1: SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER EQUED, UPLO
10: INTEGER KD, LDAB, N
11: DOUBLE PRECISION AMAX, SCOND
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION S( * )
15: COMPLEX*16 AB( LDAB, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZLAQHB equilibrates a symmetric band matrix A using the scaling
22: * factors in the vector S.
23: *
24: * Arguments
25: * =========
26: *
27: * UPLO (input) CHARACTER*1
28: * Specifies whether the upper or lower triangular part of the
29: * symmetric matrix A is stored.
30: * = 'U': Upper triangular
31: * = 'L': Lower triangular
32: *
33: * N (input) INTEGER
34: * The order of the matrix A. N >= 0.
35: *
36: * KD (input) INTEGER
37: * The number of super-diagonals of the matrix A if UPLO = 'U',
38: * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
39: *
40: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
41: * On entry, the upper or lower triangle of the symmetric band
42: * matrix A, stored in the first KD+1 rows of the array. The
43: * j-th column of A is stored in the j-th column of the array AB
44: * as follows:
45: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
46: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
47: *
48: * On exit, if INFO = 0, the triangular factor U or L from the
49: * Cholesky factorization A = U'*U or A = L*L' of the band
50: * matrix A, in the same storage format as A.
51: *
52: * LDAB (input) INTEGER
53: * The leading dimension of the array AB. LDAB >= KD+1.
54: *
55: * S (output) DOUBLE PRECISION array, dimension (N)
56: * The scale factors for A.
57: *
58: * SCOND (input) DOUBLE PRECISION
59: * Ratio of the smallest S(i) to the largest S(i).
60: *
61: * AMAX (input) DOUBLE PRECISION
62: * Absolute value of largest matrix entry.
63: *
64: * EQUED (output) CHARACTER*1
65: * Specifies whether or not equilibration was done.
66: * = 'N': No equilibration.
67: * = 'Y': Equilibration was done, i.e., A has been replaced by
68: * diag(S) * A * diag(S).
69: *
70: * Internal Parameters
71: * ===================
72: *
73: * THRESH is a threshold value used to decide if scaling should be done
74: * based on the ratio of the scaling factors. If SCOND < THRESH,
75: * scaling is done.
76: *
77: * LARGE and SMALL are threshold values used to decide if scaling should
78: * be done based on the absolute size of the largest matrix element.
79: * If AMAX > LARGE or AMAX < SMALL, scaling is done.
80: *
81: * =====================================================================
82: *
83: * .. Parameters ..
84: DOUBLE PRECISION ONE, THRESH
85: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
86: * ..
87: * .. Local Scalars ..
88: INTEGER I, J
89: DOUBLE PRECISION CJ, LARGE, SMALL
90: * ..
91: * .. External Functions ..
92: LOGICAL LSAME
93: DOUBLE PRECISION DLAMCH
94: EXTERNAL LSAME, DLAMCH
95: * ..
96: * .. Intrinsic Functions ..
97: INTRINSIC DBLE, MAX, MIN
98: * ..
99: * .. Executable Statements ..
100: *
101: * Quick return if possible
102: *
103: IF( N.LE.0 ) THEN
104: EQUED = 'N'
105: RETURN
106: END IF
107: *
108: * Initialize LARGE and SMALL.
109: *
110: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
111: LARGE = ONE / SMALL
112: *
113: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
114: *
115: * No equilibration
116: *
117: EQUED = 'N'
118: ELSE
119: *
120: * Replace A by diag(S) * A * diag(S).
121: *
122: IF( LSAME( UPLO, 'U' ) ) THEN
123: *
124: * Upper triangle of A is stored in band format.
125: *
126: DO 20 J = 1, N
127: CJ = S( J )
128: DO 10 I = MAX( 1, J-KD ), J - 1
129: AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
130: 10 CONTINUE
131: AB( KD+1, J ) = CJ*CJ*DBLE( AB( KD+1, J ) )
132: 20 CONTINUE
133: ELSE
134: *
135: * Lower triangle of A is stored.
136: *
137: DO 40 J = 1, N
138: CJ = S( J )
139: AB( 1, J ) = CJ*CJ*DBLE( AB( 1, J ) )
140: DO 30 I = J + 1, MIN( N, J+KD )
141: AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
142: 30 CONTINUE
143: 40 CONTINUE
144: END IF
145: EQUED = 'Y'
146: END IF
147: *
148: RETURN
149: *
150: * End of ZLAQHB
151: *
152: END
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