 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ clansy()

 real function clansy ( character NORM, character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) WORK )

CLANSY 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 symmetric matrix.

Purpose:
``` CLANSY  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value  of a
complex symmetric matrix A.```
Returns
CLANSY
```    CLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A),         NORM = '1', 'O' or 'o'
(
( normI(A),         NORM = 'I' or 'i'
(
( normF(A),         NORM = 'F', 'f', 'E' or 'e'

where  norm1  denotes the  one norm of a matrix (maximum column sum),
normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
normF  denotes the  Frobenius norm of a matrix (square root of sum of
squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.```
Parameters
 [in] NORM ``` NORM is CHARACTER*1 Specifies the value to be returned in CLANSY as described above.``` [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANSY is set to zero.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).``` [out] WORK ``` WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.```

Definition at line 122 of file clansy.f.

123*
124* -- LAPACK auxiliary routine --
125* -- LAPACK is a software package provided by Univ. of Tennessee, --
126* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127*
128* .. Scalar Arguments ..
129 CHARACTER NORM, UPLO
130 INTEGER LDA, N
131* ..
132* .. Array Arguments ..
133 REAL WORK( * )
134 COMPLEX A( LDA, * )
135* ..
136*
137* =====================================================================
138*
139* .. Parameters ..
140 REAL ONE, ZERO
141 parameter( one = 1.0e+0, zero = 0.0e+0 )
142* ..
143* .. Local Scalars ..
144 INTEGER I, J
145 REAL ABSA, SCALE, SUM, VALUE
146* ..
147* .. External Functions ..
148 LOGICAL LSAME, SISNAN
149 EXTERNAL lsame, sisnan
150* ..
151* .. External Subroutines ..
152 EXTERNAL classq
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC abs, sqrt
156* ..
157* .. Executable Statements ..
158*
159 IF( n.EQ.0 ) THEN
160 VALUE = zero
161 ELSE IF( lsame( norm, 'M' ) ) THEN
162*
163* Find max(abs(A(i,j))).
164*
165 VALUE = zero
166 IF( lsame( uplo, 'U' ) ) THEN
167 DO 20 j = 1, n
168 DO 10 i = 1, j
169 sum = abs( a( i, j ) )
170 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
171 10 CONTINUE
172 20 CONTINUE
173 ELSE
174 DO 40 j = 1, n
175 DO 30 i = j, n
176 sum = abs( a( i, j ) )
177 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
178 30 CONTINUE
179 40 CONTINUE
180 END IF
181 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
182 \$ ( norm.EQ.'1' ) ) THEN
183*
184* Find normI(A) ( = norm1(A), since A is symmetric).
185*
186 VALUE = zero
187 IF( lsame( uplo, 'U' ) ) THEN
188 DO 60 j = 1, n
189 sum = zero
190 DO 50 i = 1, j - 1
191 absa = abs( a( i, j ) )
192 sum = sum + absa
193 work( i ) = work( i ) + absa
194 50 CONTINUE
195 work( j ) = sum + abs( a( j, j ) )
196 60 CONTINUE
197 DO 70 i = 1, n
198 sum = work( i )
199 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
200 70 CONTINUE
201 ELSE
202 DO 80 i = 1, n
203 work( i ) = zero
204 80 CONTINUE
205 DO 100 j = 1, n
206 sum = work( j ) + abs( a( j, j ) )
207 DO 90 i = j + 1, n
208 absa = abs( a( i, j ) )
209 sum = sum + absa
210 work( i ) = work( i ) + absa
211 90 CONTINUE
212 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
213 100 CONTINUE
214 END IF
215 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
216*
217* Find normF(A).
218*
219 scale = zero
220 sum = one
221 IF( lsame( uplo, 'U' ) ) THEN
222 DO 110 j = 2, n
223 CALL classq( j-1, a( 1, j ), 1, scale, sum )
224 110 CONTINUE
225 ELSE
226 DO 120 j = 1, n - 1
227 CALL classq( n-j, a( j+1, j ), 1, scale, sum )
228 120 CONTINUE
229 END IF
230 sum = 2*sum
231 CALL classq( n, a, lda+1, scale, sum )
232 VALUE = scale*sqrt( sum )
233 END IF
234*
235 clansy = VALUE
236 RETURN
237*
238* End of CLANSY
239*
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f90:137
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansy.f:123
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