Annotation of rpl/lapack/lapack/zla_gerpvgrw.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZLA_GERPVGRW
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLA_GERPVGRW + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
! 22: * LDAF )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * INTEGER N, NCOLS, LDA, LDAF
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 A( LDA, * ), AF( LDAF, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *>
! 38: *> ZLA_GERPVGRW computes the reciprocal pivot growth factor
! 39: *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
! 40: *> much less than 1, the stability of the LU factorization of the
! 41: *> (equilibrated) matrix A could be poor. This also means that the
! 42: *> solution X, estimated condition numbers, and error bounds could be
! 43: *> unreliable.
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] N
! 50: *> \verbatim
! 51: *> N is INTEGER
! 52: *> The number of linear equations, i.e., the order of the
! 53: *> matrix A. N >= 0.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] NCOLS
! 57: *> \verbatim
! 58: *> NCOLS is INTEGER
! 59: *> The number of columns of the matrix A. NCOLS >= 0.
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] A
! 63: *> \verbatim
! 64: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 65: *> On entry, the N-by-N matrix A.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] LDA
! 69: *> \verbatim
! 70: *> LDA is INTEGER
! 71: *> The leading dimension of the array A. LDA >= max(1,N).
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] AF
! 75: *> \verbatim
! 76: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
! 77: *> The factors L and U from the factorization
! 78: *> A = P*L*U as computed by ZGETRF.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] LDAF
! 82: *> \verbatim
! 83: *> LDAF is INTEGER
! 84: *> The leading dimension of the array AF. LDAF >= max(1,N).
! 85: *> \endverbatim
! 86: *
! 87: * Authors:
! 88: * ========
! 89: *
! 90: *> \author Univ. of Tennessee
! 91: *> \author Univ. of California Berkeley
! 92: *> \author Univ. of Colorado Denver
! 93: *> \author NAG Ltd.
! 94: *
! 95: *> \date November 2011
! 96: *
! 97: *> \ingroup complex16GEcomputational
! 98: *
! 99: * =====================================================================
! 100: DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
! 101: $ LDAF )
! 102: *
! 103: * -- LAPACK computational routine (version 3.4.0) --
! 104: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 105: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 106: * November 2011
! 107: *
! 108: * .. Scalar Arguments ..
! 109: INTEGER N, NCOLS, LDA, LDAF
! 110: * ..
! 111: * .. Array Arguments ..
! 112: COMPLEX*16 A( LDA, * ), AF( LDAF, * )
! 113: * ..
! 114: *
! 115: * =====================================================================
! 116: *
! 117: * .. Local Scalars ..
! 118: INTEGER I, J
! 119: DOUBLE PRECISION AMAX, UMAX, RPVGRW
! 120: COMPLEX*16 ZDUM
! 121: * ..
! 122: * .. Intrinsic Functions ..
! 123: INTRINSIC MAX, MIN, ABS, REAL, DIMAG
! 124: * ..
! 125: * .. Statement Functions ..
! 126: DOUBLE PRECISION CABS1
! 127: * ..
! 128: * .. Statement Function Definitions ..
! 129: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 130: * ..
! 131: * .. Executable Statements ..
! 132: *
! 133: RPVGRW = 1.0D+0
! 134:
! 135: DO J = 1, NCOLS
! 136: AMAX = 0.0D+0
! 137: UMAX = 0.0D+0
! 138: DO I = 1, N
! 139: AMAX = MAX( CABS1( A( I, J ) ), AMAX )
! 140: END DO
! 141: DO I = 1, J
! 142: UMAX = MAX( CABS1( AF( I, J ) ), UMAX )
! 143: END DO
! 144: IF ( UMAX /= 0.0D+0 ) THEN
! 145: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
! 146: END IF
! 147: END DO
! 148: ZLA_GERPVGRW = RPVGRW
! 149: END
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