LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sgeequ.f
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1 *> \brief \b SGEEQU
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download SGEEQU + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgeequ.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * INTEGER INFO, LDA, M, N
26 * REAL AMAX, COLCND, ROWCND
27 * ..
28 * .. Array Arguments ..
29 * REAL A( LDA, * ), C( * ), R( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SGEEQU 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 REAL 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 REAL 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 REAL 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 REAL
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 REAL
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 REAL
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 *
129 *> \author Univ. of Tennessee
130 *> \author Univ. of California Berkeley
131 *> \author Univ. of Colorado Denver
132 *> \author NAG Ltd.
133 *
134 *> \ingroup realGEcomputational
135 *
136 * =====================================================================
137  SUBROUTINE sgeequ( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
138  $ INFO )
139 *
140 * -- LAPACK computational routine --
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  REAL AMAX, COLCND, ROWCND
147 * ..
148 * .. Array Arguments ..
149  REAL A( LDA, * ), C( * ), R( * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  REAL ONE, ZERO
156  parameter( one = 1.0e+0, zero = 0.0e+0 )
157 * ..
158 * .. Local Scalars ..
159  INTEGER I, J
160  REAL BIGNUM, RCMAX, RCMIN, SMLNUM
161 * ..
162 * .. External Functions ..
163  REAL SLAMCH
164  EXTERNAL slamch
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( 'SGEEQU', -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 = slamch( '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 SGEEQU
300 *
301  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sgeequ(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)
SGEEQU
Definition: sgeequ.f:139