LAPACK  3.10.1
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
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CLANGE + dependencies
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15 *> [TXT]</a>
16 *> \endhtmlonly
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 *> \ingroup complexGEauxiliary
112 *
113 * =====================================================================
114  REAL function clange( norm, m, n, a, lda, work )
115 *
116 * -- LAPACK auxiliary routine --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 *
120 * .. Scalar Arguments ..
121  CHARACTER norm
122  INTEGER lda, m, n
123 * ..
124 * .. Array Arguments ..
125  REAL work( * )
126  COMPLEX a( lda, * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  REAL one, zero
133  parameter( one = 1.0e+0, zero = 0.0e+0 )
134 * ..
135 * .. Local Scalars ..
136  INTEGER i, j
137  REAL scale, sum, VALUE, temp
138 * ..
139 * .. External Functions ..
140  LOGICAL lsame, sisnan
141  EXTERNAL lsame, sisnan
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL classq
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC abs, min, sqrt
148 * ..
149 * .. Executable Statements ..
150 *
151  IF( min( m, n ).EQ.0 ) THEN
152  VALUE = zero
153  ELSE IF( lsame( norm, 'M' ) ) THEN
154 *
155 * Find max(abs(A(i,j))).
156 *
157  VALUE = zero
158  DO 20 j = 1, n
159  DO 10 i = 1, m
160  temp = abs( a( i, j ) )
161  IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
162  10 CONTINUE
163  20 CONTINUE
164  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
165 *
166 * Find norm1(A).
167 *
168  VALUE = zero
169  DO 40 j = 1, n
170  sum = zero
171  DO 30 i = 1, m
172  sum = sum + abs( a( i, j ) )
173  30 CONTINUE
174  IF( VALUE.LT.sum .OR. sisnan( sum ) ) VALUE = sum
175  40 CONTINUE
176  ELSE IF( lsame( norm, 'I' ) ) THEN
177 *
178 * Find normI(A).
179 *
180  DO 50 i = 1, m
181  work( i ) = zero
182  50 CONTINUE
183  DO 70 j = 1, n
184  DO 60 i = 1, m
185  work( i ) = work( i ) + abs( a( i, j ) )
186  60 CONTINUE
187  70 CONTINUE
188  VALUE = zero
189  DO 80 i = 1, m
190  temp = work( i )
191  IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
192  80 CONTINUE
193  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
194 *
195 * Find normF(A).
196 *
197  scale = zero
198  sum = one
199  DO 90 j = 1, n
200  CALL classq( m, a( 1, j ), 1, scale, sum )
201  90 CONTINUE
202  VALUE = scale*sqrt( sum )
203  END IF
204 *
205  clange = VALUE
206  RETURN
207 *
208 * End of CLANGE
209 *
210  END
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.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 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:115