Annotation of rpl/lapack/lapack/dgeequ.f, revision 1.17
1.8 bertrand 1: *> \brief \b DGEEQU
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 9: *> Download DGEEQU + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeequ.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeequ.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeequ.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
22: * INFO )
1.14 bertrand 23: *
1.8 bertrand 24: * .. Scalar Arguments ..
25: * INTEGER INFO, LDA, M, N
26: * DOUBLE PRECISION AMAX, COLCND, ROWCND
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
30: * ..
1.14 bertrand 31: *
1.8 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DGEEQU computes row and column scalings intended to equilibrate an
39: *> M-by-N matrix A and reduce its condition number. R returns the row
40: *> scale factors and C the column scale factors, chosen to try to make
41: *> the largest element in each row and column of the matrix B with
42: *> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
43: *>
44: *> R(i) and C(j) are restricted to be between SMLNUM = smallest safe
45: *> number and BIGNUM = largest safe number. Use of these scaling
46: *> factors is not guaranteed to reduce the condition number of A but
47: *> works well in practice.
48: *> \endverbatim
49: *
50: * Arguments:
51: * ==========
52: *
53: *> \param[in] M
54: *> \verbatim
55: *> M is INTEGER
56: *> The number of rows of the matrix A. M >= 0.
57: *> \endverbatim
58: *>
59: *> \param[in] N
60: *> \verbatim
61: *> N is INTEGER
62: *> The number of columns of the matrix A. N >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] A
66: *> \verbatim
67: *> A is DOUBLE PRECISION array, dimension (LDA,N)
68: *> The M-by-N matrix whose equilibration factors are
69: *> to be computed.
70: *> \endverbatim
71: *>
72: *> \param[in] LDA
73: *> \verbatim
74: *> LDA is INTEGER
75: *> The leading dimension of the array A. LDA >= max(1,M).
76: *> \endverbatim
77: *>
78: *> \param[out] R
79: *> \verbatim
80: *> R is DOUBLE PRECISION array, dimension (M)
81: *> If INFO = 0 or INFO > M, R contains the row scale factors
82: *> for A.
83: *> \endverbatim
84: *>
85: *> \param[out] C
86: *> \verbatim
87: *> C is DOUBLE PRECISION array, dimension (N)
88: *> If INFO = 0, C contains the column scale factors for A.
89: *> \endverbatim
90: *>
91: *> \param[out] ROWCND
92: *> \verbatim
93: *> ROWCND is DOUBLE PRECISION
94: *> If INFO = 0 or INFO > M, ROWCND contains the ratio of the
95: *> smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
96: *> AMAX is neither too large nor too small, it is not worth
97: *> scaling by R.
98: *> \endverbatim
99: *>
100: *> \param[out] COLCND
101: *> \verbatim
102: *> COLCND is DOUBLE PRECISION
103: *> If INFO = 0, COLCND contains the ratio of the smallest
104: *> C(i) to the largest C(i). If COLCND >= 0.1, it is not
105: *> worth scaling by C.
106: *> \endverbatim
107: *>
108: *> \param[out] AMAX
109: *> \verbatim
110: *> AMAX is DOUBLE PRECISION
111: *> Absolute value of largest matrix element. If AMAX is very
112: *> close to overflow or very close to underflow, the matrix
113: *> should be scaled.
114: *> \endverbatim
115: *>
116: *> \param[out] INFO
117: *> \verbatim
118: *> INFO is INTEGER
119: *> = 0: successful exit
120: *> < 0: if INFO = -i, the i-th argument had an illegal value
121: *> > 0: if INFO = i, and i is
122: *> <= M: the i-th row of A is exactly zero
123: *> > M: the (i-M)-th column of A is exactly zero
124: *> \endverbatim
125: *
126: * Authors:
127: * ========
128: *
1.14 bertrand 129: *> \author Univ. of Tennessee
130: *> \author Univ. of California Berkeley
131: *> \author Univ. of Colorado Denver
132: *> \author NAG Ltd.
1.8 bertrand 133: *
134: *> \ingroup doubleGEcomputational
135: *
136: * =====================================================================
1.1 bertrand 137: SUBROUTINE DGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
138: $ INFO )
139: *
1.17 ! bertrand 140: * -- LAPACK computational routine --
1.1 bertrand 141: * -- LAPACK is a software package provided by Univ. of Tennessee, --
142: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143: *
144: * .. Scalar Arguments ..
145: INTEGER INFO, LDA, M, N
146: DOUBLE PRECISION AMAX, COLCND, ROWCND
147: * ..
148: * .. Array Arguments ..
149: DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
150: * ..
151: *
152: * =====================================================================
153: *
154: * .. Parameters ..
155: DOUBLE PRECISION ONE, ZERO
156: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
157: * ..
158: * .. Local Scalars ..
159: INTEGER I, J
160: DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
161: * ..
162: * .. External Functions ..
163: DOUBLE PRECISION DLAMCH
164: EXTERNAL DLAMCH
165: * ..
166: * .. External Subroutines ..
167: EXTERNAL XERBLA
168: * ..
169: * .. Intrinsic Functions ..
170: INTRINSIC ABS, MAX, MIN
171: * ..
172: * .. Executable Statements ..
173: *
174: * Test the input parameters.
175: *
176: INFO = 0
177: IF( M.LT.0 ) THEN
178: INFO = -1
179: ELSE IF( N.LT.0 ) THEN
180: INFO = -2
181: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
182: INFO = -4
183: END IF
184: IF( INFO.NE.0 ) THEN
185: CALL XERBLA( 'DGEEQU', -INFO )
186: RETURN
187: END IF
188: *
189: * Quick return if possible
190: *
191: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
192: ROWCND = ONE
193: COLCND = ONE
194: AMAX = ZERO
195: RETURN
196: END IF
197: *
198: * Get machine constants.
199: *
200: SMLNUM = DLAMCH( 'S' )
201: BIGNUM = ONE / SMLNUM
202: *
203: * Compute row scale factors.
204: *
205: DO 10 I = 1, M
206: R( I ) = ZERO
207: 10 CONTINUE
208: *
209: * Find the maximum element in each row.
210: *
211: DO 30 J = 1, N
212: DO 20 I = 1, M
213: R( I ) = MAX( R( I ), ABS( A( I, J ) ) )
214: 20 CONTINUE
215: 30 CONTINUE
216: *
217: * Find the maximum and minimum scale factors.
218: *
219: RCMIN = BIGNUM
220: RCMAX = ZERO
221: DO 40 I = 1, M
222: RCMAX = MAX( RCMAX, R( I ) )
223: RCMIN = MIN( RCMIN, R( I ) )
224: 40 CONTINUE
225: AMAX = RCMAX
226: *
227: IF( RCMIN.EQ.ZERO ) THEN
228: *
229: * Find the first zero scale factor and return an error code.
230: *
231: DO 50 I = 1, M
232: IF( R( I ).EQ.ZERO ) THEN
233: INFO = I
234: RETURN
235: END IF
236: 50 CONTINUE
237: ELSE
238: *
239: * Invert the scale factors.
240: *
241: DO 60 I = 1, M
242: R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM )
243: 60 CONTINUE
244: *
245: * Compute ROWCND = min(R(I)) / max(R(I))
246: *
247: ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
248: END IF
249: *
250: * Compute column scale factors
251: *
252: DO 70 J = 1, N
253: C( J ) = ZERO
254: 70 CONTINUE
255: *
256: * Find the maximum element in each column,
257: * assuming the row scaling computed above.
258: *
259: DO 90 J = 1, N
260: DO 80 I = 1, M
261: C( J ) = MAX( C( J ), ABS( A( I, J ) )*R( I ) )
262: 80 CONTINUE
263: 90 CONTINUE
264: *
265: * Find the maximum and minimum scale factors.
266: *
267: RCMIN = BIGNUM
268: RCMAX = ZERO
269: DO 100 J = 1, N
270: RCMIN = MIN( RCMIN, C( J ) )
271: RCMAX = MAX( RCMAX, C( J ) )
272: 100 CONTINUE
273: *
274: IF( RCMIN.EQ.ZERO ) THEN
275: *
276: * Find the first zero scale factor and return an error code.
277: *
278: DO 110 J = 1, N
279: IF( C( J ).EQ.ZERO ) THEN
280: INFO = M + J
281: RETURN
282: END IF
283: 110 CONTINUE
284: ELSE
285: *
286: * Invert the scale factors.
287: *
288: DO 120 J = 1, N
289: C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM )
290: 120 CONTINUE
291: *
292: * Compute COLCND = min(C(J)) / max(C(J))
293: *
294: COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
295: END IF
296: *
297: RETURN
298: *
299: * End of DGEEQU
300: *
301: END
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