Annotation of rpl/lapack/lapack/dlange.f, revision 1.10
1.8 bertrand 1: *> \brief \b DLANGE
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
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlange.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlange.f">
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: *> \date November 2011
111: *
112: *> \ingroup doubleGEauxiliary
113: *
114: * =====================================================================
1.1 bertrand 115: DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
116: *
1.8 bertrand 117: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 118: * -- LAPACK is a software package provided by Univ. of Tennessee, --
119: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 bertrand 120: * November 2011
1.1 bertrand 121: *
122: * .. Scalar Arguments ..
123: CHARACTER NORM
124: INTEGER LDA, M, N
125: * ..
126: * .. Array Arguments ..
127: DOUBLE PRECISION A( LDA, * ), WORK( * )
128: * ..
129: *
130: * =====================================================================
131: *
132: * .. Parameters ..
133: DOUBLE PRECISION ONE, ZERO
134: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
135: * ..
136: * .. Local Scalars ..
137: INTEGER I, J
138: DOUBLE PRECISION SCALE, SUM, VALUE
139: * ..
140: * .. External Subroutines ..
141: EXTERNAL DLASSQ
142: * ..
143: * .. External Functions ..
144: LOGICAL LSAME
145: EXTERNAL LSAME
146: * ..
147: * .. Intrinsic Functions ..
148: INTRINSIC ABS, MAX, 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: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
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: VALUE = MAX( 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: VALUE = MAX( VALUE, WORK( I ) )
191: 80 CONTINUE
192: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
193: *
194: * Find normF(A).
195: *
196: SCALE = ZERO
197: SUM = ONE
198: DO 90 J = 1, N
199: CALL DLASSQ( M, A( 1, J ), 1, SCALE, SUM )
200: 90 CONTINUE
201: VALUE = SCALE*SQRT( SUM )
202: END IF
203: *
204: DLANGE = VALUE
205: RETURN
206: *
207: * End of DLANGE
208: *
209: END
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