zgtsv.f.html

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      SUBROUTINE <a name="ZGTSV.1"></a><a href="zgtsv.f.html#ZGTSV.1">ZGTSV</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>      COMPLEX*16         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="ZGTSV.17"></a><a href="zgtsv.f.html#ZGTSV.1">ZGTSV</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) COMPLEX*16 array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          On entry, DL must contain the (n-1) subdiagonal elements of
</span><span class="comment">*</span><span class="comment">          A.
</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 superdiagonal 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) COMPLEX*16 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">          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) COMPLEX*16 array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          On entry, DU must contain the (n-1) superdiagonal elements
</span><span class="comment">*</span><span class="comment">          of A.
</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">          superdiagonal of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the N-by-NRHS 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>      COMPLEX*16         ZERO
      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            J, K
      COMPLEX*16         MULT, TEMP, ZDUM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, DBLE, DIMAG, MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.82"></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">     .. Statement Functions ..
</span>      DOUBLE PRECISION   CABS1
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Statement Function definitions ..
</span>      CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
<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.101"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZGTSV.101"></a><a href="zgtsv.f.html#ZGTSV.1">ZGTSV</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>      DO 30 K = 1, N - 1
         IF( DL( K ).EQ.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Subdiagonal is zero, no elimination is required.
</span><span class="comment">*</span><span class="comment">
</span>            IF( D( K ).EQ.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Diagonal is zero: set INFO = K and return; a unique
</span><span class="comment">*</span><span class="comment">              solution can not be found.
</span><span class="comment">*</span><span class="comment">
</span>               INFO = K
               RETURN
            END IF
         ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) 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>            MULT = DL( K ) / D( K )
            D( K+1 ) = D( K+1 ) - MULT*DU( K )
            DO 10 J = 1, NRHS
               B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
   10       CONTINUE
            IF( K.LT.( N-1 ) )
     $         DL( K ) = ZERO
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Interchange rows K and K+1
</span><span class="comment">*</span><span class="comment">
</span>            MULT = D( K ) / DL( K )
            D( K ) = DL( K )
            TEMP = D( K+1 )
            D( K+1 ) = DU( K ) - MULT*TEMP
            IF( K.LT.( N-1 ) ) THEN
               DL( K ) = DU( K+1 )
               DU( K+1 ) = -MULT*DL( K )
            END IF
            DU( K ) = TEMP
            DO 20 J = 1, NRHS
               TEMP = B( K, J )
               B( K, J ) = B( K+1, J )
               B( K+1, J ) = TEMP - MULT*B( K+1, J )
   20       CONTINUE
         END IF
   30 CONTINUE
      IF( D( N ).EQ.ZERO ) THEN
         INFO = N
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Back solve with the matrix U from the factorization.
</span><span class="comment">*</span><span class="comment">
</span>      DO 50 J = 1, NRHS
         B( N, J ) = B( N, J ) / D( N )
         IF( N.GT.1 )
     $      B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
         DO 40 K = N - 2, 1, -1
            B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
     $                  B( K+2, J ) ) / D( K )
   40    CONTINUE
   50 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="ZGTSV.171"></a><a href="zgtsv.f.html#ZGTSV.1">ZGTSV</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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