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
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
|
*> \brief \b SLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SLANST + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slanst.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slanst.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slanst.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* REAL FUNCTION SLANST( NORM, N, D, E )
*
* .. Scalar Arguments ..
* CHARACTER NORM
* INTEGER N
* ..
* .. Array Arguments ..
* REAL D( * ), E( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLANST returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric tridiagonal matrix A.
*> \endverbatim
*>
*> \return SLANST
*> \verbatim
*>
*> SLANST = ( 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 consistent matrix norm.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NORM
*> \verbatim
*> NORM is CHARACTER*1
*> Specifies the value to be returned in SLANST as described
*> above.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0. When N = 0, SLANST is
*> set to zero.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is REAL array, dimension (N)
*> The diagonal elements of A.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*> E is REAL array, dimension (N-1)
*> The (n-1) sub-diagonal or super-diagonal elements of A.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup OTHERauxiliary
*
* =====================================================================
REAL FUNCTION SLANST( NORM, N, D, E )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER NORM
INTEGER N
* ..
* .. Array Arguments ..
REAL D( * ), E( * )
* ..
*
* =====================================================================
*
* .. 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, SISNAN
EXTERNAL LSAME, SISNAN
* ..
* .. External Subroutines ..
EXTERNAL SLASSQ
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, 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
SUM = ABS( D( I ) )
IF( ANORM .LT. SUM .OR. SISNAN( SUM ) ) ANORM = SUM
SUM = ABS( E( I ) )
IF( ANORM .LT. SUM .OR. SISNAN( SUM ) ) ANORM = SUM
10 CONTINUE
ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
$ LSAME( NORM, 'I' ) ) THEN
*
* Find norm1(A).
*
IF( N.EQ.1 ) THEN
ANORM = ABS( D( 1 ) )
ELSE
ANORM = ABS( D( 1 ) )+ABS( E( 1 ) )
SUM = ABS( E( N-1 ) )+ABS( D( N ) )
IF( ANORM .LT. SUM .OR. SISNAN( SUM ) ) ANORM = SUM
DO 20 I = 2, N - 1
SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) )
IF( ANORM .LT. SUM .OR. SISNAN( SUM ) ) ANORM = SUM
20 CONTINUE
END IF
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
*
* Find normF(A).
*
SCALE = ZERO
SUM = ONE
IF( N.GT.1 ) THEN
CALL SLASSQ( N-1, E, 1, SCALE, SUM )
SUM = 2*SUM
END IF
CALL SLASSQ( N, D, 1, SCALE, SUM )
ANORM = SCALE*SQRT( SUM )
END IF
*
SLANST = ANORM
RETURN
*
* End of SLANST
*
END
|
