Annotation of rpl/lapack/lapack/zpoequ.f, revision 1.12
1.8 bertrand 1: *> \brief \b ZPOEQU
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZPOEQU + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpoequ.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpoequ.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpoequ.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, N
25: * DOUBLE PRECISION AMAX, SCOND
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION S( * )
29: * COMPLEX*16 A( LDA, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZPOEQU computes row and column scalings intended to equilibrate a
39: *> Hermitian positive definite matrix A and reduce its condition number
40: *> (with respect to the two-norm). S contains the scale factors,
41: *> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
42: *> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
43: *> choice of S puts the condition number of B within a factor N of the
44: *> smallest possible condition number over all possible diagonal
45: *> scalings.
46: *> \endverbatim
47: *
48: * Arguments:
49: * ==========
50: *
51: *> \param[in] N
52: *> \verbatim
53: *> N is INTEGER
54: *> The order of the matrix A. N >= 0.
55: *> \endverbatim
56: *>
57: *> \param[in] A
58: *> \verbatim
59: *> A is COMPLEX*16 array, dimension (LDA,N)
60: *> The N-by-N Hermitian positive definite matrix whose scaling
61: *> factors are to be computed. Only the diagonal elements of A
62: *> are referenced.
63: *> \endverbatim
64: *>
65: *> \param[in] LDA
66: *> \verbatim
67: *> LDA is INTEGER
68: *> The leading dimension of the array A. LDA >= max(1,N).
69: *> \endverbatim
70: *>
71: *> \param[out] S
72: *> \verbatim
73: *> S is DOUBLE PRECISION array, dimension (N)
74: *> If INFO = 0, S contains the scale factors for A.
75: *> \endverbatim
76: *>
77: *> \param[out] SCOND
78: *> \verbatim
79: *> SCOND is DOUBLE PRECISION
80: *> If INFO = 0, S contains the ratio of the smallest S(i) to
81: *> the largest S(i). If SCOND >= 0.1 and AMAX is neither too
82: *> large nor too small, it is not worth scaling by S.
83: *> \endverbatim
84: *>
85: *> \param[out] AMAX
86: *> \verbatim
87: *> AMAX is DOUBLE PRECISION
88: *> Absolute value of largest matrix element. If AMAX is very
89: *> close to overflow or very close to underflow, the matrix
90: *> should be scaled.
91: *> \endverbatim
92: *>
93: *> \param[out] INFO
94: *> \verbatim
95: *> INFO is INTEGER
96: *> = 0: successful exit
97: *> < 0: if INFO = -i, the i-th argument had an illegal value
98: *> > 0: if INFO = i, the i-th diagonal element is nonpositive.
99: *> \endverbatim
100: *
101: * Authors:
102: * ========
103: *
104: *> \author Univ. of Tennessee
105: *> \author Univ. of California Berkeley
106: *> \author Univ. of Colorado Denver
107: *> \author NAG Ltd.
108: *
109: *> \date November 2011
110: *
111: *> \ingroup complex16POcomputational
112: *
113: * =====================================================================
1.1 bertrand 114: SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
115: *
1.8 bertrand 116: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 117: * -- LAPACK is a software package provided by Univ. of Tennessee, --
118: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 bertrand 119: * November 2011
1.1 bertrand 120: *
121: * .. Scalar Arguments ..
122: INTEGER INFO, LDA, N
123: DOUBLE PRECISION AMAX, SCOND
124: * ..
125: * .. Array Arguments ..
126: DOUBLE PRECISION S( * )
127: COMPLEX*16 A( LDA, * )
128: * ..
129: *
130: * =====================================================================
131: *
132: * .. Parameters ..
133: DOUBLE PRECISION ZERO, ONE
134: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
135: * ..
136: * .. Local Scalars ..
137: INTEGER I
138: DOUBLE PRECISION SMIN
139: * ..
140: * .. External Subroutines ..
141: EXTERNAL XERBLA
142: * ..
143: * .. Intrinsic Functions ..
144: INTRINSIC DBLE, MAX, MIN, SQRT
145: * ..
146: * .. Executable Statements ..
147: *
148: * Test the input parameters.
149: *
150: INFO = 0
151: IF( N.LT.0 ) THEN
152: INFO = -1
153: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
154: INFO = -3
155: END IF
156: IF( INFO.NE.0 ) THEN
157: CALL XERBLA( 'ZPOEQU', -INFO )
158: RETURN
159: END IF
160: *
161: * Quick return if possible
162: *
163: IF( N.EQ.0 ) THEN
164: SCOND = ONE
165: AMAX = ZERO
166: RETURN
167: END IF
168: *
169: * Find the minimum and maximum diagonal elements.
170: *
171: S( 1 ) = DBLE( A( 1, 1 ) )
172: SMIN = S( 1 )
173: AMAX = S( 1 )
174: DO 10 I = 2, N
175: S( I ) = DBLE( A( I, I ) )
176: SMIN = MIN( SMIN, S( I ) )
177: AMAX = MAX( AMAX, S( I ) )
178: 10 CONTINUE
179: *
180: IF( SMIN.LE.ZERO ) THEN
181: *
182: * Find the first non-positive diagonal element and return.
183: *
184: DO 20 I = 1, N
185: IF( S( I ).LE.ZERO ) THEN
186: INFO = I
187: RETURN
188: END IF
189: 20 CONTINUE
190: ELSE
191: *
192: * Set the scale factors to the reciprocals
193: * of the diagonal elements.
194: *
195: DO 30 I = 1, N
196: S( I ) = ONE / SQRT( S( I ) )
197: 30 CONTINUE
198: *
199: * Compute SCOND = min(S(I)) / max(S(I))
200: *
201: SCOND = SQRT( SMIN ) / SQRT( AMAX )
202: END IF
203: RETURN
204: *
205: * End of ZPOEQU
206: *
207: END
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