sgetc2.f.html

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      SUBROUTINE <a name="SGETC2.1"></a><a href="sgetc2.f.html#SGETC2.1">SGETC2</a>( N, A, LDA, IPIV, JPIV, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary 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, LDA, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * ), JPIV( * )
      REAL               A( LDA, * )
<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="SGETC2.18"></a><a href="sgetc2.f.html#SGETC2.1">SGETC2</a> computes an LU factorization with complete pivoting of the
</span><span class="comment">*</span><span class="comment">  n-by-n matrix A. The factorization has the form A = P * L * U * Q,
</span><span class="comment">*</span><span class="comment">  where P and Q are permutation matrices, L is lower triangular with
</span><span class="comment">*</span><span class="comment">  unit diagonal elements and U is upper triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  This is the Level 2 BLAS algorithm.
</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 order of the matrix A. N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) REAL array, dimension (LDA, N)
</span><span class="comment">*</span><span class="comment">          On entry, the n-by-n matrix A to be factored.
</span><span class="comment">*</span><span class="comment">          On exit, the factors L and U from the factorization
</span><span class="comment">*</span><span class="comment">          A = P*L*U*Q; the unit diagonal elements of L are not stored.
</span><span class="comment">*</span><span class="comment">          If U(k, k) appears to be less than SMIN, U(k, k) is given the
</span><span class="comment">*</span><span class="comment">          value of SMIN, i.e., giving a nonsingular perturbed system.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</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; for 1 &lt;= i &lt;= N, row i of the
</span><span class="comment">*</span><span class="comment">          matrix has been interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JPIV    (output) INTEGER array, dimension(N).
</span><span class="comment">*</span><span class="comment">          The pivot indices; for 1 &lt;= j &lt;= N, column j of the
</span><span class="comment">*</span><span class="comment">          matrix has been interchanged with column JPIV(j).
</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">           &gt; 0: if INFO = k, U(k, k) is likely to produce owerflow if
</span><span class="comment">*</span><span class="comment">                we try to solve for x in Ax = b. So U is perturbed to
</span><span class="comment">*</span><span class="comment">                avoid the overflow.
</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">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
</span><span class="comment">*</span><span class="comment">     Umea University, S-901 87 Umea, Sweden.
</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               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, IP, IPV, J, JP, JPV
      REAL               BIGNUM, EPS, SMIN, SMLNUM, XMAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           SGER, <a name="SLABAD.73"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>, SSWAP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      REAL               <a name="SLAMCH.76"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="SLAMCH.77"></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">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, 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">     Set constants to control overflow
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      EPS = <a name="SLAMCH.87"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'P'</span> )
      SMLNUM = <a name="SLAMCH.88"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> ) / EPS
      BIGNUM = ONE / SMLNUM
      CALL <a name="SLABAD.90"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>( SMLNUM, BIGNUM )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Factorize A using complete pivoting.
</span><span class="comment">*</span><span class="comment">     Set pivots less than SMIN to SMIN.
</span><span class="comment">*</span><span class="comment">
</span>      DO 40 I = 1, N - 1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find max element in matrix A
</span><span class="comment">*</span><span class="comment">
</span>         XMAX = ZERO
         DO 20 IP = I, N
            DO 10 JP = I, N
               IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
                  XMAX = ABS( A( IP, JP ) )
                  IPV = IP
                  JPV = JP
               END IF
   10       CONTINUE
   20    CONTINUE
         IF( I.EQ.1 )
     $      SMIN = MAX( EPS*XMAX, SMLNUM )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Swap rows
</span><span class="comment">*</span><span class="comment">
</span>         IF( IPV.NE.I )
     $      CALL SSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
         IPIV( I ) = IPV
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Swap columns
</span><span class="comment">*</span><span class="comment">
</span>         IF( JPV.NE.I )
     $      CALL SSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
         JPIV( I ) = JPV
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Check for singularity
</span><span class="comment">*</span><span class="comment">
</span>         IF( ABS( A( I, I ) ).LT.SMIN ) THEN
            INFO = I
            A( I, I ) = SMIN
         END IF
         DO 30 J = I + 1, N
            A( J, I ) = A( J, I ) / A( I, I )
   30    CONTINUE
         CALL SGER( N-I, N-I, -ONE, A( I+1, I ), 1, A( I, I+1 ), LDA,
     $              A( I+1, I+1 ), LDA )
   40 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      IF( ABS( A( N, N ) ).LT.SMIN ) THEN
         INFO = N
         A( N, N ) = SMIN
      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="SGETC2.144"></a><a href="sgetc2.f.html#SGETC2.1">SGETC2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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