LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zlanhp.f
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1*> \brief \b ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhp.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK )
22*
23* .. Scalar Arguments ..
24* CHARACTER NORM, UPLO
25* INTEGER N
26* ..
27* .. Array Arguments ..
28* DOUBLE PRECISION WORK( * )
29* COMPLEX*16 AP( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> ZLANHP 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 hermitian matrix A, supplied in packed form.
41*> \endverbatim
42*>
43*> \return ZLANHP
44*> \verbatim
45*>
46*> ZLANHP = ( 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 ZLANHP as described
67*> above.
68*> \endverbatim
69*>
70*> \param[in] UPLO
71*> \verbatim
72*> UPLO is CHARACTER*1
73*> Specifies whether the upper or lower triangular part of the
74*> hermitian matrix A is supplied.
75*> = 'U': Upper triangular part of A is supplied
76*> = 'L': Lower triangular part of A is supplied
77*> \endverbatim
78*>
79*> \param[in] N
80*> \verbatim
81*> N is INTEGER
82*> The order of the matrix A. N >= 0. When N = 0, ZLANHP is
83*> set to zero.
84*> \endverbatim
85*>
86*> \param[in] AP
87*> \verbatim
88*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
89*> The upper or lower triangle of the hermitian matrix A, packed
90*> columnwise in a linear array. The j-th column of A is stored
91*> in the array AP as follows:
92*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
93*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
94*> Note that the imaginary parts of the diagonal elements need
95*> not be set and are assumed to be zero.
96*> \endverbatim
97*>
98*> \param[out] WORK
99*> \verbatim
100*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
101*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
102*> WORK is not referenced.
103*> \endverbatim
104*
105* Authors:
106* ========
107*
108*> \author Univ. of Tennessee
109*> \author Univ. of California Berkeley
110*> \author Univ. of Colorado Denver
111*> \author NAG Ltd.
112*
113*> \ingroup lanhp
114*
115* =====================================================================
116 DOUBLE PRECISION FUNCTION zlanhp( NORM, UPLO, N, AP, WORK )
117*
118* -- LAPACK auxiliary routine --
119* -- LAPACK is a software package provided by Univ. of Tennessee, --
120* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121*
122* .. Scalar Arguments ..
123 CHARACTER norm, uplo
124 INTEGER n
125* ..
126* .. Array Arguments ..
127 DOUBLE PRECISION work( * )
128 COMPLEX*16 ap( * )
129* ..
130*
131* =====================================================================
132*
133* .. Parameters ..
134 DOUBLE PRECISION one, zero
135 parameter( one = 1.0d+0, zero = 0.0d+0 )
136* ..
137* .. Local Scalars ..
138 INTEGER i, j, k
139 DOUBLE PRECISION absa, scale, sum, value
140* ..
141* .. External Functions ..
142 LOGICAL lsame, disnan
143 EXTERNAL lsame, disnan
144* ..
145* .. External Subroutines ..
146 EXTERNAL zlassq
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC abs, dble, sqrt
150* ..
151* .. Executable Statements ..
152*
153 IF( n.EQ.0 ) THEN
154 VALUE = zero
155 ELSE IF( lsame( norm, 'M' ) ) THEN
156*
157* Find max(abs(A(i,j))).
158*
159 VALUE = zero
160 IF( lsame( uplo, 'U' ) ) THEN
161 k = 0
162 DO 20 j = 1, n
163 DO 10 i = k + 1, k + j - 1
164 sum = abs( ap( i ) )
165 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
166 10 CONTINUE
167 k = k + j
168 sum = abs( dble( ap( k ) ) )
169 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
170 20 CONTINUE
171 ELSE
172 k = 1
173 DO 40 j = 1, n
174 sum = abs( dble( ap( k ) ) )
175 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
176 DO 30 i = k + 1, k + n - j
177 sum = abs( ap( i ) )
178 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
179 30 CONTINUE
180 k = k + n - j + 1
181 40 CONTINUE
182 END IF
183 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
184 \$ ( norm.EQ.'1' ) ) THEN
185*
186* Find normI(A) ( = norm1(A), since A is hermitian).
187*
188 VALUE = zero
189 k = 1
190 IF( lsame( uplo, 'U' ) ) THEN
191 DO 60 j = 1, n
192 sum = zero
193 DO 50 i = 1, j - 1
194 absa = abs( ap( k ) )
195 sum = sum + absa
196 work( i ) = work( i ) + absa
197 k = k + 1
198 50 CONTINUE
199 work( j ) = sum + abs( dble( ap( k ) ) )
200 k = k + 1
201 60 CONTINUE
202 DO 70 i = 1, n
203 sum = work( i )
204 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
205 70 CONTINUE
206 ELSE
207 DO 80 i = 1, n
208 work( i ) = zero
209 80 CONTINUE
210 DO 100 j = 1, n
211 sum = work( j ) + abs( dble( ap( k ) ) )
212 k = k + 1
213 DO 90 i = j + 1, n
214 absa = abs( ap( k ) )
215 sum = sum + absa
216 work( i ) = work( i ) + absa
217 k = k + 1
218 90 CONTINUE
219 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
220 100 CONTINUE
221 END IF
222 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
223*
224* Find normF(A).
225*
226 scale = zero
227 sum = one
228 k = 2
229 IF( lsame( uplo, 'U' ) ) THEN
230 DO 110 j = 2, n
231 CALL zlassq( j-1, ap( k ), 1, scale, sum )
232 k = k + j
233 110 CONTINUE
234 ELSE
235 DO 120 j = 1, n - 1
236 CALL zlassq( n-j, ap( k ), 1, scale, sum )
237 k = k + n - j + 1
238 120 CONTINUE
239 END IF
240 sum = 2*sum
241 k = 1
242 DO 130 i = 1, n
243 IF( dble( ap( k ) ).NE.zero ) THEN
244 absa = abs( dble( ap( k ) ) )
245 IF( scale.LT.absa ) THEN
246 sum = one + sum*( scale / absa )**2
247 scale = absa
248 ELSE
249 sum = sum + ( absa / scale )**2
250 END IF
251 END IF
252 IF( lsame( uplo, 'U' ) ) THEN
253 k = k + i + 1
254 ELSE
255 k = k + n - i + 1
256 END IF
257 130 CONTINUE
258 VALUE = scale*sqrt( sum )
259 END IF
260*
261 zlanhp = VALUE
262 RETURN
263*
264* End of ZLANHP
265*
266 END
logical function disnan(din)
DISNAN tests input for NaN.
Definition disnan.f:59
double precision function zlanhp(norm, uplo, n, ap, work)
ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlanhp.f:117
subroutine zlassq(n, x, incx, scale, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition zlassq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48