cpttrs.f.html

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      SUBROUTINE <a name="CPTTRS.1"></a><a href="cpttrs.f.html#CPTTRS.1">CPTTRS</a>( UPLO, N, NRHS, D, E, 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>      CHARACTER          UPLO
      INTEGER            INFO, LDB, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               D( * )
      COMPLEX            B( LDB, * ), 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="CPTTRS.19"></a><a href="cpttrs.f.html#CPTTRS.1">CPTTRS</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 factorization A = U'*D*U or A = L*D*L' computed by <a name="CPTTRF.21"></a><a href="cpttrf.f.html#CPTTRF.1">CPTTRF</a>.
</span><span class="comment">*</span><span class="comment">  D is a diagonal matrix specified in the vector D, U (or L) is a unit
</span><span class="comment">*</span><span class="comment">  bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
</span><span class="comment">*</span><span class="comment">  the vector E, and X and B 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">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the form of the factorization and whether the
</span><span class="comment">*</span><span class="comment">          vector E is the superdiagonal of the upper bidiagonal factor
</span><span class="comment">*</span><span class="comment">          U or the subdiagonal of the lower bidiagonal factor L.
</span><span class="comment">*</span><span class="comment">          = 'U':  A = U'*D*U, E is the superdiagonal of U
</span><span class="comment">*</span><span class="comment">          = 'L':  A = L*D*L', E is the subdiagonal of L
</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">          factorization A = U'*D*U or A = L*D*L'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (input) COMPLEX array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
</span><span class="comment">*</span><span class="comment">          bidiagonal factor U from the factorization A = U'*D*U.
</span><span class="comment">*</span><span class="comment">          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
</span><span class="comment">*</span><span class="comment">          bidiagonal factor L from the factorization A = L*D*L'.
</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">  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 = -k, the k-th argument had an illegal value
</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>      LOGICAL            UPPER
      INTEGER            IUPLO, J, JB, NB
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      INTEGER            <a name="ILAENV.72"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      EXTERNAL           <a name="ILAENV.73"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CPTTS2.76"></a><a href="cptts2.f.html#CPTTS2.1">CPTTS2</a>, <a name="XERBLA.76"></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, MIN
<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">     Test the input arguments.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      UPPER = ( UPLO.EQ.<span class="string">'U'</span> .OR. UPLO.EQ.<span class="string">'u'</span> )
      IF( .NOT.UPPER .AND. .NOT.( UPLO.EQ.<span class="string">'L'</span> .OR. UPLO.EQ.<span class="string">'l'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -7
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.97"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CPTTRS.97"></a><a href="cpttrs.f.html#CPTTRS.1">CPTTRS</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 .OR. NRHS.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Determine the number of right-hand sides to solve at a time.
</span><span class="comment">*</span><span class="comment">
</span>      IF( NRHS.EQ.1 ) THEN
         NB = 1
      ELSE
         NB = MAX( 1, <a name="ILAENV.111"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="CPTTRS.111"></a><a href="cpttrs.f.html#CPTTRS.1">CPTTRS</a>'</span>, UPLO, N, NRHS, -1, -1 ) )
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Decode UPLO
</span><span class="comment">*</span><span class="comment">
</span>      IF( UPPER ) THEN
         IUPLO = 1
      ELSE
         IUPLO = 0
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( NB.GE.NRHS ) THEN
         CALL <a name="CPTTS2.123"></a><a href="cptts2.f.html#CPTTS2.1">CPTTS2</a>( IUPLO, N, NRHS, D, E, B, LDB )
      ELSE
         DO 10 J = 1, NRHS, NB
            JB = MIN( NRHS-J+1, NB )
            CALL <a name="CPTTS2.127"></a><a href="cptts2.f.html#CPTTS2.1">CPTTS2</a>( IUPLO, N, JB, D, E, B( 1, J ), LDB )
   10    CONTINUE
      END IF
<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="CPTTRS.133"></a><a href="cpttrs.f.html#CPTTRS.1">CPTTRS</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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