Annotation of rpl/lapack/lapack/dppequ.f, revision 1.15
1.8 bertrand 1: *> \brief \b DPPEQU
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 DPPEQU + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dppequ.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dppequ.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dppequ.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
1.14 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, N
26: * DOUBLE PRECISION AMAX, SCOND
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION AP( * ), S( * )
30: * ..
1.14 bertrand 31: *
1.8 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DPPEQU computes row and column scalings intended to equilibrate a
39: *> symmetric positive definite matrix A in packed storage and reduce
40: *> its condition number (with respect to the two-norm). S contains the
41: *> scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
42: *> B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
43: *> This choice of S puts the condition number of B within a factor N of
44: *> the smallest possible condition number over all possible diagonal
45: *> scalings.
46: *> \endverbatim
47: *
48: * Arguments:
49: * ==========
50: *
51: *> \param[in] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> = 'U': Upper triangle of A is stored;
55: *> = 'L': Lower triangle of A is stored.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] AP
65: *> \verbatim
66: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
67: *> The upper or lower triangle of the symmetric matrix A, packed
68: *> columnwise in a linear array. The j-th column of A is stored
69: *> in the array AP as follows:
70: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
71: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
72: *> \endverbatim
73: *>
74: *> \param[out] S
75: *> \verbatim
76: *> S is DOUBLE PRECISION array, dimension (N)
77: *> If INFO = 0, S contains the scale factors for A.
78: *> \endverbatim
79: *>
80: *> \param[out] SCOND
81: *> \verbatim
82: *> SCOND is DOUBLE PRECISION
83: *> If INFO = 0, S contains the ratio of the smallest S(i) to
84: *> the largest S(i). If SCOND >= 0.1 and AMAX is neither too
85: *> large nor too small, it is not worth scaling by S.
86: *> \endverbatim
87: *>
88: *> \param[out] AMAX
89: *> \verbatim
90: *> AMAX is DOUBLE PRECISION
91: *> Absolute value of largest matrix element. If AMAX is very
92: *> close to overflow or very close to underflow, the matrix
93: *> should be scaled.
94: *> \endverbatim
95: *>
96: *> \param[out] INFO
97: *> \verbatim
98: *> INFO is INTEGER
99: *> = 0: successful exit
100: *> < 0: if INFO = -i, the i-th argument had an illegal value
101: *> > 0: if INFO = i, the i-th diagonal element is nonpositive.
102: *> \endverbatim
103: *
104: * Authors:
105: * ========
106: *
1.14 bertrand 107: *> \author Univ. of Tennessee
108: *> \author Univ. of California Berkeley
109: *> \author Univ. of Colorado Denver
110: *> \author NAG Ltd.
1.8 bertrand 111: *
1.14 bertrand 112: *> \date December 2016
1.8 bertrand 113: *
114: *> \ingroup doubleOTHERcomputational
115: *
116: * =====================================================================
1.1 bertrand 117: SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
118: *
1.14 bertrand 119: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 120: * -- LAPACK is a software package provided by Univ. of Tennessee, --
121: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 bertrand 122: * December 2016
1.1 bertrand 123: *
124: * .. Scalar Arguments ..
125: CHARACTER UPLO
126: INTEGER INFO, N
127: DOUBLE PRECISION AMAX, SCOND
128: * ..
129: * .. Array Arguments ..
130: DOUBLE PRECISION AP( * ), S( * )
131: * ..
132: *
133: * =====================================================================
134: *
135: * .. Parameters ..
136: DOUBLE PRECISION ONE, ZERO
137: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
138: * ..
139: * .. Local Scalars ..
140: LOGICAL UPPER
141: INTEGER I, JJ
142: DOUBLE PRECISION SMIN
143: * ..
144: * .. External Functions ..
145: LOGICAL LSAME
146: EXTERNAL LSAME
147: * ..
148: * .. External Subroutines ..
149: EXTERNAL XERBLA
150: * ..
151: * .. Intrinsic Functions ..
152: INTRINSIC MAX, MIN, SQRT
153: * ..
154: * .. Executable Statements ..
155: *
156: * Test the input parameters.
157: *
158: INFO = 0
159: UPPER = LSAME( UPLO, 'U' )
160: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
161: INFO = -1
162: ELSE IF( N.LT.0 ) THEN
163: INFO = -2
164: END IF
165: IF( INFO.NE.0 ) THEN
166: CALL XERBLA( 'DPPEQU', -INFO )
167: RETURN
168: END IF
169: *
170: * Quick return if possible
171: *
172: IF( N.EQ.0 ) THEN
173: SCOND = ONE
174: AMAX = ZERO
175: RETURN
176: END IF
177: *
178: * Initialize SMIN and AMAX.
179: *
180: S( 1 ) = AP( 1 )
181: SMIN = S( 1 )
182: AMAX = S( 1 )
183: *
184: IF( UPPER ) THEN
185: *
186: * UPLO = 'U': Upper triangle of A is stored.
187: * Find the minimum and maximum diagonal elements.
188: *
189: JJ = 1
190: DO 10 I = 2, N
191: JJ = JJ + I
192: S( I ) = AP( JJ )
193: SMIN = MIN( SMIN, S( I ) )
194: AMAX = MAX( AMAX, S( I ) )
195: 10 CONTINUE
196: *
197: ELSE
198: *
199: * UPLO = 'L': Lower triangle of A is stored.
200: * Find the minimum and maximum diagonal elements.
201: *
202: JJ = 1
203: DO 20 I = 2, N
204: JJ = JJ + N - I + 2
205: S( I ) = AP( JJ )
206: SMIN = MIN( SMIN, S( I ) )
207: AMAX = MAX( AMAX, S( I ) )
208: 20 CONTINUE
209: END IF
210: *
211: IF( SMIN.LE.ZERO ) THEN
212: *
213: * Find the first non-positive diagonal element and return.
214: *
215: DO 30 I = 1, N
216: IF( S( I ).LE.ZERO ) THEN
217: INFO = I
218: RETURN
219: END IF
220: 30 CONTINUE
221: ELSE
222: *
223: * Set the scale factors to the reciprocals
224: * of the diagonal elements.
225: *
226: DO 40 I = 1, N
227: S( I ) = ONE / SQRT( S( I ) )
228: 40 CONTINUE
229: *
230: * Compute SCOND = min(S(I)) / max(S(I))
231: *
232: SCOND = SQRT( SMIN ) / SQRT( AMAX )
233: END IF
234: RETURN
235: *
236: * End of DPPEQU
237: *
238: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dppequ.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack