spbsv.f.html

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      SUBROUTINE <a name="SPBSV.1"></a><a href="spbsv.f.html#SPBSV.1">SPBSV</a>( UPLO, N, KD, NRHS, AB, LDAB, 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>      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, LDB, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               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="SPBSV.18"></a><a href="spbsv.f.html#SPBSV.1">SPBSV</a> computes the solution to a real system of linear equations
</span><span class="comment">*</span><span class="comment">     A * X = B,
</span><span class="comment">*</span><span class="comment">  where A is an N-by-N symmetric positive definite band matrix and X
</span><span class="comment">*</span><span class="comment">  and B are N-by-NRHS matrices.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The Cholesky decomposition is used to factor A as
</span><span class="comment">*</span><span class="comment">     A = U**T * U,  if UPLO = 'U', or
</span><span class="comment">*</span><span class="comment">     A = L * L**T,  if UPLO = 'L',
</span><span class="comment">*</span><span class="comment">  where U is an upper triangular band matrix, and L is a lower
</span><span class="comment">*</span><span class="comment">  triangular band matrix, with the same number of superdiagonals or
</span><span class="comment">*</span><span class="comment">  subdiagonals as A.  The factored form of A is then used to solve the
</span><span class="comment">*</span><span class="comment">  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">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangle of A is stored.
</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">  KD      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of superdiagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment">          or the number of subdiagonals if UPLO = 'L'.  KD &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) REAL array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the symmetric band
</span><span class="comment">*</span><span class="comment">          matrix A, stored in the first KD+1 rows of the array.  The
</span><span class="comment">*</span><span class="comment">          j-th column of A is stored in the j-th column of the array AB
</span><span class="comment">*</span><span class="comment">          as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j&lt;=i&lt;=min(N,j+KD).
</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">          On exit, if INFO = 0, the triangular factor U or L from the
</span><span class="comment">*</span><span class="comment">          Cholesky factorization A = U**T*U or A = L*L**T of the band
</span><span class="comment">*</span><span class="comment">          matrix A, in the same storage format as A.
</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;= KD+1.
</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 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, the leading minor of order i of A is not
</span><span class="comment">*</span><span class="comment">                positive definite, so the factorization could not be
</span><span class="comment">*</span><span class="comment">                completed, 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">  N = 6, KD = 2, and UPLO = 'U':
</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">      *    *   a13  a24  a35  a46      *    *   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">
</span><span class="comment">*</span><span class="comment">  Similarly, if UPLO = 'L' the format of A is as follows:
</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">     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
</span><span class="comment">*</span><span class="comment">     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
</span><span class="comment">*</span><span class="comment">     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
</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.
</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 Functions ..
</span>      LOGICAL            <a name="LSAME.105"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.106"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SPBTRF.109"></a><a href="spbtrf.f.html#SPBTRF.1">SPBTRF</a>, <a name="SPBTRS.109"></a><a href="spbtrs.f.html#SPBTRS.1">SPBTRS</a>, <a name="XERBLA.109"></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( .NOT.<a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) .AND. .NOT.<a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KD.LT.0 ) THEN
         INFO = -3
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -6
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.133"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SPBSV.133"></a><a href="spbsv.f.html#SPBSV.1">SPBSV</a> '</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the Cholesky factorization A = U'*U or A = L*L'.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SPBTRF.139"></a><a href="spbtrf.f.html#SPBTRF.1">SPBTRF</a>( UPLO, N, KD, AB, LDAB, 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="SPBTRS.144"></a><a href="spbtrs.f.html#SPBTRS.1">SPBTRS</a>( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
<span class="comment">*</span><span class="comment">
</span>      END IF
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SPBSV.149"></a><a href="spbsv.f.html#SPBSV.1">SPBSV</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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