LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlanhs()

double precision function dlanhs ( character  norm,
integer  n,
double precision, dimension( lda, * )  a,
integer  lda,
double precision, dimension( * )  work 
)

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

Download DLANHS + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLANHS  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
DLANHS
    DLANHS = ( 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 DLANHS as described
          above.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, DLANHS is
          set to zero.
[in]A
          A is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
          referenced.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 107 of file dlanhs.f.

108*
109* -- LAPACK auxiliary routine --
110* -- LAPACK is a software package provided by Univ. of Tennessee, --
111* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112*
113* .. Scalar Arguments ..
114 CHARACTER NORM
115 INTEGER LDA, N
116* ..
117* .. Array Arguments ..
118 DOUBLE PRECISION A( LDA, * ), WORK( * )
119* ..
120*
121* =====================================================================
122*
123* .. Parameters ..
124 DOUBLE PRECISION ONE, ZERO
125 parameter( one = 1.0d+0, zero = 0.0d+0 )
126* ..
127* .. Local Scalars ..
128 INTEGER I, J
129 DOUBLE PRECISION SCALE, SUM, VALUE
130* ..
131* .. External Subroutines ..
132 EXTERNAL dlassq
133* ..
134* .. External Functions ..
135 LOGICAL LSAME, DISNAN
136 EXTERNAL lsame, disnan
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC abs, min, sqrt
140* ..
141* .. Executable Statements ..
142*
143 IF( n.EQ.0 ) THEN
144 VALUE = zero
145 ELSE IF( lsame( norm, 'M' ) ) THEN
146*
147* Find max(abs(A(i,j))).
148*
149 VALUE = zero
150 DO 20 j = 1, n
151 DO 10 i = 1, min( n, j+1 )
152 sum = abs( a( i, j ) )
153 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
154 10 CONTINUE
155 20 CONTINUE
156 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
157*
158* Find norm1(A).
159*
160 VALUE = zero
161 DO 40 j = 1, n
162 sum = zero
163 DO 30 i = 1, min( n, j+1 )
164 sum = sum + abs( a( i, j ) )
165 30 CONTINUE
166 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
167 40 CONTINUE
168 ELSE IF( lsame( norm, 'I' ) ) THEN
169*
170* Find normI(A).
171*
172 DO 50 i = 1, n
173 work( i ) = zero
174 50 CONTINUE
175 DO 70 j = 1, n
176 DO 60 i = 1, min( n, j+1 )
177 work( i ) = work( i ) + abs( a( i, j ) )
178 60 CONTINUE
179 70 CONTINUE
180 VALUE = zero
181 DO 80 i = 1, n
182 sum = work( i )
183 IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
184 80 CONTINUE
185 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
186*
187* Find normF(A).
188*
189 scale = zero
190 sum = one
191 DO 90 j = 1, n
192 CALL dlassq( min( n, j+1 ), a( 1, j ), 1, scale, sum )
193 90 CONTINUE
194 VALUE = scale*sqrt( sum )
195 END IF
196*
197 dlanhs = VALUE
198 RETURN
199*
200* End of DLANHS
201*
logical function disnan(din)
DISNAN tests input for NaN.
Definition disnan.f:59
double precision function dlanhs(norm, n, a, lda, work)
DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition dlanhs.f:108
subroutine dlassq(n, x, incx, scale, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
Definition dlassq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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