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
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
|
*> \brief \b DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLANSP + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansp.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansp.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansp.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )
*
* .. Scalar Arguments ..
* CHARACTER NORM, UPLO
* INTEGER N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLANSP 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 matrix A, supplied in packed form.
*> \endverbatim
*>
*> \return DLANSP
*> \verbatim
*>
*> DLANSP = ( 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 DLANSP as described
*> above.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> symmetric matrix A is supplied.
*> = 'U': Upper triangular part of A is supplied
*> = 'L': Lower triangular part of A is supplied
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0. When N = 0, DLANSP is
*> set to zero.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
*> The upper or lower triangle of the symmetric matrix A, packed
*> columnwise in a linear array. The j-th column of A is stored
*> in the array AP as follows:
*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup lanhp
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER NORM, UPLO
INTEGER N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, K
DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
* ..
* .. External Subroutines ..
EXTERNAL DLASSQ
* ..
* .. External Functions ..
LOGICAL LSAME, DISNAN
EXTERNAL LSAME, DISNAN
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, SQRT
* ..
* .. Executable Statements ..
*
IF( N.EQ.0 ) THEN
VALUE = ZERO
ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
* Find max(abs(A(i,j))).
*
VALUE = ZERO
IF( LSAME( UPLO, 'U' ) ) THEN
K = 1
DO 20 J = 1, N
DO 10 I = K, K + J - 1
SUM = ABS( AP( I ) )
IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
10 CONTINUE
K = K + J
20 CONTINUE
ELSE
K = 1
DO 40 J = 1, N
DO 30 I = K, K + N - J
SUM = ABS( AP( I ) )
IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
30 CONTINUE
K = K + N - J + 1
40 CONTINUE
END IF
ELSE IF( ( LSAME( NORM, 'I' ) ) .OR.
$ ( LSAME( NORM, 'O' ) ) .OR.
$ ( NORM.EQ.'1' ) ) THEN
*
* Find normI(A) ( = norm1(A), since A is symmetric).
*
VALUE = ZERO
K = 1
IF( LSAME( UPLO, 'U' ) ) THEN
DO 60 J = 1, N
SUM = ZERO
DO 50 I = 1, J - 1
ABSA = ABS( AP( K ) )
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
K = K + 1
50 CONTINUE
WORK( J ) = SUM + ABS( AP( K ) )
K = K + 1
60 CONTINUE
DO 70 I = 1, N
SUM = WORK( I )
IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
70 CONTINUE
ELSE
DO 80 I = 1, N
WORK( I ) = ZERO
80 CONTINUE
DO 100 J = 1, N
SUM = WORK( J ) + ABS( AP( K ) )
K = K + 1
DO 90 I = J + 1, N
ABSA = ABS( AP( K ) )
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
K = K + 1
90 CONTINUE
IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
100 CONTINUE
END IF
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR.
$ ( LSAME( NORM, 'E' ) ) ) THEN
*
* Find normF(A).
*
SCALE = ZERO
SUM = ONE
K = 2
IF( LSAME( UPLO, 'U' ) ) THEN
DO 110 J = 2, N
CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
K = K + J
110 CONTINUE
ELSE
DO 120 J = 1, N - 1
CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
K = K + N - J + 1
120 CONTINUE
END IF
SUM = 2*SUM
K = 1
DO 130 I = 1, N
IF( AP( K ).NE.ZERO ) THEN
ABSA = ABS( AP( K ) )
IF( SCALE.LT.ABSA ) THEN
SUM = ONE + SUM*( SCALE / ABSA )**2
SCALE = ABSA
ELSE
SUM = SUM + ( ABSA / SCALE )**2
END IF
END IF
IF( LSAME( UPLO, 'U' ) ) THEN
K = K + I + 1
ELSE
K = K + N - I + 1
END IF
130 CONTINUE
VALUE = SCALE*SQRT( SUM )
END IF
*
DLANSP = VALUE
RETURN
*
* End of DLANSP
*
END
|
