Annotation of rpl/lapack/lapack/dla_porpvgrw.f, revision 1.9
1.8 bertrand 1: *> \brief \b DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite 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_PORPVGRW + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_porpvgrw.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_porpvgrw.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_porpvgrw.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
22: * LDAF, WORK )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER*1 UPLO
26: * INTEGER NCOLS, LDA, LDAF
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *>
39: *> DLA_PORPVGRW computes the reciprocal pivot growth factor
40: *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
41: *> much less than 1, the stability of the LU factorization of the
42: *> (equilibrated) matrix A could be poor. This also means that the
43: *> solution X, estimated condition numbers, and error bounds could be
44: *> unreliable.
45: *> \endverbatim
46: *
47: * Arguments:
48: * ==========
49: *
50: *> \param[in] UPLO
51: *> \verbatim
52: *> UPLO is CHARACTER*1
53: *> = 'U': Upper triangle of A is stored;
54: *> = 'L': Lower triangle of A is stored.
55: *> \endverbatim
56: *>
57: *> \param[in] NCOLS
58: *> \verbatim
59: *> NCOLS is INTEGER
60: *> The number of columns of the matrix A. NCOLS >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in] A
64: *> \verbatim
65: *> A is DOUBLE PRECISION array, dimension (LDA,N)
66: *> On entry, the N-by-N matrix A.
67: *> \endverbatim
68: *>
69: *> \param[in] LDA
70: *> \verbatim
71: *> LDA is INTEGER
72: *> The leading dimension of the array A. LDA >= max(1,N).
73: *> \endverbatim
74: *>
75: *> \param[in] AF
76: *> \verbatim
77: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
78: *> The triangular factor U or L from the Cholesky factorization
79: *> A = U**T*U or A = L*L**T, as computed by DPOTRF.
80: *> \endverbatim
81: *>
82: *> \param[in] LDAF
83: *> \verbatim
84: *> LDAF is INTEGER
85: *> The leading dimension of the array AF. LDAF >= max(1,N).
86: *> \endverbatim
87: *>
88: *> \param[in] WORK
89: *> \verbatim
90: *> WORK is DOUBLE PRECISION array, dimension (2*N)
91: *> \endverbatim
92: *
93: * Authors:
94: * ========
95: *
96: *> \author Univ. of Tennessee
97: *> \author Univ. of California Berkeley
98: *> \author Univ. of Colorado Denver
99: *> \author NAG Ltd.
100: *
1.8 bertrand 101: *> \date September 2012
1.5 bertrand 102: *
103: *> \ingroup doublePOcomputational
104: *
105: * =====================================================================
1.1 bertrand 106: DOUBLE PRECISION FUNCTION DLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
107: $ LDAF, WORK )
108: *
1.8 bertrand 109: * -- LAPACK computational routine (version 3.4.2) --
1.5 bertrand 110: * -- LAPACK is a software package provided by Univ. of Tennessee, --
111: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 bertrand 112: * September 2012
1.1 bertrand 113: *
114: * .. Scalar Arguments ..
115: CHARACTER*1 UPLO
116: INTEGER NCOLS, LDA, LDAF
117: * ..
118: * .. Array Arguments ..
119: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * )
120: * ..
121: *
122: * =====================================================================
123: *
124: * .. Local Scalars ..
125: INTEGER I, J
126: DOUBLE PRECISION AMAX, UMAX, RPVGRW
127: LOGICAL UPPER
128: * ..
129: * .. Intrinsic Functions ..
130: INTRINSIC ABS, MAX, MIN
131: * ..
132: * .. External Functions ..
133: EXTERNAL LSAME, DLASET
134: LOGICAL LSAME
135: * ..
136: * .. Executable Statements ..
137: *
138: UPPER = LSAME( 'Upper', UPLO )
139: *
140: * DPOTRF will have factored only the NCOLSxNCOLS leading minor, so
141: * we restrict the growth search to that minor and use only the first
142: * 2*NCOLS workspace entries.
143: *
144: RPVGRW = 1.0D+0
145: DO I = 1, 2*NCOLS
146: WORK( I ) = 0.0D+0
147: END DO
148: *
149: * Find the max magnitude entry of each column.
150: *
151: IF ( UPPER ) THEN
152: DO J = 1, NCOLS
153: DO I = 1, J
154: WORK( NCOLS+J ) =
155: $ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) )
156: END DO
157: END DO
158: ELSE
159: DO J = 1, NCOLS
160: DO I = J, NCOLS
161: WORK( NCOLS+J ) =
162: $ MAX( ABS( A( I, J ) ), WORK( NCOLS+J ) )
163: END DO
164: END DO
165: END IF
166: *
167: * Now find the max magnitude entry of each column of the factor in
168: * AF. No pivoting, so no permutations.
169: *
170: IF ( LSAME( 'Upper', UPLO ) ) THEN
171: DO J = 1, NCOLS
172: DO I = 1, J
173: WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) )
174: END DO
175: END DO
176: ELSE
177: DO J = 1, NCOLS
178: DO I = J, NCOLS
179: WORK( J ) = MAX( ABS( AF( I, J ) ), WORK( J ) )
180: END DO
181: END DO
182: END IF
183: *
184: * Compute the *inverse* of the max element growth factor. Dividing
185: * by zero would imply the largest entry of the factor's column is
186: * zero. Than can happen when either the column of A is zero or
187: * massive pivots made the factor underflow to zero. Neither counts
188: * as growth in itself, so simply ignore terms with zero
189: * denominators.
190: *
191: IF ( LSAME( 'Upper', UPLO ) ) THEN
192: DO I = 1, NCOLS
193: UMAX = WORK( I )
194: AMAX = WORK( NCOLS+I )
195: IF ( UMAX /= 0.0D+0 ) THEN
196: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
197: END IF
198: END DO
199: ELSE
200: DO I = 1, NCOLS
201: UMAX = WORK( I )
202: AMAX = WORK( NCOLS+I )
203: IF ( UMAX /= 0.0D+0 ) THEN
204: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
205: END IF
206: END DO
207: END IF
208:
209: DLA_PORPVGRW = RPVGRW
210: END
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