Annotation of rpl/lapack/lapack/dpoequb.f, revision 1.3
1.1 bertrand 1: SUBROUTINE DPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
5: * -- Jason Riedy of Univ. of California Berkeley. --
6: * -- November 2008 --
7: *
8: * -- LAPACK is a software package provided by Univ. of Tennessee, --
9: * -- Univ. of California Berkeley and NAG Ltd. --
10: *
11: IMPLICIT NONE
12: * ..
13: * .. Scalar Arguments ..
14: INTEGER INFO, LDA, N
15: DOUBLE PRECISION AMAX, SCOND
16: * ..
17: * .. Array Arguments ..
18: DOUBLE PRECISION A( LDA, * ), S( * )
19: * ..
20: *
21: * Purpose
22: * =======
23: *
24: * DPOEQU computes row and column scalings intended to equilibrate a
25: * symmetric positive definite matrix A and reduce its condition number
26: * (with respect to the two-norm). S contains the scale factors,
27: * S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
28: * elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
29: * choice of S puts the condition number of B within a factor N of the
30: * smallest possible condition number over all possible diagonal
31: * scalings.
32: *
33: * Arguments
34: * =========
35: *
36: * N (input) INTEGER
37: * The order of the matrix A. N >= 0.
38: *
39: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
40: * The N-by-N symmetric positive definite matrix whose scaling
41: * factors are to be computed. Only the diagonal elements of A
42: * are referenced.
43: *
44: * LDA (input) INTEGER
45: * The leading dimension of the array A. LDA >= max(1,N).
46: *
47: * S (output) DOUBLE PRECISION array, dimension (N)
48: * If INFO = 0, S contains the scale factors for A.
49: *
50: * SCOND (output) DOUBLE PRECISION
51: * If INFO = 0, S contains the ratio of the smallest S(i) to
52: * the largest S(i). If SCOND >= 0.1 and AMAX is neither too
53: * large nor too small, it is not worth scaling by S.
54: *
55: * AMAX (output) DOUBLE PRECISION
56: * Absolute value of largest matrix element. If AMAX is very
57: * close to overflow or very close to underflow, the matrix
58: * should be scaled.
59: *
60: * INFO (output) INTEGER
61: * = 0: successful exit
62: * < 0: if INFO = -i, the i-th argument had an illegal value
63: * > 0: if INFO = i, the i-th diagonal element is nonpositive.
64: *
65: * =====================================================================
66: *
67: * .. Parameters ..
68: DOUBLE PRECISION ZERO, ONE
69: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
70: * ..
71: * .. Local Scalars ..
72: INTEGER I
73: DOUBLE PRECISION SMIN, BASE, TMP
74: * ..
75: * .. External Functions ..
76: DOUBLE PRECISION DLAMCH
77: EXTERNAL DLAMCH
78: * ..
79: * .. External Subroutines ..
80: EXTERNAL XERBLA
81: * ..
82: * .. Intrinsic Functions ..
83: INTRINSIC MAX, MIN, SQRT, LOG, INT
84: * ..
85: * .. Executable Statements ..
86: *
87: * Test the input parameters.
88: *
89: * Positive definite only performs 1 pass of equilibration.
90: *
91: INFO = 0
92: IF( N.LT.0 ) THEN
93: INFO = -1
94: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
95: INFO = -3
96: END IF
97: IF( INFO.NE.0 ) THEN
98: CALL XERBLA( 'DPOEQUB', -INFO )
99: RETURN
100: END IF
101: *
102: * Quick return if possible.
103: *
104: IF( N.EQ.0 ) THEN
105: SCOND = ONE
106: AMAX = ZERO
107: RETURN
108: END IF
109:
110: BASE = DLAMCH( 'B' )
111: TMP = -0.5D+0 / LOG ( BASE )
112: *
113: * Find the minimum and maximum diagonal elements.
114: *
115: S( 1 ) = A( 1, 1 )
116: SMIN = S( 1 )
117: AMAX = S( 1 )
118: DO 10 I = 2, N
119: S( I ) = A( I, I )
120: SMIN = MIN( SMIN, S( I ) )
121: AMAX = MAX( AMAX, S( I ) )
122: 10 CONTINUE
123: *
124: IF( SMIN.LE.ZERO ) THEN
125: *
126: * Find the first non-positive diagonal element and return.
127: *
128: DO 20 I = 1, N
129: IF( S( I ).LE.ZERO ) THEN
130: INFO = I
131: RETURN
132: END IF
133: 20 CONTINUE
134: ELSE
135: *
136: * Set the scale factors to the reciprocals
137: * of the diagonal elements.
138: *
139: DO 30 I = 1, N
140: S( I ) = BASE ** INT( TMP * LOG( S( I ) ) )
141: 30 CONTINUE
142: *
143: * Compute SCOND = min(S(I)) / max(S(I)).
144: *
145: SCOND = SQRT( SMIN ) / SQRT( AMAX )
146: END IF
147: *
148: RETURN
149: *
150: * End of DPOEQUB
151: *
152: END
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