1: *> \brief \b ZLANGE 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 ZLANGE + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlange.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlange.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlange.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANGE( 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 WORK( * )
29: * COMPLEX*16 A( LDA, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZLANGE 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 ZLANGE
44: *> \verbatim
45: *>
46: *> ZLANGE = ( 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 ZLANGE 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: *> ZLANGE 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: *> ZLANGE is set to zero.
82: *> \endverbatim
83: *>
84: *> \param[in] A
85: *> \verbatim
86: *> A is COMPLEX*16 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 DOUBLE PRECISION 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 complex16GEauxiliary
114: *
115: * =====================================================================
116: DOUBLE PRECISION FUNCTION ZLANGE( 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: DOUBLE PRECISION WORK( * )
129: COMPLEX*16 A( LDA, * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: DOUBLE PRECISION ONE, ZERO
136: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
137: * ..
138: * .. Local Scalars ..
139: INTEGER I, J
140: DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
141: * ..
142: * .. External Functions ..
143: LOGICAL LSAME, DISNAN
144: EXTERNAL LSAME, DISNAN
145: * ..
146: * .. External Subroutines ..
147: EXTERNAL ZLASSQ
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. DISNAN( 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. DISNAN( 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. DISNAN( 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 ZLASSQ( M, A( 1, J ), 1, SCALE, SUM )
204: 90 CONTINUE
205: VALUE = SCALE*SQRT( SUM )
206: END IF
207: *
208: ZLANGE = VALUE
209: RETURN
210: *
211: * End of ZLANGE
212: *
213: END
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