Annotation of rpl/lapack/lapack/zlaqgb.f, revision 1.4
1.1 bertrand 1: SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
2: $ AMAX, EQUED )
3: *
4: * -- LAPACK auxiliary routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: CHARACTER EQUED
11: INTEGER KL, KU, LDAB, M, N
12: DOUBLE PRECISION AMAX, COLCND, ROWCND
13: * ..
14: * .. Array Arguments ..
15: DOUBLE PRECISION C( * ), R( * )
16: COMPLEX*16 AB( LDAB, * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * ZLAQGB equilibrates a general M by N band matrix A with KL
23: * subdiagonals and KU superdiagonals using the row and scaling factors
24: * in the vectors R and C.
25: *
26: * Arguments
27: * =========
28: *
29: * M (input) INTEGER
30: * The number of rows of the matrix A. M >= 0.
31: *
32: * N (input) INTEGER
33: * The number of columns of the matrix A. N >= 0.
34: *
35: * KL (input) INTEGER
36: * The number of subdiagonals within the band of A. KL >= 0.
37: *
38: * KU (input) INTEGER
39: * The number of superdiagonals within the band of A. KU >= 0.
40: *
41: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
42: * On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
43: * The j-th column of A is stored in the j-th column of the
44: * array AB as follows:
45: * AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
46: *
47: * On exit, the equilibrated matrix, in the same storage format
48: * as A. See EQUED for the form of the equilibrated matrix.
49: *
50: * LDAB (input) INTEGER
51: * The leading dimension of the array AB. LDA >= KL+KU+1.
52: *
53: * R (input) DOUBLE PRECISION array, dimension (M)
54: * The row scale factors for A.
55: *
56: * C (input) DOUBLE PRECISION array, dimension (N)
57: * The column scale factors for A.
58: *
59: * ROWCND (input) DOUBLE PRECISION
60: * Ratio of the smallest R(i) to the largest R(i).
61: *
62: * COLCND (input) DOUBLE PRECISION
63: * Ratio of the smallest C(i) to the largest C(i).
64: *
65: * AMAX (input) DOUBLE PRECISION
66: * Absolute value of largest matrix entry.
67: *
68: * EQUED (output) CHARACTER*1
69: * Specifies the form of equilibration that was done.
70: * = 'N': No equilibration
71: * = 'R': Row equilibration, i.e., A has been premultiplied by
72: * diag(R).
73: * = 'C': Column equilibration, i.e., A has been postmultiplied
74: * by diag(C).
75: * = 'B': Both row and column equilibration, i.e., A has been
76: * replaced by diag(R) * A * diag(C).
77: *
78: * Internal Parameters
79: * ===================
80: *
81: * THRESH is a threshold value used to decide if row or column scaling
82: * should be done based on the ratio of the row or column scaling
83: * factors. If ROWCND < THRESH, row scaling is done, and if
84: * COLCND < THRESH, column scaling is done.
85: *
86: * LARGE and SMALL are threshold values used to decide if row scaling
87: * should be done based on the absolute size of the largest matrix
88: * element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
89: *
90: * =====================================================================
91: *
92: * .. Parameters ..
93: DOUBLE PRECISION ONE, THRESH
94: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
95: * ..
96: * .. Local Scalars ..
97: INTEGER I, J
98: DOUBLE PRECISION CJ, LARGE, SMALL
99: * ..
100: * .. External Functions ..
101: DOUBLE PRECISION DLAMCH
102: EXTERNAL DLAMCH
103: * ..
104: * .. Intrinsic Functions ..
105: INTRINSIC MAX, MIN
106: * ..
107: * .. Executable Statements ..
108: *
109: * Quick return if possible
110: *
111: IF( M.LE.0 .OR. N.LE.0 ) THEN
112: EQUED = 'N'
113: RETURN
114: END IF
115: *
116: * Initialize LARGE and SMALL.
117: *
118: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
119: LARGE = ONE / SMALL
120: *
121: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
122: $ THEN
123: *
124: * No row scaling
125: *
126: IF( COLCND.GE.THRESH ) THEN
127: *
128: * No column scaling
129: *
130: EQUED = 'N'
131: ELSE
132: *
133: * Column scaling
134: *
135: DO 20 J = 1, N
136: CJ = C( J )
137: DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
138: AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
139: 10 CONTINUE
140: 20 CONTINUE
141: EQUED = 'C'
142: END IF
143: ELSE IF( COLCND.GE.THRESH ) THEN
144: *
145: * Row scaling, no column scaling
146: *
147: DO 40 J = 1, N
148: DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
149: AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
150: 30 CONTINUE
151: 40 CONTINUE
152: EQUED = 'R'
153: ELSE
154: *
155: * Row and column scaling
156: *
157: DO 60 J = 1, N
158: CJ = C( J )
159: DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
160: AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
161: 50 CONTINUE
162: 60 CONTINUE
163: EQUED = 'B'
164: END IF
165: *
166: RETURN
167: *
168: * End of ZLAQGB
169: *
170: END
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