LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
slangb.f
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1 *> \brief \b SLANGB 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
9 *> Download SLANGB + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slangb.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION SLANGB( 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 * REAL AB( LDAB, * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SLANGB 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 SLANGB
44 *> \verbatim
45 *>
46 *> SLANGB = ( 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 SLANGB 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, SLANGB 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 REAL 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 REAL 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 *> \ingroup realGBauxiliary
120 *
121 * =====================================================================
122  REAL function slangb( norm, n, kl, ku, ab, ldab,
123  $ work )
124 *
125 * -- LAPACK auxiliary routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER norm
131  INTEGER kl, ku, ldab, n
132 * ..
133 * .. Array Arguments ..
134  REAL ab( ldab, * ), work( * )
135 * ..
136 *
137 * =====================================================================
138 *
139 *
140 * .. Parameters ..
141  REAL one, zero
142  parameter( one = 1.0e+0, zero = 0.0e+0 )
143 * ..
144 * .. Local Scalars ..
145  INTEGER i, j, k, l
146  REAL scale, sum, VALUE, temp
147 * ..
148 * .. External Subroutines ..
149  EXTERNAL slassq
150 * ..
151 * .. External Functions ..
152  LOGICAL lsame, sisnan
153  EXTERNAL lsame, sisnan
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC abs, max, min, sqrt
157 * ..
158 * .. Executable Statements ..
159 *
160  IF( n.EQ.0 ) THEN
161  VALUE = zero
162  ELSE IF( lsame( norm, 'M' ) ) THEN
163 *
164 * Find max(abs(A(i,j))).
165 *
166  VALUE = zero
167  DO 20 j = 1, n
168  DO 10 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
169  temp = abs( ab( i, j ) )
170  IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
171  10 CONTINUE
172  20 CONTINUE
173  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
174 *
175 * Find norm1(A).
176 *
177  VALUE = zero
178  DO 40 j = 1, n
179  sum = zero
180  DO 30 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
181  sum = sum + abs( ab( i, j ) )
182  30 CONTINUE
183  IF( VALUE.LT.sum .OR. sisnan( sum ) ) VALUE = sum
184  40 CONTINUE
185  ELSE IF( lsame( norm, 'I' ) ) THEN
186 *
187 * Find normI(A).
188 *
189  DO 50 i = 1, n
190  work( i ) = zero
191  50 CONTINUE
192  DO 70 j = 1, n
193  k = ku + 1 - j
194  DO 60 i = max( 1, j-ku ), min( n, j+kl )
195  work( i ) = work( i ) + abs( ab( k+i, j ) )
196  60 CONTINUE
197  70 CONTINUE
198  VALUE = zero
199  DO 80 i = 1, n
200  temp = work( i )
201  IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
202  80 CONTINUE
203  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
204 *
205 * Find normF(A).
206 *
207  scale = zero
208  sum = one
209  DO 90 j = 1, n
210  l = max( 1, j-ku )
211  k = ku + 1 - j + l
212  CALL slassq( min( n, j+kl )-l+1, ab( k, j ), 1, scale, sum )
213  90 CONTINUE
214  VALUE = scale*sqrt( sum )
215  END IF
216 *
217  slangb = VALUE
218  RETURN
219 *
220 * End of SLANGB
221 *
222  END
subroutine slassq(n, x, incx, scl, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f90:137
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slangb(NORM, N, KL, KU, AB, LDAB, WORK)
SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slangb.f:124