127"></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.129"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(TRANS,<span class="string">'N'</span>) .AND. .NOT.<a name="LSAME.129"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(TRANS,<span class="string">'T'</span>) .AND.
     +         .NOT.<a name="LSAME.130"></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.132"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(DIAG,<span class="string">'U'</span>) .AND. .NOT.<a name="LSAME.132"></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
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