LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dlange.f
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1 *> \brief \b DLANGE 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 DLANGE + 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/dlange.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM
25 * INTEGER LDA, M, N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION A( LDA, * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DLANGE 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 DLANGE
43 *> \verbatim
44 *>
45 *> DLANGE = ( 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 DLANGE 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 *> DLANGE 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 *> DLANGE is set to zero.
81 *> \endverbatim
82 *>
83 *> \param[in] A
84 *> \verbatim
85 *> A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 *> \ingroup doubleGEauxiliary
111 *
112 * =====================================================================
113  DOUBLE PRECISION FUNCTION dlange( NORM, M, N, A, LDA, WORK )
114 *
115 * -- LAPACK auxiliary routine --
116 * -- LAPACK is a software package provided by Univ. of Tennessee, --
117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118 *
119 * .. Scalar Arguments ..
120  CHARACTER norm
121  INTEGER lda, m, n
122 * ..
123 * .. Array Arguments ..
124  DOUBLE PRECISION a( lda, * ), work( * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130  DOUBLE PRECISION one, zero
131  parameter( one = 1.0d+0, zero = 0.0d+0 )
132 * ..
133 * .. Local Scalars ..
134  INTEGER i, j
135  DOUBLE PRECISION scale, sum, VALUE, temp
136 * ..
137 * .. External Subroutines ..
138  EXTERNAL dlassq
139 * ..
140 * .. External Functions ..
141  LOGICAL lsame, disnan
142  EXTERNAL lsame, disnan
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC abs, min, sqrt
146 * ..
147 * .. Executable Statements ..
148 *
149  IF( min( m, n ).EQ.0 ) THEN
150  VALUE = zero
151  ELSE IF( lsame( norm, 'M' ) ) THEN
152 *
153 * Find max(abs(A(i,j))).
154 *
155  VALUE = zero
156  DO 20 j = 1, n
157  DO 10 i = 1, m
158  temp = abs( a( i, j ) )
159  IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
160  10 CONTINUE
161  20 CONTINUE
162  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
163 *
164 * Find norm1(A).
165 *
166  VALUE = zero
167  DO 40 j = 1, n
168  sum = zero
169  DO 30 i = 1, m
170  sum = sum + abs( a( i, j ) )
171  30 CONTINUE
172  IF( VALUE.LT.sum .OR. disnan( sum ) ) VALUE = sum
173  40 CONTINUE
174  ELSE IF( lsame( norm, 'I' ) ) THEN
175 *
176 * Find normI(A).
177 *
178  DO 50 i = 1, m
179  work( i ) = zero
180  50 CONTINUE
181  DO 70 j = 1, n
182  DO 60 i = 1, m
183  work( i ) = work( i ) + abs( a( i, j ) )
184  60 CONTINUE
185  70 CONTINUE
186  VALUE = zero
187  DO 80 i = 1, m
188  temp = work( i )
189  IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
190  80 CONTINUE
191  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
192 *
193 * Find normF(A).
194 *
195  scale = zero
196  sum = one
197  DO 90 j = 1, n
198  CALL dlassq( m, a( 1, j ), 1, scale, sum )
199  90 CONTINUE
200  VALUE = scale*sqrt( sum )
201  END IF
202 *
203  dlange = VALUE
204  RETURN
205 *
206 * End of DLANGE
207 *
208  END
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine dlassq(n, x, incx, scl, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f90:137
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:114