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