Refs #247. Included lapack source codes. Avoid downloading tar.gz from netlib.org

Based on 3.4.2 version, apply patch.for_lapack-3.4.2.

lapack-netlib/SRC/sla_gerpvgrw.f

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+*> \brief \b SLA_GERPVGRW
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download SLA_GERPVGRW + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_gerpvgrw.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sla_gerpvgrw.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_gerpvgrw.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       REAL FUNCTION SLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            N, NCOLS, LDA, LDAF
+*       ..
+*       .. Array Arguments ..
+*       REAL               A( LDA, * ), AF( LDAF, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> SLA_GERPVGRW computes the reciprocal pivot growth factor
+*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
+*> much less than 1, the stability of the LU factorization of the
+*> (equilibrated) matrix A could be poor. This also means that the
+*> solution X, estimated condition numbers, and error bounds could be
+*> unreliable.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>     The number of linear equations, i.e., the order of the
+*>     matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NCOLS
+*> \verbatim
+*>          NCOLS is INTEGER
+*>     The number of columns of the matrix A. NCOLS >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is REAL array, dimension (LDA,N)
+*>     On entry, the N-by-N matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>     The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] AF
+*> \verbatim
+*>          AF is REAL array, dimension (LDAF,N)
+*>     The factors L and U from the factorization
+*>     A = P*L*U as computed by SGETRF.
+*> \endverbatim
+*>
+*> \param[in] LDAF
+*> \verbatim
+*>          LDAF is INTEGER
+*>     The leading dimension of the array AF.  LDAF >= max(1,N).
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup realGEcomputational
+*
+*  =====================================================================
+      REAL FUNCTION SLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      INTEGER            N, NCOLS, LDA, LDAF
+*     ..
+*     .. Array Arguments ..
+      REAL               A( LDA, * ), AF( LDAF, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      INTEGER            I, J
+      REAL               AMAX, UMAX, RPVGRW
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN
+*     ..
+*     .. Executable Statements ..
+*
+      RPVGRW = 1.0
+
+      DO J = 1, NCOLS
+         AMAX = 0.0
+         UMAX = 0.0
+         DO I = 1, N
+            AMAX = MAX( ABS( A( I, J ) ), AMAX )
+         END DO
+         DO I = 1, J
+            UMAX = MAX( ABS( AF( I, J ) ), UMAX )
+         END DO
+         IF ( UMAX /= 0.0 ) THEN
+            RPVGRW = MIN( AMAX / UMAX, RPVGRW )
+         END IF
+      END DO
+      SLA_GERPVGRW = RPVGRW
+      END