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
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
|
REAL FUNCTION CLANGT( NORM, N, DL, D, DU )
*
* -- LAPACK auxiliary routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER NORM
INTEGER N
* ..
* .. Array Arguments ..
COMPLEX D( * ), DL( * ), DU( * )
* ..
*
* Purpose
* =======
*
* CLANGT returns the value of the one norm, or the Frobenius norm, or
* the infinity norm, or the element of largest absolute value of a
* complex tridiagonal matrix A.
*
* Description
* ===========
*
* CLANGT returns the value
*
* CLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
* (
* ( norm1(A), NORM = '1', 'O' or 'o'
* (
* ( normI(A), NORM = 'I' or 'i'
* (
* ( normF(A), NORM = 'F', 'f', 'E' or 'e'
*
* where norm1 denotes the one norm of a matrix (maximum column sum),
* normI denotes the infinity norm of a matrix (maximum row sum) and
* normF denotes the Frobenius norm of a matrix (square root of sum of
* squares). Note that max(abs(A(i,j))) is not a matrix norm.
*
* Arguments
* =========
*
* NORM (input) CHARACTER*1
* Specifies the value to be returned in CLANGT as described
* above.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0. When N = 0, CLANGT is
* set to zero.
*
* DL (input) COMPLEX array, dimension (N-1)
* The (n-1) sub-diagonal elements of A.
*
* D (input) COMPLEX array, dimension (N)
* The diagonal elements of A.
*
* DU (input) COMPLEX array, dimension (N-1)
* The (n-1) super-diagonal elements of A.
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I
REAL ANORM, SCALE, SUM
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLASSQ
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SQRT
* ..
* .. Executable Statements ..
*
IF( N.LE.0 ) THEN
ANORM = ZERO
ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
* Find max(abs(A(i,j))).
*
ANORM = ABS( D( N ) )
DO 10 I = 1, N - 1
ANORM = MAX( ANORM, ABS( DL( I ) ) )
ANORM = MAX( ANORM, ABS( D( I ) ) )
ANORM = MAX( ANORM, ABS( DU( I ) ) )
10 CONTINUE
ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' ) THEN
*
* Find norm1(A).
*
IF( N.EQ.1 ) THEN
ANORM = ABS( D( 1 ) )
ELSE
ANORM = MAX( ABS( D( 1 ) )+ABS( DL( 1 ) ),
$ ABS( D( N ) )+ABS( DU( N-1 ) ) )
DO 20 I = 2, N - 1
ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DL( I ) )+
$ ABS( DU( I-1 ) ) )
20 CONTINUE
END IF
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
* Find normI(A).
*
IF( N.EQ.1 ) THEN
ANORM = ABS( D( 1 ) )
ELSE
ANORM = MAX( ABS( D( 1 ) )+ABS( DU( 1 ) ),
$ ABS( D( N ) )+ABS( DL( N-1 ) ) )
DO 30 I = 2, N - 1
ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DU( I ) )+
$ ABS( DL( I-1 ) ) )
30 CONTINUE
END IF
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
*
* Find normF(A).
*
SCALE = ZERO
SUM = ONE
CALL CLASSQ( N, D, 1, SCALE, SUM )
IF( N.GT.1 ) THEN
CALL CLASSQ( N-1, DL, 1, SCALE, SUM )
CALL CLASSQ( N-1, DU, 1, SCALE, SUM )
END IF
ANORM = SCALE*SQRT( SUM )
END IF
*
CLANGT = ANORM
RETURN
*
* End of CLANGT
*
END
|
