Annotation of rpl/lapack/lapack/dla_gbrpvgrw.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
1.5 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLA_GBRPVGRW + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbrpvgrw.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbrpvgrw.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbrpvgrw.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLA_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: * DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DLA_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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAFB,N)
91: *> Details of the LU factorization of the band matrix A, as
92: *> computed by DGBTRF. 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: *
1.8 ! bertrand 112: *> \date September 2012
1.5 bertrand 113: *
114: *> \ingroup doubleGBcomputational
115: *
116: * =====================================================================
1.1 bertrand 117: DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
118: $ LDAB, AFB, LDAFB )
119: *
1.8 ! bertrand 120: * -- LAPACK computational routine (version 3.4.2) --
1.5 bertrand 121: * -- LAPACK is a software package provided by Univ. of Tennessee, --
122: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 123: * September 2012
1.1 bertrand 124: *
125: * .. Scalar Arguments ..
126: INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
127: * ..
128: * .. Array Arguments ..
129: DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Local Scalars ..
135: INTEGER I, J, KD
136: DOUBLE PRECISION AMAX, UMAX, RPVGRW
137: * ..
138: * .. Intrinsic Functions ..
139: INTRINSIC ABS, MAX, MIN
140: * ..
141: * .. Executable Statements ..
142: *
143: RPVGRW = 1.0D+0
144:
145: KD = KU + 1
146: DO J = 1, NCOLS
147: AMAX = 0.0D+0
148: UMAX = 0.0D+0
149: DO I = MAX( J-KU, 1 ), MIN( J+KL, N )
150: AMAX = MAX( ABS( AB( KD+I-J, J)), AMAX )
151: END DO
152: DO I = MAX( J-KU, 1 ), J
153: UMAX = MAX( ABS( AFB( KD+I-J, J ) ), UMAX )
154: END DO
155: IF ( UMAX /= 0.0D+0 ) THEN
156: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
157: END IF
158: END DO
159: DLA_GBRPVGRW = RPVGRW
160: END
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