Annotation of rpl/lapack/lapack/zla_gbrpvgrw.f, revision 1.5
1.5 ! bertrand 1: *> \brief \b ZLA_GBRPVGRW
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLA_GBRPVGRW + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gbrpvgrw.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
! 22: * LDAB, AFB, LDAFB )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZLA_GBRPVGRW computes the reciprocal pivot growth factor
! 38: *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
! 39: *> much less than 1, the stability of the LU factorization of the
! 40: *> (equilibrated) matrix A could be poor. This also means that the
! 41: *> solution X, estimated condition numbers, and error bounds could be
! 42: *> unreliable.
! 43: *> \endverbatim
! 44: *
! 45: * Arguments:
! 46: * ==========
! 47: *
! 48: *> \param[in] N
! 49: *> \verbatim
! 50: *> N is INTEGER
! 51: *> The number of linear equations, i.e., the order of the
! 52: *> matrix A. N >= 0.
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] KL
! 56: *> \verbatim
! 57: *> KL is INTEGER
! 58: *> The number of subdiagonals within the band of A. KL >= 0.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] KU
! 62: *> \verbatim
! 63: *> KU is INTEGER
! 64: *> The number of superdiagonals within the band of A. KU >= 0.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] NCOLS
! 68: *> \verbatim
! 69: *> NCOLS is INTEGER
! 70: *> The number of columns of the matrix A. NCOLS >= 0.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] AB
! 74: *> \verbatim
! 75: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 76: *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 77: *> The j-th column of A is stored in the j-th column of the
! 78: *> array AB as follows:
! 79: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] LDAB
! 83: *> \verbatim
! 84: *> LDAB is INTEGER
! 85: *> The leading dimension of the array AB. LDAB >= KL+KU+1.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] AFB
! 89: *> \verbatim
! 90: *> AFB is COMPLEX*16 array, dimension (LDAFB,N)
! 91: *> Details of the LU factorization of the band matrix A, as
! 92: *> computed by ZGBTRF. U is stored as an upper triangular
! 93: *> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
! 94: *> and the multipliers used during the factorization are stored
! 95: *> in rows KL+KU+2 to 2*KL+KU+1.
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[in] LDAFB
! 99: *> \verbatim
! 100: *> LDAFB is INTEGER
! 101: *> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
! 102: *> \endverbatim
! 103: *
! 104: * Authors:
! 105: * ========
! 106: *
! 107: *> \author Univ. of Tennessee
! 108: *> \author Univ. of California Berkeley
! 109: *> \author Univ. of Colorado Denver
! 110: *> \author NAG Ltd.
! 111: *
! 112: *> \date November 2011
! 113: *
! 114: *> \ingroup complex16GBcomputational
! 115: *
! 116: * =====================================================================
1.1 bertrand 117: DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
118: $ LDAB, AFB, LDAFB )
119: *
1.5 ! bertrand 120: * -- LAPACK computational routine (version 3.4.0) --
! 121: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 122: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 123: * November 2011
1.1 bertrand 124: *
125: * .. Scalar Arguments ..
126: INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
127: * ..
128: * .. Array Arguments ..
129: COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Local Scalars ..
135: INTEGER I, J, KD
136: DOUBLE PRECISION AMAX, UMAX, RPVGRW
137: COMPLEX*16 ZDUM
138: * ..
139: * .. Intrinsic Functions ..
140: INTRINSIC ABS, MAX, MIN, REAL, DIMAG
141: * ..
142: * .. Statement Functions ..
143: DOUBLE PRECISION CABS1
144: * ..
145: * .. Statement Function Definitions ..
146: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
147: * ..
148: * .. Executable Statements ..
149: *
150: RPVGRW = 1.0D+0
151:
152: KD = KU + 1
153: DO J = 1, NCOLS
154: AMAX = 0.0D+0
155: UMAX = 0.0D+0
156: DO I = MAX( J-KU, 1 ), MIN( J+KL, N )
157: AMAX = MAX( CABS1( AB( KD+I-J, J ) ), AMAX )
158: END DO
159: DO I = MAX( J-KU, 1 ), J
160: UMAX = MAX( CABS1( AFB( KD+I-J, J ) ), UMAX )
161: END DO
162: IF ( UMAX /= 0.0D+0 ) THEN
163: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
164: END IF
165: END DO
166: ZLA_GBRPVGRW = RPVGRW
167: END
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