1: SUBROUTINE ZGEEQUB( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
2: $ INFO )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
6: * -- Jason Riedy of Univ. of California Berkeley. --
7: * -- November 2008 --
8: *
9: * -- LAPACK is a software package provided by Univ. of Tennessee, --
10: * -- Univ. of California Berkeley and NAG Ltd. --
11: *
12: IMPLICIT NONE
13: * ..
14: * .. Scalar Arguments ..
15: INTEGER INFO, LDA, M, N
16: DOUBLE PRECISION AMAX, COLCND, ROWCND
17: * ..
18: * .. Array Arguments ..
19: DOUBLE PRECISION C( * ), R( * )
20: COMPLEX*16 A( LDA, * )
21: * ..
22: *
23: * Purpose
24: * =======
25: *
26: * ZGEEQUB computes row and column scalings intended to equilibrate an
27: * M-by-N matrix A and reduce its condition number. R returns the row
28: * scale factors and C the column scale factors, chosen to try to make
29: * the largest element in each row and column of the matrix B with
30: * elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
31: * the radix.
32: *
33: * R(i) and C(j) are restricted to be a power of the radix between
34: * SMLNUM = smallest safe number and BIGNUM = largest safe number. Use
35: * of these scaling factors is not guaranteed to reduce the condition
36: * number of A but works well in practice.
37: *
38: * This routine differs from ZGEEQU by restricting the scaling factors
39: * to a power of the radix. Baring over- and underflow, scaling by
40: * these factors introduces no additional rounding errors. However, the
41: * scaled entries' magnitured are no longer approximately 1 but lie
42: * between sqrt(radix) and 1/sqrt(radix).
43: *
44: * Arguments
45: * =========
46: *
47: * M (input) INTEGER
48: * The number of rows of the matrix A. M >= 0.
49: *
50: * N (input) INTEGER
51: * The number of columns of the matrix A. N >= 0.
52: *
53: * A (input) COMPLEX*16 array, dimension (LDA,N)
54: * The M-by-N matrix whose equilibration factors are
55: * to be computed.
56: *
57: * LDA (input) INTEGER
58: * The leading dimension of the array A. LDA >= max(1,M).
59: *
60: * R (output) DOUBLE PRECISION array, dimension (M)
61: * If INFO = 0 or INFO > M, R contains the row scale factors
62: * for A.
63: *
64: * C (output) DOUBLE PRECISION array, dimension (N)
65: * If INFO = 0, C contains the column scale factors for A.
66: *
67: * ROWCND (output) DOUBLE PRECISION
68: * If INFO = 0 or INFO > M, ROWCND contains the ratio of the
69: * smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
70: * AMAX is neither too large nor too small, it is not worth
71: * scaling by R.
72: *
73: * COLCND (output) DOUBLE PRECISION
74: * If INFO = 0, COLCND contains the ratio of the smallest
75: * C(i) to the largest C(i). If COLCND >= 0.1, it is not
76: * worth scaling by C.
77: *
78: * AMAX (output) DOUBLE PRECISION
79: * Absolute value of largest matrix element. If AMAX is very
80: * close to overflow or very close to underflow, the matrix
81: * should be scaled.
82: *
83: * INFO (output) INTEGER
84: * = 0: successful exit
85: * < 0: if INFO = -i, the i-th argument had an illegal value
86: * > 0: if INFO = i, and i is
87: * <= M: the i-th row of A is exactly zero
88: * > M: the (i-M)-th column of A is exactly zero
89: *
90: * =====================================================================
91: *
92: * .. Parameters ..
93: DOUBLE PRECISION ONE, ZERO
94: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
95: * ..
96: * .. Local Scalars ..
97: INTEGER I, J
98: DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM, RADIX, LOGRDX
99: COMPLEX*16 ZDUM
100: * ..
101: * .. External Functions ..
102: DOUBLE PRECISION DLAMCH
103: EXTERNAL DLAMCH
104: * ..
105: * .. External Subroutines ..
106: EXTERNAL XERBLA
107: * ..
108: * .. Intrinsic Functions ..
109: INTRINSIC ABS, MAX, MIN, LOG, REAL, DIMAG
110: * ..
111: * .. Statement Functions ..
112: DOUBLE PRECISION CABS1
113: * ..
114: * .. Statement Function definitions ..
115: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
116: * ..
117: * .. Executable Statements ..
118: *
119: * Test the input parameters.
120: *
121: INFO = 0
122: IF( M.LT.0 ) THEN
123: INFO = -1
124: ELSE IF( N.LT.0 ) THEN
125: INFO = -2
126: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
127: INFO = -4
128: END IF
129: IF( INFO.NE.0 ) THEN
130: CALL XERBLA( 'ZGEEQUB', -INFO )
131: RETURN
132: END IF
133: *
134: * Quick return if possible.
135: *
136: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
137: ROWCND = ONE
138: COLCND = ONE
139: AMAX = ZERO
140: RETURN
141: END IF
142: *
143: * Get machine constants. Assume SMLNUM is a power of the radix.
144: *
145: SMLNUM = DLAMCH( 'S' )
146: BIGNUM = ONE / SMLNUM
147: RADIX = DLAMCH( 'B' )
148: LOGRDX = LOG( RADIX )
149: *
150: * Compute row scale factors.
151: *
152: DO 10 I = 1, M
153: R( I ) = ZERO
154: 10 CONTINUE
155: *
156: * Find the maximum element in each row.
157: *
158: DO 30 J = 1, N
159: DO 20 I = 1, M
160: R( I ) = MAX( R( I ), CABS1( A( I, J ) ) )
161: 20 CONTINUE
162: 30 CONTINUE
163: DO I = 1, M
164: IF( R( I ).GT.ZERO ) THEN
165: R( I ) = RADIX**INT( LOG(R( I ) ) / LOGRDX )
166: END IF
167: END DO
168: *
169: * Find the maximum and minimum scale factors.
170: *
171: RCMIN = BIGNUM
172: RCMAX = ZERO
173: DO 40 I = 1, M
174: RCMAX = MAX( RCMAX, R( I ) )
175: RCMIN = MIN( RCMIN, R( I ) )
176: 40 CONTINUE
177: AMAX = RCMAX
178: *
179: IF( RCMIN.EQ.ZERO ) THEN
180: *
181: * Find the first zero scale factor and return an error code.
182: *
183: DO 50 I = 1, M
184: IF( R( I ).EQ.ZERO ) THEN
185: INFO = I
186: RETURN
187: END IF
188: 50 CONTINUE
189: ELSE
190: *
191: * Invert the scale factors.
192: *
193: DO 60 I = 1, M
194: R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM )
195: 60 CONTINUE
196: *
197: * Compute ROWCND = min(R(I)) / max(R(I)).
198: *
199: ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
200: END IF
201: *
202: * Compute column scale factors.
203: *
204: DO 70 J = 1, N
205: C( J ) = ZERO
206: 70 CONTINUE
207: *
208: * Find the maximum element in each column,
209: * assuming the row scaling computed above.
210: *
211: DO 90 J = 1, N
212: DO 80 I = 1, M
213: C( J ) = MAX( C( J ), CABS1( A( I, J ) )*R( I ) )
214: 80 CONTINUE
215: IF( C( J ).GT.ZERO ) THEN
216: C( J ) = RADIX**INT( LOG( C( J ) ) / LOGRDX )
217: END IF
218: 90 CONTINUE
219: *
220: * Find the maximum and minimum scale factors.
221: *
222: RCMIN = BIGNUM
223: RCMAX = ZERO
224: DO 100 J = 1, N
225: RCMIN = MIN( RCMIN, C( J ) )
226: RCMAX = MAX( RCMAX, C( J ) )
227: 100 CONTINUE
228: *
229: IF( RCMIN.EQ.ZERO ) THEN
230: *
231: * Find the first zero scale factor and return an error code.
232: *
233: DO 110 J = 1, N
234: IF( C( J ).EQ.ZERO ) THEN
235: INFO = M + J
236: RETURN
237: END IF
238: 110 CONTINUE
239: ELSE
240: *
241: * Invert the scale factors.
242: *
243: DO 120 J = 1, N
244: C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM )
245: 120 CONTINUE
246: *
247: * Compute COLCND = min(C(J)) / max(C(J)).
248: *
249: COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
250: END IF
251: *
252: RETURN
253: *
254: * End of ZGEEQUB
255: *
256: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zgeequb.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack