sgbcon.f.html

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      SUBROUTINE <a name="SGBCON.1"></a><a href="sgbcon.f.html#SGBCON.1">SGBCON</a>( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
     $                   WORK, IWORK, 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">     Modified to call <a name="SLACN2.8"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a> in place of <a name="SLACON.8"></a><a href="slacon.f.html#SLACON.1">SLACON</a>, 7 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          NORM
      INTEGER            INFO, KL, KU, LDAB, N
      REAL               ANORM, RCOND
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * ), IWORK( * )
      REAL               AB( LDAB, * ), WORK( * )
<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="SGBCON.23"></a><a href="sgbcon.f.html#SGBCON.1">SGBCON</a> estimates the reciprocal of the condition number of a real
</span><span class="comment">*</span><span class="comment">  general band matrix A, in either the 1-norm or the infinity-norm,
</span><span class="comment">*</span><span class="comment">  using the LU factorization computed by <a name="SGBTRF.25"></a><a href="sgbtrf.f.html#SGBTRF.1">SGBTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  An estimate is obtained for norm(inv(A)), and the reciprocal of the
</span><span class="comment">*</span><span class="comment">  condition number is computed as
</span><span class="comment">*</span><span class="comment">     RCOND = 1 / ( norm(A) * norm(inv(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">  NORM    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether the 1-norm condition number or the
</span><span class="comment">*</span><span class="comment">          infinity-norm condition number is required:
</span><span class="comment">*</span><span class="comment">          = '1' or 'O':  1-norm;
</span><span class="comment">*</span><span class="comment">          = 'I':         Infinity-norm.
</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">  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">  AB      (input) REAL array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          Details of the LU factorization of the band matrix A, as
</span><span class="comment">*</span><span class="comment">          computed by <a name="SGBTRF.51"></a><a href="sgbtrf.f.html#SGBTRF.1">SGBTRF</a>.  U is stored as an upper triangular band
</span><span class="comment">*</span><span class="comment">          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
</span><span class="comment">*</span><span class="comment">          the multipliers used during the factorization are stored in
</span><span class="comment">*</span><span class="comment">          rows KL+KU+2 to 2*KL+KU+1.
</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    (input) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The pivot indices; for 1 &lt;= i &lt;= N, row i of the matrix was
</span><span class="comment">*</span><span class="comment">          interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ANORM   (input) REAL
</span><span class="comment">*</span><span class="comment">          If NORM = '1' or 'O', the 1-norm of the original matrix A.
</span><span class="comment">*</span><span class="comment">          If NORM = 'I', the infinity-norm of the original matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RCOND   (output) REAL
</span><span class="comment">*</span><span class="comment">          The reciprocal of the condition number of the matrix A,
</span><span class="comment">*</span><span class="comment">          computed as RCOND = 1/(norm(A) * norm(inv(A))).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) REAL array, dimension (3*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK   (workspace) INTEGER array, dimension (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">     .. Parameters ..
</span>      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LNOTI, ONENRM
      CHARACTER          NORMIN
      INTEGER            IX, J, JP, KASE, KASE1, KD, LM
      REAL               AINVNM, SCALE, SMLNUM, T
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      INTEGER            ISAVE( 3 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.95"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            ISAMAX
      REAL               SDOT, <a name="SLAMCH.97"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="LSAME.98"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, ISAMAX, SDOT, <a name="SLAMCH.98"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           SAXPY, <a name="SLACN2.101"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a>, <a name="SLATBS.101"></a><a href="slatbs.f.html#SLATBS.1">SLATBS</a>, <a name="SRSCL.101"></a><a href="srscl.f.html#SRSCL.1">SRSCL</a>, <a name="XERBLA.101"></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          ABS, 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">
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