dpbtrs.f.html

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      SUBROUTINE <a name="DPBTRS.1"></a><a href="dpbtrs.f.html#DPBTRS.1">DPBTRS</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 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>      DOUBLE PRECISION   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="DPBTRS.18"></a><a href="dpbtrs.f.html#DPBTRS.1">DPBTRS</a> solves a system of linear equations A*X = B with a symmetric
</span><span class="comment">*</span><span class="comment">  positive definite band matrix A using the Cholesky factorization
</span><span class="comment">*</span><span class="comment">  A = U**T*U or A = L*L**T computed by <a name="DPBTRF.20"></a><a href="dpbtrf.f.html#DPBTRF.1">DPBTRF</a>.
</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 triangular factor stored in AB;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangular factor stored in AB.
</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">  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) DOUBLE PRECISION array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          The triangular factor U or L from the Cholesky factorization
</span><span class="comment">*</span><span class="comment">          A = U**T*U or A = L*L**T of the band matrix A, stored in the
</span><span class="comment">*</span><span class="comment">          first KD+1 rows of the array.  The j-th column of U or L is
</span><span class="comment">*</span><span class="comment">          stored in the j-th column of the array AB as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO ='U', AB(kd+1+i-j,j) = U(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)    = L(i,j) for j&lt;=i&lt;=min(n,j+kd).
</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) DOUBLE PRECISION array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the right hand side matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, the 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">
</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            J
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.69"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.70"></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           DTBSV, <a name="XERBLA.73"></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
      UPPER = <a name="LSAME.83"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.84"></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.98"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DPBTRS.98"></a><a href="dpbtrs.f.html#DPBTRS.1">DPBTRS</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>      IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve A*X = B where A = U'*U.
</span><span class="comment">*</span><span class="comment">
</span>         DO 10 J = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U'*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL DTBSV( <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, N, KD, AB,
     $                  LDAB, B( 1, J ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL DTBSV( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, N, KD, AB,
     $                  LDAB, B( 1, J ), 1 )
   10    CONTINUE
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve A*X = B where A = L*L'.
</span><span class="comment">*</span><span class="comment">
</span>         DO 20 J = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL DTBSV( <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, N, KD, AB,
     $                  LDAB, B( 1, J ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L'*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL DTBSV( <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, N, KD, AB,
     $                  LDAB, B( 1, J ), 1 )
   20    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="DPBTRS.143"></a><a href="dpbtrs.f.html#DPBTRS.1">DPBTRS</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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