LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dlangb.f
Go to the documentation of this file.
1 *> \brief \b DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlangb.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlangb.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlangb.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
22 * WORK )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER NORM
26 * INTEGER KL, KU, LDAB, N
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION AB( LDAB, * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> DLANGB returns the value of the one norm, or the Frobenius norm, or
39 *> the infinity norm, or the element of largest absolute value of an
40 *> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
41 *> \endverbatim
42 *>
43 *> \return DLANGB
44 *> \verbatim
45 *>
46 *> DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
47 *> (
48 *> ( norm1(A), NORM = '1', 'O' or 'o'
49 *> (
50 *> ( normI(A), NORM = 'I' or 'i'
51 *> (
52 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
53 *>
54 *> where norm1 denotes the one norm of a matrix (maximum column sum),
55 *> normI denotes the infinity norm of a matrix (maximum row sum) and
56 *> normF denotes the Frobenius norm of a matrix (square root of sum of
57 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
58 *> \endverbatim
59 *
60 * Arguments:
61 * ==========
62 *
63 *> \param[in] NORM
64 *> \verbatim
65 *> NORM is CHARACTER*1
66 *> Specifies the value to be returned in DLANGB as described
67 *> above.
68 *> \endverbatim
69 *>
70 *> \param[in] N
71 *> \verbatim
72 *> N is INTEGER
73 *> The order of the matrix A. N >= 0. When N = 0, DLANGB is
74 *> set to zero.
75 *> \endverbatim
76 *>
77 *> \param[in] KL
78 *> \verbatim
79 *> KL is INTEGER
80 *> The number of sub-diagonals of the matrix A. KL >= 0.
81 *> \endverbatim
82 *>
83 *> \param[in] KU
84 *> \verbatim
85 *> KU is INTEGER
86 *> The number of super-diagonals of the matrix A. KU >= 0.
87 *> \endverbatim
88 *>
89 *> \param[in] AB
90 *> \verbatim
91 *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
92 *> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
93 *> column of A is stored in the j-th column of the array AB as
94 *> follows:
95 *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
96 *> \endverbatim
97 *>
98 *> \param[in] LDAB
99 *> \verbatim
100 *> LDAB is INTEGER
101 *> The leading dimension of the array AB. LDAB >= KL+KU+1.
102 *> \endverbatim
103 *>
104 *> \param[out] WORK
105 *> \verbatim
106 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
107 *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
108 *> referenced.
109 *> \endverbatim
110 *
111 * Authors:
112 * ========
113 *
114 *> \author Univ. of Tennessee
115 *> \author Univ. of California Berkeley
116 *> \author Univ. of Colorado Denver
117 *> \author NAG Ltd.
118 *
119 *> \date September 2012
120 *
121 *> \ingroup doubleGBauxiliary
122 *
123 * =====================================================================
124  DOUBLE PRECISION FUNCTION dlangb( NORM, N, KL, KU, AB, LDAB,
125  \$ work )
126 *
127 * -- LAPACK auxiliary routine (version 3.4.2) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * September 2012
131 *
132 * .. Scalar Arguments ..
133  CHARACTER NORM
134  INTEGER KL, KU, LDAB, N
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION AB( ldab, * ), WORK( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 *
143 * .. Parameters ..
144  DOUBLE PRECISION ONE, ZERO
145  parameter ( one = 1.0d+0, zero = 0.0d+0 )
146 * ..
147 * .. Local Scalars ..
148  INTEGER I, J, K, L
149  DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
150 * ..
151 * .. External Subroutines ..
152  EXTERNAL dlassq
153 * ..
154 * .. External Functions ..
155  LOGICAL LSAME, DISNAN
156  EXTERNAL lsame, disnan
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC abs, max, min, sqrt
160 * ..
161 * .. Executable Statements ..
162 *
163  IF( n.EQ.0 ) THEN
164  VALUE = zero
165  ELSE IF( lsame( norm, 'M' ) ) THEN
166 *
167 * Find max(abs(A(i,j))).
168 *
169  VALUE = zero
170  DO 20 j = 1, n
171  DO 10 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
172  temp = abs( ab( i, j ) )
173  IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
174  10 CONTINUE
175  20 CONTINUE
176  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
177 *
178 * Find norm1(A).
179 *
180  VALUE = zero
181  DO 40 j = 1, n
182  sum = zero
183  DO 30 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
184  sum = sum + abs( ab( i, j ) )
185  30 CONTINUE
186  IF( VALUE.LT.sum .OR. disnan( sum ) ) VALUE = sum
187  40 CONTINUE
188  ELSE IF( lsame( norm, 'I' ) ) THEN
189 *
190 * Find normI(A).
191 *
192  DO 50 i = 1, n
193  work( i ) = zero
194  50 CONTINUE
195  DO 70 j = 1, n
196  k = ku + 1 - j
197  DO 60 i = max( 1, j-ku ), min( n, j+kl )
198  work( i ) = work( i ) + abs( ab( k+i, j ) )
199  60 CONTINUE
200  70 CONTINUE
201  VALUE = zero
202  DO 80 i = 1, n
203  temp = work( i )
204  IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
205  80 CONTINUE
206  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
207 *
208 * Find normF(A).
209 *
210  scale = zero
211  sum = one
212  DO 90 j = 1, n
213  l = max( 1, j-ku )
214  k = ku + 1 - j + l
215  CALL dlassq( min( n, j+kl )-l+1, ab( k, j ), 1, scale, sum )
216  90 CONTINUE
217  VALUE = scale*sqrt( sum )
218  END IF
219 *
220  dlangb = VALUE
221  RETURN
222 *
223 * End of DLANGB
224 *
225  END
double precision function dlangb(NORM, N, KL, KU, AB, LDAB, WORK)
DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlangb.f:126
subroutine dlassq(N, X, INCX, SCALE, SUMSQ)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f:105