1 DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
2 $ LDAB, AFB, LDAFB )
3 *
4 * -- LAPACK routine (version 3.2.2) --
5 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
6 * -- Jason Riedy of Univ. of California Berkeley. --
7 * -- June 2010 --
8 *
9 * -- LAPACK is a software package provided by Univ. of Tennessee, --
10 * -- Univ. of California Berkeley and NAG Ltd. --
11 *
12 IMPLICIT NONE
13 * ..
14 * .. Scalar Arguments ..
15 INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
16 * ..
17 * .. Array Arguments ..
18 COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * ZLA_GBRPVGRW computes the reciprocal pivot growth factor
25 * norm(A)/norm(U). The "max absolute element" norm is used. If this is
26 * much less than 1, the stability of the LU factorization of the
27 * (equilibrated) matrix A could be poor. This also means that the
28 * solution X, estimated condition numbers, and error bounds could be
29 * unreliable.
30 *
31 * Arguments
32 * =========
33 *
34 * N (input) INTEGER
35 * The number of linear equations, i.e., the order of the
36 * matrix A. N >= 0.
37 *
38 * KL (input) INTEGER
39 * The number of subdiagonals within the band of A. KL >= 0.
40 *
41 * KU (input) INTEGER
42 * The number of superdiagonals within the band of A. KU >= 0.
43 *
44 * NCOLS (input) INTEGER
45 * The number of columns of the matrix A. NCOLS >= 0.
46 *
47 * AB (input) COMPLEX*16 array, dimension (LDAB,N)
48 * On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
49 * The j-th column of A is stored in the j-th column of the
50 * array AB as follows:
51 * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
52 *
53 * LDAB (input) INTEGER
54 * The leading dimension of the array AB. LDAB >= KL+KU+1.
55 *
56 * AFB (input) COMPLEX*16 array, dimension (LDAFB,N)
57 * Details of the LU factorization of the band matrix A, as
58 * computed by ZGBTRF. U is stored as an upper triangular
59 * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
60 * and the multipliers used during the factorization are stored
61 * in rows KL+KU+2 to 2*KL+KU+1.
62 *
63 * LDAFB (input) INTEGER
64 * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
65 *
66 * =====================================================================
67 *
68 * .. Local Scalars ..
69 INTEGER I, J, KD
70 DOUBLE PRECISION AMAX, UMAX, RPVGRW
71 COMPLEX*16 ZDUM
72 * ..
73 * .. Intrinsic Functions ..
74 INTRINSIC ABS, MAX, MIN, REAL, DIMAG
75 * ..
76 * .. Statement Functions ..
77 DOUBLE PRECISION CABS1
78 * ..
79 * .. Statement Function Definitions ..
80 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
81 * ..
82 * .. Executable Statements ..
83 *
84 RPVGRW = 1.0D+0
85
86 KD = KU + 1
87 DO J = 1, NCOLS
88 AMAX = 0.0D+0
89 UMAX = 0.0D+0
90 DO I = MAX( J-KU, 1 ), MIN( J+KL, N )
91 AMAX = MAX( CABS1( AB( KD+I-J, J ) ), AMAX )
92 END DO
93 DO I = MAX( J-KU, 1 ), J
94 UMAX = MAX( CABS1( AFB( KD+I-J, J ) ), UMAX )
95 END DO
96 IF ( UMAX /= 0.0D+0 ) THEN
97 RPVGRW = MIN( AMAX / UMAX, RPVGRW )
98 END IF
99 END DO
100 ZLA_GBRPVGRW = RPVGRW
101 END
2 $ LDAB, AFB, LDAFB )
3 *
4 * -- LAPACK routine (version 3.2.2) --
5 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
6 * -- Jason Riedy of Univ. of California Berkeley. --
7 * -- June 2010 --
8 *
9 * -- LAPACK is a software package provided by Univ. of Tennessee, --
10 * -- Univ. of California Berkeley and NAG Ltd. --
11 *
12 IMPLICIT NONE
13 * ..
14 * .. Scalar Arguments ..
15 INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
16 * ..
17 * .. Array Arguments ..
18 COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * ZLA_GBRPVGRW computes the reciprocal pivot growth factor
25 * norm(A)/norm(U). The "max absolute element" norm is used. If this is
26 * much less than 1, the stability of the LU factorization of the
27 * (equilibrated) matrix A could be poor. This also means that the
28 * solution X, estimated condition numbers, and error bounds could be
29 * unreliable.
30 *
31 * Arguments
32 * =========
33 *
34 * N (input) INTEGER
35 * The number of linear equations, i.e., the order of the
36 * matrix A. N >= 0.
37 *
38 * KL (input) INTEGER
39 * The number of subdiagonals within the band of A. KL >= 0.
40 *
41 * KU (input) INTEGER
42 * The number of superdiagonals within the band of A. KU >= 0.
43 *
44 * NCOLS (input) INTEGER
45 * The number of columns of the matrix A. NCOLS >= 0.
46 *
47 * AB (input) COMPLEX*16 array, dimension (LDAB,N)
48 * On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
49 * The j-th column of A is stored in the j-th column of the
50 * array AB as follows:
51 * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
52 *
53 * LDAB (input) INTEGER
54 * The leading dimension of the array AB. LDAB >= KL+KU+1.
55 *
56 * AFB (input) COMPLEX*16 array, dimension (LDAFB,N)
57 * Details of the LU factorization of the band matrix A, as
58 * computed by ZGBTRF. U is stored as an upper triangular
59 * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
60 * and the multipliers used during the factorization are stored
61 * in rows KL+KU+2 to 2*KL+KU+1.
62 *
63 * LDAFB (input) INTEGER
64 * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
65 *
66 * =====================================================================
67 *
68 * .. Local Scalars ..
69 INTEGER I, J, KD
70 DOUBLE PRECISION AMAX, UMAX, RPVGRW
71 COMPLEX*16 ZDUM
72 * ..
73 * .. Intrinsic Functions ..
74 INTRINSIC ABS, MAX, MIN, REAL, DIMAG
75 * ..
76 * .. Statement Functions ..
77 DOUBLE PRECISION CABS1
78 * ..
79 * .. Statement Function Definitions ..
80 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
81 * ..
82 * .. Executable Statements ..
83 *
84 RPVGRW = 1.0D+0
85
86 KD = KU + 1
87 DO J = 1, NCOLS
88 AMAX = 0.0D+0
89 UMAX = 0.0D+0
90 DO I = MAX( J-KU, 1 ), MIN( J+KL, N )
91 AMAX = MAX( CABS1( AB( KD+I-J, J ) ), AMAX )
92 END DO
93 DO I = MAX( J-KU, 1 ), J
94 UMAX = MAX( CABS1( AFB( KD+I-J, J ) ), UMAX )
95 END DO
96 IF ( UMAX /= 0.0D+0 ) THEN
97 RPVGRW = MIN( AMAX / UMAX, RPVGRW )
98 END IF
99 END DO
100 ZLA_GBRPVGRW = RPVGRW
101 END