LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

◆ slanhs()

 real function slanhs ( character norm, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work )

SLANHS 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:
``` SLANHS  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
SLANHS
```    SLANHS = ( 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 SLANHS as described above.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0. When N = 0, SLANHS is set to zero.``` [in] A ``` A is REAL 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 107 of file slanhs.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 REAL A( LDA, * ), WORK( * )
119* ..
120*
121* =====================================================================
122*
123* .. Parameters ..
124 REAL ONE, ZERO
125 parameter( one = 1.0e+0, zero = 0.0e+0 )
126* ..
127* .. Local Scalars ..
128 INTEGER I, J
129 REAL SCALE, SUM, VALUE
130* ..
131* .. External Subroutines ..
132 EXTERNAL slassq
133* ..
134* .. External Functions ..
135 LOGICAL LSAME, SISNAN
136 EXTERNAL lsame, sisnan
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. sisnan( 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. sisnan( 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. sisnan( 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 slassq( min( n, j+1 ), a( 1, j ), 1, scale, sum )
193 90 CONTINUE
194 VALUE = scale*sqrt( sum )
195 END IF
196*
197 slanhs = VALUE
198 RETURN
199*
200* End of SLANHS
201*
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
real function slanhs(norm, n, a, lda, work)
SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition slanhs.f:108
subroutine slassq(n, x, incx, scale, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition slassq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
Here is the call graph for this function:
Here is the caller graph for this function: