sgtsv.f.html

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      SUBROUTINE <a name="SGTSV.1"></a><a href="sgtsv.f.html#SGTSV.1">SGTSV</a>( N, NRHS, DL, D, DU, B, LDB, 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>      INTEGER            INFO, 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( * ), DL( * ), DU( * )
<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="SGTSV.17"></a><a href="sgtsv.f.html#SGTSV.1">SGTSV</a>  solves the equation
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     A*X = B,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where A is an n by n tridiagonal matrix, by Gaussian elimination with
</span><span class="comment">*</span><span class="comment">  partial pivoting.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Note that the equation  A'*X = B  may be solved by interchanging the
</span><span class="comment">*</span><span class="comment">  order of the arguments DU and DL.
</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 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">  DL      (input/output) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          On entry, DL must contain the (n-1) sub-diagonal elements of
</span><span class="comment">*</span><span class="comment">          A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, DL is overwritten by the (n-2) elements of the
</span><span class="comment">*</span><span class="comment">          second super-diagonal of the upper triangular matrix U from
</span><span class="comment">*</span><span class="comment">          the LU factorization of A, in DL(1), ..., DL(n-2).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input/output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, D must contain the diagonal elements of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, D is overwritten by the n diagonal elements of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DU      (input/output) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          On entry, DU must contain the (n-1) super-diagonal elements
</span><span class="comment">*</span><span class="comment">          of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, DU is overwritten by the (n-1) elements of the first
</span><span class="comment">*</span><span class="comment">          super-diagonal of 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 N by NRHS matrix of right hand side matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, the N by NRHS solution matrix 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">  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, U(i,i) is exactly zero, and the solution
</span><span class="comment">*</span><span class="comment">               has not been computed.  The factorization has not been
</span><span class="comment">*</span><span class="comment">               completed unless i = 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">     .. Parameters ..
</span>      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J
      REAL               FACT, TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.85"></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">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -7
      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="SGTSV.98"></a><a href="sgtsv.f.html#SGTSV.1">SGTSV</a> '</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( NRHS.EQ.1 ) THEN
         DO 10 I = 1, N - 2
            IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              No row interchange required
</span><span class="comment">*</span><span class="comment">
</span>               IF( D( I ).NE.ZERO ) THEN
                  FACT = DL( I ) / D( I )
                  D( I+1 ) = D( I+1 ) - FACT*DU( I )
                  B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
               ELSE
                  INFO = I
                  RETURN
               END IF
               DL( I ) = ZERO
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Interchange rows I and I+1
</span><span class="comment">*</span><span class="comment">
</span>               FACT = D( I ) / DL( I )
               D( I ) = DL( I )
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