Annotation of rpl/lapack/lapack/zla_porpvgrw.f, revision 1.17
1.8 bertrand 1: *> \brief \b ZLA_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: *
1.13 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.5 bertrand 7: *
8: *> \htmlonly
1.13 bertrand 9: *> Download ZLA_PORPVGRW + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_porpvgrw.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_porpvgrw.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_porpvgrw.f">
1.5 bertrand 15: *> [TXT]</a>
1.13 bertrand 16: *> \endhtmlonly
1.5 bertrand 17: *
18: * Definition:
19: * ===========
20: *
1.13 bertrand 21: * DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
1.5 bertrand 22: * LDAF, WORK )
1.13 bertrand 23: *
1.5 bertrand 24: * .. Scalar Arguments ..
25: * CHARACTER*1 UPLO
26: * INTEGER NCOLS, LDA, LDAF
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 A( LDA, * ), AF( LDAF, * )
30: * DOUBLE PRECISION WORK( * )
31: * ..
1.13 bertrand 32: *
1.5 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
1.13 bertrand 39: *>
1.5 bertrand 40: *> ZLA_PORPVGRW computes the reciprocal pivot growth factor
41: *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
42: *> much less than 1, the stability of the LU factorization of the
43: *> (equilibrated) matrix A could be poor. This also means that the
44: *> solution X, estimated condition numbers, and error bounds could be
45: *> unreliable.
46: *> \endverbatim
47: *
48: * Arguments:
49: * ==========
50: *
51: *> \param[in] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> = 'U': Upper triangle of A is stored;
55: *> = 'L': Lower triangle of A is stored.
56: *> \endverbatim
57: *>
58: *> \param[in] NCOLS
59: *> \verbatim
60: *> NCOLS is INTEGER
61: *> The number of columns of the matrix A. NCOLS >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] A
65: *> \verbatim
66: *> A is COMPLEX*16 array, dimension (LDA,N)
67: *> On entry, the N-by-N matrix A.
68: *> \endverbatim
69: *>
70: *> \param[in] LDA
71: *> \verbatim
72: *> LDA is INTEGER
73: *> The leading dimension of the array A. LDA >= max(1,N).
74: *> \endverbatim
75: *>
76: *> \param[in] AF
77: *> \verbatim
78: *> AF is COMPLEX*16 array, dimension (LDAF,N)
79: *> The triangular factor U or L from the Cholesky factorization
80: *> A = U**T*U or A = L*L**T, as computed by ZPOTRF.
81: *> \endverbatim
82: *>
83: *> \param[in] LDAF
84: *> \verbatim
85: *> LDAF is INTEGER
86: *> The leading dimension of the array AF. LDAF >= max(1,N).
87: *> \endverbatim
88: *>
1.16 bertrand 89: *> \param[out] WORK
1.5 bertrand 90: *> \verbatim
1.11 bertrand 91: *> WORK is DOUBLE PRECISION array, dimension (2*N)
1.5 bertrand 92: *> \endverbatim
93: *
94: * Authors:
95: * ========
96: *
1.13 bertrand 97: *> \author Univ. of Tennessee
98: *> \author Univ. of California Berkeley
99: *> \author Univ. of Colorado Denver
100: *> \author NAG Ltd.
1.5 bertrand 101: *
102: *> \ingroup complex16POcomputational
103: *
104: * =====================================================================
1.13 bertrand 105: DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
1.1 bertrand 106: $ LDAF, WORK )
107: *
1.17 ! bertrand 108: * -- LAPACK computational routine --
1.5 bertrand 109: * -- LAPACK is a software package provided by Univ. of Tennessee, --
110: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.1 bertrand 111: *
112: * .. Scalar Arguments ..
113: CHARACTER*1 UPLO
114: INTEGER NCOLS, LDA, LDAF
115: * ..
116: * .. Array Arguments ..
117: COMPLEX*16 A( LDA, * ), AF( LDAF, * )
118: DOUBLE PRECISION WORK( * )
119: * ..
120: *
121: * =====================================================================
122: *
123: * .. Local Scalars ..
124: INTEGER I, J
125: DOUBLE PRECISION AMAX, UMAX, RPVGRW
126: LOGICAL UPPER
127: COMPLEX*16 ZDUM
128: * ..
129: * .. External Functions ..
1.13 bertrand 130: EXTERNAL LSAME
1.1 bertrand 131: LOGICAL LSAME
132: * ..
133: * .. Intrinsic Functions ..
134: INTRINSIC ABS, MAX, MIN, REAL, DIMAG
135: * ..
136: * .. Statement Functions ..
137: DOUBLE PRECISION CABS1
138: * ..
139: * .. Statement Function Definitions ..
140: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
141: * ..
142: * .. Executable Statements ..
143: UPPER = LSAME( 'Upper', UPLO )
144: *
145: * DPOTRF will have factored only the NCOLSxNCOLS leading minor, so
146: * we restrict the growth search to that minor and use only the first
147: * 2*NCOLS workspace entries.
148: *
149: RPVGRW = 1.0D+0
150: DO I = 1, 2*NCOLS
151: WORK( I ) = 0.0D+0
152: END DO
153: *
154: * Find the max magnitude entry of each column.
155: *
156: IF ( UPPER ) THEN
157: DO J = 1, NCOLS
158: DO I = 1, J
159: WORK( NCOLS+J ) =
160: $ MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) )
161: END DO
162: END DO
163: ELSE
164: DO J = 1, NCOLS
165: DO I = J, NCOLS
166: WORK( NCOLS+J ) =
167: $ MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) )
168: END DO
169: END DO
170: END IF
171: *
172: * Now find the max magnitude entry of each column of the factor in
173: * AF. No pivoting, so no permutations.
174: *
175: IF ( LSAME( 'Upper', UPLO ) ) THEN
176: DO J = 1, NCOLS
177: DO I = 1, J
178: WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) )
179: END DO
180: END DO
181: ELSE
182: DO J = 1, NCOLS
183: DO I = J, NCOLS
184: WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) )
185: END DO
186: END DO
187: END IF
188: *
189: * Compute the *inverse* of the max element growth factor. Dividing
190: * by zero would imply the largest entry of the factor's column is
191: * zero. Than can happen when either the column of A is zero or
192: * massive pivots made the factor underflow to zero. Neither counts
193: * as growth in itself, so simply ignore terms with zero
194: * denominators.
195: *
196: IF ( LSAME( 'Upper', UPLO ) ) THEN
197: DO I = 1, NCOLS
198: UMAX = WORK( I )
199: AMAX = WORK( NCOLS+I )
200: IF ( UMAX /= 0.0D+0 ) THEN
201: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
202: END IF
203: END DO
204: ELSE
205: DO I = 1, NCOLS
206: UMAX = WORK( I )
207: AMAX = WORK( NCOLS+I )
208: IF ( UMAX /= 0.0D+0 ) THEN
209: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
210: END IF
211: END DO
212: END IF
213:
214: ZLA_PORPVGRW = RPVGRW
1.17 ! bertrand 215: *
! 216: * End of ZLA_PORPVGRW
! 217: *
1.1 bertrand 218: END
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