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
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: *> \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
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