LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
clange.f
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1 *> \brief \b CLANGE 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
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17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLANGE( NORM, M, N, A, LDA, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM
25 * INTEGER LDA, M, N
26 * ..
27 * .. Array Arguments ..
28 * REAL WORK( * )
29 * COMPLEX A( LDA, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> CLANGE returns the value of the one norm, or the Frobenius norm, or
39 *> the infinity norm, or the element of largest absolute value of a
40 *> complex matrix A.
41 *> \endverbatim
42 *>
43 *> \return CLANGE
44 *> \verbatim
45 *>
46 *> CLANGE = ( 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 CLANGE as described
67 *> above.
68 *> \endverbatim
69 *>
70 *> \param[in] M
71 *> \verbatim
72 *> M is INTEGER
73 *> The number of rows of the matrix A. M >= 0. When M = 0,
74 *> CLANGE is set to zero.
75 *> \endverbatim
76 *>
77 *> \param[in] N
78 *> \verbatim
79 *> N is INTEGER
80 *> The number of columns of the matrix A. N >= 0. When N = 0,
81 *> CLANGE is set to zero.
82 *> \endverbatim
83 *>
84 *> \param[in] A
85 *> \verbatim
86 *> A is COMPLEX array, dimension (LDA,N)
87 *> The m by n matrix A.
88 *> \endverbatim
89 *>
90 *> \param[in] LDA
91 *> \verbatim
92 *> LDA is INTEGER
93 *> The leading dimension of the array A. LDA >= max(M,1).
94 *> \endverbatim
95 *>
96 *> \param[out] WORK
97 *> \verbatim
98 *> WORK is REAL array, dimension (MAX(1,LWORK)),
99 *> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
100 *> referenced.
101 *> \endverbatim
102 *
103 * Authors:
104 * ========
105 *
106 *> \author Univ. of Tennessee
107 *> \author Univ. of California Berkeley
108 *> \author Univ. of Colorado Denver
109 *> \author NAG Ltd.
110 *
111 *> \date December 2016
112 *
113 *> \ingroup complexGEauxiliary
114 *
115 * =====================================================================
116  REAL FUNCTION clange( NORM, M, N, A, LDA, WORK )
117 *
118 * -- LAPACK auxiliary routine (version 3.7.0) --
119 * -- LAPACK is a software package provided by Univ. of Tennessee, --
120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121 * December 2016
122 *
123 * .. Scalar Arguments ..
124  CHARACTER NORM
125  INTEGER LDA, M, N
126 * ..
127 * .. Array Arguments ..
128  REAL WORK( * )
129  COMPLEX A( lda, * )
130 * ..
131 *
132 * =====================================================================
133 *
134 * .. Parameters ..
135  REAL ONE, ZERO
136  parameter( one = 1.0e+0, zero = 0.0e+0 )
137 * ..
138 * .. Local Scalars ..
139  INTEGER I, J
140  REAL SCALE, SUM, VALUE, TEMP
141 * ..
142 * .. External Functions ..
143  LOGICAL LSAME, SISNAN
144  EXTERNAL lsame, sisnan
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL classq
148 * ..
149 * .. Intrinsic Functions ..
150  INTRINSIC abs, min, sqrt
151 * ..
152 * .. Executable Statements ..
153 *
154  IF( min( m, n ).EQ.0 ) THEN
155  VALUE = zero
156  ELSE IF( lsame( norm, 'M' ) ) THEN
157 *
158 * Find max(abs(A(i,j))).
159 *
160  VALUE = zero
161  DO 20 j = 1, n
162  DO 10 i = 1, m
163  temp = abs( a( i, j ) )
164  IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
165  10 CONTINUE
166  20 CONTINUE
167  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
168 *
169 * Find norm1(A).
170 *
171  VALUE = zero
172  DO 40 j = 1, n
173  sum = zero
174  DO 30 i = 1, m
175  sum = sum + abs( a( i, j ) )
176  30 CONTINUE
177  IF( VALUE.LT.sum .OR. sisnan( sum ) ) VALUE = sum
178  40 CONTINUE
179  ELSE IF( lsame( norm, 'I' ) ) THEN
180 *
181 * Find normI(A).
182 *
183  DO 50 i = 1, m
184  work( i ) = zero
185  50 CONTINUE
186  DO 70 j = 1, n
187  DO 60 i = 1, m
188  work( i ) = work( i ) + abs( a( i, j ) )
189  60 CONTINUE
190  70 CONTINUE
191  VALUE = zero
192  DO 80 i = 1, m
193  temp = work( i )
194  IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
195  80 CONTINUE
196  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
197 *
198 * Find normF(A).
199 *
200  scale = zero
201  sum = one
202  DO 90 j = 1, n
203  CALL classq( m, a( 1, j ), 1, scale, sum )
204  90 CONTINUE
205  VALUE = scale*sqrt( sum )
206  END IF
207 *
208  clange = VALUE
209  RETURN
210 *
211 * End of CLANGE
212 *
213  END
subroutine classq(N, X, INCX, SCALE, SUMSQ)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f:108
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:117