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Mon Jan 27 09:28:38 2014 UTC (10 years, 4 months ago) by
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1: *> \brief \b ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLANHS + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhs.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhs.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhs.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANHS( NORM, N, A, LDA, WORK )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER NORM
25: * INTEGER LDA, 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: *> ZLANHS 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: *> Hessenberg matrix A.
41: *> \endverbatim
42: *>
43: *> \return ZLANHS
44: *> \verbatim
45: *>
46: *> ZLANHS = ( 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 ZLANHS as described
67: *> above.
68: *> \endverbatim
69: *>
70: *> \param[in] N
71: *> \verbatim
72: *> N is INTEGER
73: *> The order of the matrix A. N >= 0. When N = 0, ZLANHS is
74: *> set to zero.
75: *> \endverbatim
76: *>
77: *> \param[in] A
78: *> \verbatim
79: *> A is COMPLEX*16 array, dimension (LDA,N)
80: *> The n by n upper Hessenberg matrix A; the part of A below the
81: *> first sub-diagonal is not referenced.
82: *> \endverbatim
83: *>
84: *> \param[in] LDA
85: *> \verbatim
86: *> LDA is INTEGER
87: *> The leading dimension of the array A. LDA >= max(N,1).
88: *> \endverbatim
89: *>
90: *> \param[out] WORK
91: *> \verbatim
92: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
93: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
94: *> referenced.
95: *> \endverbatim
96: *
97: * Authors:
98: * ========
99: *
100: *> \author Univ. of Tennessee
101: *> \author Univ. of California Berkeley
102: *> \author Univ. of Colorado Denver
103: *> \author NAG Ltd.
104: *
105: *> \date September 2012
106: *
107: *> \ingroup complex16OTHERauxiliary
108: *
109: * =====================================================================
110: DOUBLE PRECISION FUNCTION ZLANHS( NORM, N, A, LDA, WORK )
111: *
112: * -- LAPACK auxiliary routine (version 3.4.2) --
113: * -- LAPACK is a software package provided by Univ. of Tennessee, --
114: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115: * September 2012
116: *
117: * .. Scalar Arguments ..
118: CHARACTER NORM
119: INTEGER LDA, N
120: * ..
121: * .. Array Arguments ..
122: DOUBLE PRECISION WORK( * )
123: COMPLEX*16 A( LDA, * )
124: * ..
125: *
126: * =====================================================================
127: *
128: * .. Parameters ..
129: DOUBLE PRECISION ONE, ZERO
130: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
131: * ..
132: * .. Local Scalars ..
133: INTEGER I, J
134: DOUBLE PRECISION SCALE, SUM, VALUE
135: * ..
136: * .. External Functions ..
137: LOGICAL LSAME, DISNAN
138: EXTERNAL LSAME, DISNAN
139: * ..
140: * .. External Subroutines ..
141: EXTERNAL ZLASSQ
142: * ..
143: * .. Intrinsic Functions ..
144: INTRINSIC ABS, MIN, SQRT
145: * ..
146: * .. Executable Statements ..
147: *
148: IF( N.EQ.0 ) THEN
149: VALUE = ZERO
150: ELSE IF( LSAME( NORM, 'M' ) ) THEN
151: *
152: * Find max(abs(A(i,j))).
153: *
154: VALUE = ZERO
155: DO 20 J = 1, N
156: DO 10 I = 1, MIN( N, J+1 )
157: SUM = ABS( A( I, J ) )
158: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
159: 10 CONTINUE
160: 20 CONTINUE
161: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
162: *
163: * Find norm1(A).
164: *
165: VALUE = ZERO
166: DO 40 J = 1, N
167: SUM = ZERO
168: DO 30 I = 1, MIN( N, J+1 )
169: SUM = SUM + ABS( A( I, J ) )
170: 30 CONTINUE
171: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
172: 40 CONTINUE
173: ELSE IF( LSAME( NORM, 'I' ) ) THEN
174: *
175: * Find normI(A).
176: *
177: DO 50 I = 1, N
178: WORK( I ) = ZERO
179: 50 CONTINUE
180: DO 70 J = 1, N
181: DO 60 I = 1, MIN( N, J+1 )
182: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
183: 60 CONTINUE
184: 70 CONTINUE
185: VALUE = ZERO
186: DO 80 I = 1, N
187: SUM = WORK( I )
188: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
189: 80 CONTINUE
190: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
191: *
192: * Find normF(A).
193: *
194: SCALE = ZERO
195: SUM = ONE
196: DO 90 J = 1, N
197: CALL ZLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
198: 90 CONTINUE
199: VALUE = SCALE*SQRT( SUM )
200: END IF
201: *
202: ZLANHS = VALUE
203: RETURN
204: *
205: * End of ZLANHS
206: *
207: END
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