LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zlanhs.f
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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 *
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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 *> \ingroup complex16OTHERauxiliary
106 *
107 * =====================================================================
108  DOUBLE PRECISION FUNCTION zlanhs( NORM, N, A, LDA, WORK )
109 *
110 * -- LAPACK auxiliary routine --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 *
114 * .. Scalar Arguments ..
115  CHARACTER norm
116  INTEGER lda, n
117 * ..
118 * .. Array Arguments ..
119  DOUBLE PRECISION work( * )
120  COMPLEX*16 a( lda, * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  DOUBLE PRECISION one, zero
127  parameter( one = 1.0d+0, zero = 0.0d+0 )
128 * ..
129 * .. Local Scalars ..
130  INTEGER i, j
131  DOUBLE PRECISION scale, sum, value
132 * ..
133 * .. External Functions ..
134  LOGICAL lsame, disnan
135  EXTERNAL lsame, disnan
136 * ..
137 * .. External Subroutines ..
138  EXTERNAL zlassq
139 * ..
140 * .. Intrinsic Functions ..
141  INTRINSIC abs, min, sqrt
142 * ..
143 * .. Executable Statements ..
144 *
145  IF( n.EQ.0 ) THEN
146  VALUE = zero
147  ELSE IF( lsame( norm, 'M' ) ) THEN
148 *
149 * Find max(abs(A(i,j))).
150 *
151  VALUE = zero
152  DO 20 j = 1, n
153  DO 10 i = 1, min( n, j+1 )
154  sum = abs( a( i, j ) )
155  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
156  10 CONTINUE
157  20 CONTINUE
158  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
159 *
160 * Find norm1(A).
161 *
162  VALUE = zero
163  DO 40 j = 1, n
164  sum = zero
165  DO 30 i = 1, min( n, j+1 )
166  sum = sum + abs( a( i, j ) )
167  30 CONTINUE
168  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
169  40 CONTINUE
170  ELSE IF( lsame( norm, 'I' ) ) THEN
171 *
172 * Find normI(A).
173 *
174  DO 50 i = 1, n
175  work( i ) = zero
176  50 CONTINUE
177  DO 70 j = 1, n
178  DO 60 i = 1, min( n, j+1 )
179  work( i ) = work( i ) + abs( a( i, j ) )
180  60 CONTINUE
181  70 CONTINUE
182  VALUE = zero
183  DO 80 i = 1, n
184  sum = work( i )
185  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
186  80 CONTINUE
187  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
188 *
189 * Find normF(A).
190 *
191  scale = zero
192  sum = one
193  DO 90 j = 1, n
194  CALL zlassq( min( n, j+1 ), a( 1, j ), 1, scale, sum )
195  90 CONTINUE
196  VALUE = scale*sqrt( sum )
197  END IF
198 *
199  zlanhs = VALUE
200  RETURN
201 *
202 * End of ZLANHS
203 *
204  END
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine zlassq(n, x, incx, scl, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f90:137
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function zlanhs(NORM, N, A, LDA, WORK)
ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlanhs.f:109