 LAPACK  3.9.0 LAPACK: Linear Algebra PACKage

## ◆ 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.```
Date
December 2016

Definition at line 111 of file clanhs.f.

111 *
112 * -- LAPACK auxiliary routine (version 3.7.0) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 * December 2016
116 *
117  IMPLICIT NONE
118 * .. Scalar Arguments ..
119  CHARACTER NORM
120  INTEGER LDA, N
121 * ..
122 * .. Array Arguments ..
123  REAL WORK( * )
124  COMPLEX A( LDA, * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130  REAL ONE, ZERO
131  parameter( one = 1.0e+0, zero = 0.0e+0 )
132 * ..
133 * .. Local Scalars ..
134  INTEGER I, J
135  REAL SUM, VALUE
136 * ..
137 * .. Local Arrays ..
138  REAL SSQ( 2 ), COLSSQ( 2 )
139 * ..
140 * .. External Functions ..
141  LOGICAL LSAME, SISNAN
142  EXTERNAL lsame, sisnan
143 * ..
144 * .. External Subroutines ..
145  EXTERNAL classq, scombssq
146 * ..
147 * .. Intrinsic Functions ..
148  INTRINSIC abs, min, sqrt
149 * ..
150 * .. Executable Statements ..
151 *
152  IF( n.EQ.0 ) THEN
153  VALUE = zero
154  ELSE IF( lsame( norm, 'M' ) ) THEN
155 *
156 * Find max(abs(A(i,j))).
157 *
158  VALUE = zero
159  DO 20 j = 1, n
160  DO 10 i = 1, min( n, j+1 )
161  sum = abs( a( i, j ) )
162  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
163  10 CONTINUE
164  20 CONTINUE
165  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
166 *
167 * Find norm1(A).
168 *
169  VALUE = zero
170  DO 40 j = 1, n
171  sum = zero
172  DO 30 i = 1, min( n, j+1 )
173  sum = sum + abs( a( i, j ) )
174  30 CONTINUE
175  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
176  40 CONTINUE
177  ELSE IF( lsame( norm, 'I' ) ) THEN
178 *
179 * Find normI(A).
180 *
181  DO 50 i = 1, n
182  work( i ) = zero
183  50 CONTINUE
184  DO 70 j = 1, n
185  DO 60 i = 1, min( n, j+1 )
186  work( i ) = work( i ) + abs( a( i, j ) )
187  60 CONTINUE
188  70 CONTINUE
189  VALUE = zero
190  DO 80 i = 1, n
191  sum = work( i )
192  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
193  80 CONTINUE
194  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
195 *
196 * Find normF(A).
197 * SSQ(1) is scale
198 * SSQ(2) is sum-of-squares
199 * For better accuracy, sum each column separately.
200 *
201  ssq( 1 ) = zero
202  ssq( 2 ) = one
203  DO 90 j = 1, n
204  colssq( 1 ) = zero
205  colssq( 2 ) = one
206  CALL classq( min( n, j+1 ), a( 1, j ), 1,
207  \$ colssq( 1 ), colssq( 2 ) )
208  CALL scombssq( ssq, colssq )
209  90 CONTINUE
210  VALUE = ssq( 1 )*sqrt( ssq( 2 ) )
211  END IF
212 *
213  clanhs = VALUE
214  RETURN
215 *
216 * End of CLANHS
217 *
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clanhs
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:111
classq
subroutine classq(N, X, INCX, SCALE, SUMSQ)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f:108
sisnan
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:61
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
scombssq
subroutine scombssq(V1, V2)
SCOMBSSQ adds two scaled sum of squares quantities
Definition: scombssq.f:62