Annotation of rpl/lapack/lapack/zgeequ.f, revision 1.17
1.8 bertrand 1: *> \brief \b ZGEEQU
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 ZGEEQU + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeequ.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeequ.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeequ.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGEEQU( 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 C( * ), R( * )
30: * COMPLEX*16 A( LDA, * )
31: * ..
1.14 bertrand 32: *
1.8 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZGEEQU computes row and column scalings intended to equilibrate an
40: *> M-by-N matrix A and reduce its condition number. R returns the row
41: *> scale factors and C the column scale factors, chosen to try to make
42: *> the largest element in each row and column of the matrix B with
43: *> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
44: *>
45: *> R(i) and C(j) are restricted to be between SMLNUM = smallest safe
46: *> number and BIGNUM = largest safe number. Use of these scaling
47: *> factors is not guaranteed to reduce the condition number of A but
48: *> works well in practice.
49: *> \endverbatim
50: *
51: * Arguments:
52: * ==========
53: *
54: *> \param[in] M
55: *> \verbatim
56: *> M is INTEGER
57: *> The number of rows of the matrix A. M >= 0.
58: *> \endverbatim
59: *>
60: *> \param[in] N
61: *> \verbatim
62: *> N is INTEGER
63: *> The number of columns of the matrix A. N >= 0.
64: *> \endverbatim
65: *>
66: *> \param[in] A
67: *> \verbatim
68: *> A is COMPLEX*16 array, dimension (LDA,N)
69: *> The M-by-N matrix whose equilibration factors are
70: *> to be computed.
71: *> \endverbatim
72: *>
73: *> \param[in] LDA
74: *> \verbatim
75: *> LDA is INTEGER
76: *> The leading dimension of the array A. LDA >= max(1,M).
77: *> \endverbatim
78: *>
79: *> \param[out] R
80: *> \verbatim
81: *> R is DOUBLE PRECISION array, dimension (M)
82: *> If INFO = 0 or INFO > M, R contains the row scale factors
83: *> for A.
84: *> \endverbatim
85: *>
86: *> \param[out] C
87: *> \verbatim
88: *> C is DOUBLE PRECISION array, dimension (N)
89: *> If INFO = 0, C contains the column scale factors for A.
90: *> \endverbatim
91: *>
92: *> \param[out] ROWCND
93: *> \verbatim
94: *> ROWCND is DOUBLE PRECISION
95: *> If INFO = 0 or INFO > M, ROWCND contains the ratio of the
96: *> smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
97: *> AMAX is neither too large nor too small, it is not worth
98: *> scaling by R.
99: *> \endverbatim
100: *>
101: *> \param[out] COLCND
102: *> \verbatim
103: *> COLCND is DOUBLE PRECISION
104: *> If INFO = 0, COLCND contains the ratio of the smallest
105: *> C(i) to the largest C(i). If COLCND >= 0.1, it is not
106: *> worth scaling by C.
107: *> \endverbatim
108: *>
109: *> \param[out] AMAX
110: *> \verbatim
111: *> AMAX is DOUBLE PRECISION
112: *> Absolute value of largest matrix element. If AMAX is very
113: *> close to overflow or very close to underflow, the matrix
114: *> should be scaled.
115: *> \endverbatim
116: *>
117: *> \param[out] INFO
118: *> \verbatim
119: *> INFO is INTEGER
120: *> = 0: successful exit
121: *> < 0: if INFO = -i, the i-th argument had an illegal value
122: *> > 0: if INFO = i, and i is
123: *> <= M: the i-th row of A is exactly zero
124: *> > M: the (i-M)-th column of A is exactly zero
125: *> \endverbatim
126: *
127: * Authors:
128: * ========
129: *
1.14 bertrand 130: *> \author Univ. of Tennessee
131: *> \author Univ. of California Berkeley
132: *> \author Univ. of Colorado Denver
133: *> \author NAG Ltd.
1.8 bertrand 134: *
135: *> \ingroup complex16GEcomputational
136: *
137: * =====================================================================
1.1 bertrand 138: SUBROUTINE ZGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
139: $ INFO )
140: *
1.17 ! bertrand 141: * -- LAPACK computational routine --
1.1 bertrand 142: * -- LAPACK is a software package provided by Univ. of Tennessee, --
143: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144: *
145: * .. Scalar Arguments ..
146: INTEGER INFO, LDA, M, N
147: DOUBLE PRECISION AMAX, COLCND, ROWCND
148: * ..
149: * .. Array Arguments ..
150: DOUBLE PRECISION C( * ), R( * )
151: COMPLEX*16 A( LDA, * )
152: * ..
153: *
154: * =====================================================================
155: *
156: * .. Parameters ..
157: DOUBLE PRECISION ONE, ZERO
158: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
159: * ..
160: * .. Local Scalars ..
161: INTEGER I, J
162: DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
163: COMPLEX*16 ZDUM
164: * ..
165: * .. External Functions ..
166: DOUBLE PRECISION DLAMCH
167: EXTERNAL DLAMCH
168: * ..
169: * .. External Subroutines ..
170: EXTERNAL XERBLA
171: * ..
172: * .. Intrinsic Functions ..
173: INTRINSIC ABS, DBLE, DIMAG, MAX, MIN
174: * ..
175: * .. Statement Functions ..
176: DOUBLE PRECISION CABS1
177: * ..
178: * .. Statement Function definitions ..
179: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
180: * ..
181: * .. Executable Statements ..
182: *
183: * Test the input parameters.
184: *
185: INFO = 0
186: IF( M.LT.0 ) THEN
187: INFO = -1
188: ELSE IF( N.LT.0 ) THEN
189: INFO = -2
190: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
191: INFO = -4
192: END IF
193: IF( INFO.NE.0 ) THEN
194: CALL XERBLA( 'ZGEEQU', -INFO )
195: RETURN
196: END IF
197: *
198: * Quick return if possible
199: *
200: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
201: ROWCND = ONE
202: COLCND = ONE
203: AMAX = ZERO
204: RETURN
205: END IF
206: *
207: * Get machine constants.
208: *
209: SMLNUM = DLAMCH( 'S' )
210: BIGNUM = ONE / SMLNUM
211: *
212: * Compute row scale factors.
213: *
214: DO 10 I = 1, M
215: R( I ) = ZERO
216: 10 CONTINUE
217: *
218: * Find the maximum element in each row.
219: *
220: DO 30 J = 1, N
221: DO 20 I = 1, M
222: R( I ) = MAX( R( I ), CABS1( A( I, J ) ) )
223: 20 CONTINUE
224: 30 CONTINUE
225: *
226: * Find the maximum and minimum scale factors.
227: *
228: RCMIN = BIGNUM
229: RCMAX = ZERO
230: DO 40 I = 1, M
231: RCMAX = MAX( RCMAX, R( I ) )
232: RCMIN = MIN( RCMIN, R( I ) )
233: 40 CONTINUE
234: AMAX = RCMAX
235: *
236: IF( RCMIN.EQ.ZERO ) THEN
237: *
238: * Find the first zero scale factor and return an error code.
239: *
240: DO 50 I = 1, M
241: IF( R( I ).EQ.ZERO ) THEN
242: INFO = I
243: RETURN
244: END IF
245: 50 CONTINUE
246: ELSE
247: *
248: * Invert the scale factors.
249: *
250: DO 60 I = 1, M
251: R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM )
252: 60 CONTINUE
253: *
254: * Compute ROWCND = min(R(I)) / max(R(I))
255: *
256: ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
257: END IF
258: *
259: * Compute column scale factors
260: *
261: DO 70 J = 1, N
262: C( J ) = ZERO
263: 70 CONTINUE
264: *
265: * Find the maximum element in each column,
266: * assuming the row scaling computed above.
267: *
268: DO 90 J = 1, N
269: DO 80 I = 1, M
270: C( J ) = MAX( C( J ), CABS1( A( I, J ) )*R( I ) )
271: 80 CONTINUE
272: 90 CONTINUE
273: *
274: * Find the maximum and minimum scale factors.
275: *
276: RCMIN = BIGNUM
277: RCMAX = ZERO
278: DO 100 J = 1, N
279: RCMIN = MIN( RCMIN, C( J ) )
280: RCMAX = MAX( RCMAX, C( J ) )
281: 100 CONTINUE
282: *
283: IF( RCMIN.EQ.ZERO ) THEN
284: *
285: * Find the first zero scale factor and return an error code.
286: *
287: DO 110 J = 1, N
288: IF( C( J ).EQ.ZERO ) THEN
289: INFO = M + J
290: RETURN
291: END IF
292: 110 CONTINUE
293: ELSE
294: *
295: * Invert the scale factors.
296: *
297: DO 120 J = 1, N
298: C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM )
299: 120 CONTINUE
300: *
301: * Compute COLCND = min(C(J)) / max(C(J))
302: *
303: COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
304: END IF
305: *
306: RETURN
307: *
308: * End of ZGEEQU
309: *
310: END
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