1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
|
DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
$ LDAB, AFB, LDAFB )
*
* -- LAPACK routine (version 3.2.1) --
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
* -- Jason Riedy of Univ. of California Berkeley. --
* -- April 2009 --
*
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley and NAG Ltd. --
*
IMPLICIT NONE
* ..
* .. Scalar Arguments ..
INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
* ..
* .. Array Arguments ..
COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
* ..
*
* Purpose
* =======
*
* ZLA_GBRPVGRW computes the reciprocal pivot growth factor
* norm(A)/norm(U). The "max absolute element" norm is used. If this is
* much less than 1, the stability of the LU factorization of the
* (equilibrated) matrix A could be poor. This also means that the
* solution X, estimated condition numbers, and error bounds could be
* unreliable.
*
* Arguments
* =========
*
* N (input) INTEGER
* The number of linear equations, i.e., the order of the
* matrix A. N >= 0.
*
* KL (input) INTEGER
* The number of subdiagonals within the band of A. KL >= 0.
*
* KU (input) INTEGER
* The number of superdiagonals within the band of A. KU >= 0.
*
* NCOLS (input) INTEGER
* The number of columns of the matrix A. NCOLS >= 0.
*
* AB (input) COMPLEX*16 array, dimension (LDAB,N)
* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
* The j-th column of A is stored in the j-th column of the
* array AB as follows:
* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KL+KU+1.
*
* AFB (input) COMPLEX*16 array, dimension (LDAFB,N)
* Details of the LU factorization of the band matrix A, as
* computed by ZGBTRF. U is stored as an upper triangular
* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
* and the multipliers used during the factorization are stored
* in rows KL+KU+2 to 2*KL+KU+1.
*
* LDAFB (input) INTEGER
* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J, KD
DOUBLE PRECISION AMAX, UMAX, RPVGRW
COMPLEX*16 ZDUM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, REAL, DIMAG
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function Definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
RPVGRW = 1.0D+0
KD = KU + 1
DO J = 1, NCOLS
AMAX = 0.0D+0
UMAX = 0.0D+0
DO I = MAX( J-KU, 1 ), MIN( J+KL, N )
AMAX = MAX( CABS1( AB( KD+I-J, J ) ), AMAX )
END DO
DO I = MAX( J-KU, 1 ), J
UMAX = MAX( CABS1( AFB( KD+I-J, J ) ), UMAX )
END DO
IF ( UMAX /= 0.0D+0 ) THEN
RPVGRW = MIN( AMAX / UMAX, RPVGRW )
END IF
END DO
ZLA_GBRPVGRW = RPVGRW
END FUNCTION
|
