cgbsv.f.html

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      SUBROUTINE <a name="CGBSV.1"></a><a href="cgbsv.f.html#CGBSV.1">CGBSV</a>( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK driver 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, KL, KU, LDAB, LDB, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * )
      COMPLEX            AB( LDAB, * ), B( LDB, * )
<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="CGBSV.18"></a><a href="cgbsv.f.html#CGBSV.1">CGBSV</a> computes the solution to a complex system of linear equations
</span><span class="comment">*</span><span class="comment">  A * X = B, where A is a band matrix of order N with KL subdiagonals
</span><span class="comment">*</span><span class="comment">  and KU superdiagonals, 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">  The LU decomposition with partial pivoting and row interchanges is
</span><span class="comment">*</span><span class="comment">  used to factor A as A = L * U, where L is a product of permutation
</span><span class="comment">*</span><span class="comment">  and unit lower triangular matrices with KL subdiagonals, and U is
</span><span class="comment">*</span><span class="comment">  upper triangular with KL+KU superdiagonals.  The factored form of A
</span><span class="comment">*</span><span class="comment">  is then used to solve the system of equations A * X = B.
</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 number of linear equations, i.e., the order of the
</span><span class="comment">*</span><span class="comment">          matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KL      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of subdiagonals within the band of A.  KL &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KU      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of superdiagonals within the band of A.  KU &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">  AB      (input/output) COMPLEX array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          On entry, the matrix A in band storage, in rows KL+1 to
</span><span class="comment">*</span><span class="comment">          2*KL+KU+1; rows 1 to KL of the array need not be set.
</span><span class="comment">*</span><span class="comment">          The j-th column of A is stored in the j-th column of the
</span><span class="comment">*</span><span class="comment">          array AB as follows:
</span><span class="comment">*</span><span class="comment">          AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)&lt;=i&lt;=min(N,j+KL)
</span><span class="comment">*</span><span class="comment">          On exit, details of the factorization: U is stored as an
</span><span class="comment">*</span><span class="comment">          upper triangular band matrix with KL+KU superdiagonals in
</span><span class="comment">*</span><span class="comment">          rows 1 to KL+KU+1, and the multipliers used during the
</span><span class="comment">*</span><span class="comment">          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment">          See below for further details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDAB    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array AB.  LDAB &gt;= 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IPIV    (output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The pivot indices that define the permutation matrix P;
</span><span class="comment">*</span><span class="comment">          row i of the matrix was interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX 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.  The factorization
</span><span class="comment">*</span><span class="comment">                has been completed, but the factor U is exactly
</span><span class="comment">*</span><span class="comment">                singular, and the solution has not been computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The band storage scheme is illustrated by the following example, when
</span><span class="comment">*</span><span class="comment">  M = N = 6, KL = 2, KU = 1:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  On entry:                       On exit:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">      *    *    *    +    +    +       *    *    *   u14  u25  u36
</span><span class="comment">*</span><span class="comment">      *    *    +    +    +    +       *    *   u13  u24  u35  u46
</span><span class="comment">*</span><span class="comment">      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
</span><span class="comment">*</span><span class="comment">     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
</span><span class="comment">*</span><span class="comment">     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
</span><span class="comment">*</span><span class="comment">     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Array elements marked * are not used by the routine; elements marked
</span><span class="comment">*</span><span class="comment">  + need not be set on entry, but are required by the routine to store
</span><span class="comment">*</span><span class="comment">  elements of U because of fill-in resulting from the row interchanges.
</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">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CGBTRF.100"></a><a href="cgbtrf.f.html#CGBTRF.1">CGBTRF</a>, <a name="CGBTRS.100"></a><a href="cgbtrs.f.html#CGBTRS.1">CGBTRS</a>, <a name="XERBLA.100"></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">     .. Executable Statements ..
</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( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( KL.LT.0 ) THEN
         INFO = -2
      ELSE IF( KU.LT.0 ) THEN
         INFO = -3
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
         INFO = -6
      ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
         INFO = -9
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.124"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CGBSV.124"></a><a href="cgbsv.f.html#CGBSV.1">CGBSV</a> '</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the LU factorization of the band matrix A.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="CGBTRF.130"></a><a href="cgbtrf.f.html#CGBTRF.1">CGBTRF</a>( N, N, KL, KU, AB, LDAB, IPIV, INFO )
      IF( INFO.EQ.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve the system A*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="CGBTRS.135"></a><a href="cgbtrs.f.html#CGBTRS.1">CGBTRS</a>( <span class="string">'No transpose'</span>, N, KL, KU, NRHS, AB, LDAB, IPIV,
     $                B, LDB, INFO )
      END IF
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CGBSV.140"></a><a href="cgbsv.f.html#CGBSV.1">CGBSV</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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