sptts2.f.html

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<pre>
      SUBROUTINE <a name="SPTTS2.1"></a><a href="sptts2.f.html#SPTTS2.1">SPTTS2</a>( N, NRHS, D, E, B, LDB )
<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>      INTEGER            LDB, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               B( LDB, * ), D( * ), E( * )
<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="SPTTS2.17"></a><a href="sptts2.f.html#SPTTS2.1">SPTTS2</a> solves a tridiagonal system of the form
</span><span class="comment">*</span><span class="comment">     A * X = B
</span><span class="comment">*</span><span class="comment">  using the L*D*L' factorization of A computed by <a name="SPTTRF.19"></a><a href="spttrf.f.html#SPTTRF.1">SPTTRF</a>.  D is a
</span><span class="comment">*</span><span class="comment">  diagonal matrix specified in the vector D, L is a unit bidiagonal
</span><span class="comment">*</span><span class="comment">  matrix whose subdiagonal is specified in the vector E, and X and B
</span><span class="comment">*</span><span class="comment">  are N by NRHS matrices.
</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">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the tridiagonal matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NRHS    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment">          of the matrix B.  NRHS &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The n diagonal elements of the diagonal matrix D from the
</span><span class="comment">*</span><span class="comment">          L*D*L' factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (input) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) subdiagonal elements of the unit bidiagonal factor
</span><span class="comment">*</span><span class="comment">          L from the L*D*L' factorization of A.  E can also be regarded
</span><span class="comment">*</span><span class="comment">          as the superdiagonal of the unit bidiagonal factor U from the
</span><span class="comment">*</span><span class="comment">          factorization A = U'*D*U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) REAL array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the right hand side vectors B for the system of
</span><span class="comment">*</span><span class="comment">          linear equations.
</span><span class="comment">*</span><span class="comment">          On exit, the solution vectors, X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &gt;= max(1,N).
</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">     .. Local Scalars ..
</span>      INTEGER            I, J
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           SSCAL
<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">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.LE.1 ) THEN
         IF( N.EQ.1 )
     $      CALL SSCAL( NRHS, 1. / D( 1 ), B, LDB )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Solve A * X = B using the factorization A = L*D*L',
</span><span class="comment">*</span><span class="comment">     overwriting each right hand side vector with its solution.
</span><span class="comment">*</span><span class="comment">
</span>      DO 30 J = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L * x = b.
</span><span class="comment">*</span><span class="comment">
</span>         DO 10 I = 2, N
            B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
   10    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve D * L' * x = b.
</span><span class="comment">*</span><span class="comment">
</span>         B( N, J ) = B( N, J ) / D( N )
         DO 20 I = N - 1, 1, -1
            B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
   20    CONTINUE
   30 CONTINUE
<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="SPTTS2.91"></a><a href="sptts2.f.html#SPTTS2.1">SPTTS2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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