LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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◆ clanhs()

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

CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

Purpose:
``` CLANHS  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value  of a
Hessenberg matrix A.```
Returns
CLANHS
```    CLANHS = ( 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 CLANHS as described above.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHS is set to zero.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal 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'; otherwise, WORK is not referenced.```

Definition at line 108 of file clanhs.f.

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 REAL WORK( * )
120 COMPLEX A( LDA, * )
121* ..
122*
123* =====================================================================
124*
125* .. Parameters ..
126 REAL ONE, ZERO
127 parameter( one = 1.0e+0, zero = 0.0e+0 )
128* ..
129* .. Local Scalars ..
130 INTEGER I, J
131 REAL SCALE, SUM, VALUE
132* ..
133* .. External Functions ..
134 LOGICAL LSAME, SISNAN
135 EXTERNAL lsame, sisnan
136* ..
137* .. External Subroutines ..
138 EXTERNAL classq
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. sisnan( 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. sisnan( 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. sisnan( 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 classq( min( n, j+1 ), a( 1, j ), 1, scale, sum )
195 90 CONTINUE
196 VALUE = scale*sqrt( sum )
197 END IF
198*
199 clanhs = VALUE
200 RETURN
201*
202* End of CLANHS
203*
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 clanhs(NORM, N, A, LDA, WORK)
CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clanhs.f:109
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