double precision function zla_gerpvgrw	(	integer	N,
		integer	NCOLS,
		complex*16, dimension( lda, * )	A,
		integer	LDA,
		complex*16, dimension( ldaf, * )	AF,
		integer	LDAF
	)

ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.

Download ZLA_GERPVGRW + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 ZLA_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.

Parameters

[in]	N	N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	NCOLS	NCOLS is INTEGER The number of columns of the matrix A. NCOLS >= 0.
[in]	A	A is COMPLEX*16 array, dimension (LDA,N) On entry, the N-by-N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	AF	AF is COMPLEX*16 array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF.
[in]	LDAF	LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

June 2016

Definition at line 102 of file zla_gerpvgrw.f.

*
*  -- LAPACK computational routine (version 3.6.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..
      INTEGER            n, ncols, lda, ldaf
*     ..
*     .. Array Arguments ..
      COMPLEX*16         a( lda, * ), af( ldaf, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            i, j
      DOUBLE PRECISION   amax, umax, rpvgrw
      COMPLEX*16         zdum
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min, abs, REAL, dimag
*     ..
*     .. Statement Functions ..
      DOUBLE PRECISION   cabs1
*     ..
*     .. Statement Function Definitions ..
      cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
*     ..
*     .. Executable Statements ..
*
      rpvgrw = 1.0d+0

      DO j = 1, ncols
         amax = 0.0d+0
         umax = 0.0d+0
         DO i = 1, n
            amax = max( cabs1( a( i, j ) ), amax )
         END DO
         DO i = 1, j
            umax = max( cabs1( af( i, j ) ), umax )
         END DO
         IF ( umax /= 0.0d+0 ) THEN
            rpvgrw = min( amax / umax, rpvgrw )
         END IF
      END DO
      zla_gerpvgrw = rpvgrw

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