LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ slange()

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

SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

Purpose:
``` SLANGE  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value  of a
real matrix A.```
Returns
SLANGE
```    SLANGE = ( 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 SLANGE as described above.``` [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0. When M = 0, SLANGE is set to zero.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0. When N = 0, SLANGE is set to zero.``` [in] A ``` A is REAL array, dimension (LDA,N) The m by n matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(M,1).``` [out] WORK ``` WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced.```

Definition at line 113 of file slange.f.

114*
115* -- LAPACK auxiliary routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 CHARACTER NORM
121 INTEGER LDA, M, N
122* ..
123* .. Array Arguments ..
124 REAL A( LDA, * ), WORK( * )
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 SCALE, SUM, VALUE, TEMP
136* ..
137* .. External Subroutines ..
138 EXTERNAL slassq
139* ..
140* .. External Functions ..
141 LOGICAL LSAME, SISNAN
142 EXTERNAL lsame, sisnan
143* ..
144* .. Intrinsic Functions ..
145 INTRINSIC abs, min, sqrt
146* ..
147* .. Executable Statements ..
148*
149 IF( min( m, n ).EQ.0 ) THEN
150 VALUE = zero
151 ELSE IF( lsame( norm, 'M' ) ) THEN
152*
153* Find max(abs(A(i,j))).
154*
155 VALUE = zero
156 DO 20 j = 1, n
157 DO 10 i = 1, m
158 temp = abs( a( i, j ) )
159 IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
160 10 CONTINUE
161 20 CONTINUE
162 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
163*
164* Find norm1(A).
165*
166 VALUE = zero
167 DO 40 j = 1, n
168 sum = zero
169 DO 30 i = 1, m
170 sum = sum + abs( a( i, j ) )
171 30 CONTINUE
172 IF( VALUE.LT.sum .OR. sisnan( sum ) ) VALUE = sum
173 40 CONTINUE
174 ELSE IF( lsame( norm, 'I' ) ) THEN
175*
176* Find normI(A).
177*
178 DO 50 i = 1, m
179 work( i ) = zero
180 50 CONTINUE
181 DO 70 j = 1, n
182 DO 60 i = 1, m
183 work( i ) = work( i ) + abs( a( i, j ) )
184 60 CONTINUE
185 70 CONTINUE
186 VALUE = zero
187 DO 80 i = 1, m
188 temp = work( i )
189 IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
190 80 CONTINUE
191 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
192*
193* Find normF(A).
194*
195 scale = zero
196 sum = one
197 DO 90 j = 1, n
198 CALL slassq( m, a( 1, j ), 1, scale, sum )
199 90 CONTINUE
200 VALUE = scale*sqrt( sum )
201 END IF
202*
203 slange = VALUE
204 RETURN
205*
206* End of SLANGE
207*
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
real function slange(norm, m, n, a, lda, work)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition slange.f:114
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
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