LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Macros Modules Pages

◆ 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.

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

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. !>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 111 of file slange.f.

112*
113* -- LAPACK auxiliary routine --
114* -- LAPACK is a software package provided by Univ. of Tennessee, --
115* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116*
117* .. Scalar Arguments ..
118 CHARACTER NORM
119 INTEGER LDA, M, N
120* ..
121* .. Array Arguments ..
122 REAL A( LDA, * ), WORK( * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 REAL ONE, ZERO
129 parameter( one = 1.0e+0, zero = 0.0e+0 )
130* ..
131* .. Local Scalars ..
132 INTEGER I, J
133 REAL SCALE, SUM, VALUE, TEMP
134* ..
135* .. External Subroutines ..
136 EXTERNAL slassq
137* ..
138* .. External Functions ..
139 LOGICAL LSAME, SISNAN
140 EXTERNAL lsame, sisnan
141* ..
142* .. Intrinsic Functions ..
143 INTRINSIC abs, min, sqrt
144* ..
145* .. Executable Statements ..
146*
147 IF( min( m, n ).EQ.0 ) THEN
148 VALUE = zero
149 ELSE IF( lsame( norm, 'M' ) ) THEN
150*
151* Find max(abs(A(i,j))).
152*
153 VALUE = zero
154 DO 20 j = 1, n
155 DO 10 i = 1, m
156 temp = abs( a( i, j ) )
157 IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
158 10 CONTINUE
159 20 CONTINUE
160 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
161*
162* Find norm1(A).
163*
164 VALUE = zero
165 DO 40 j = 1, n
166 sum = zero
167 DO 30 i = 1, m
168 sum = sum + abs( a( i, j ) )
169 30 CONTINUE
170 IF( VALUE.LT.sum .OR. sisnan( sum ) ) VALUE = sum
171 40 CONTINUE
172 ELSE IF( lsame( norm, 'I' ) ) THEN
173*
174* Find normI(A).
175*
176 DO 50 i = 1, m
177 work( i ) = zero
178 50 CONTINUE
179 DO 70 j = 1, n
180 DO 60 i = 1, m
181 work( i ) = work( i ) + abs( a( i, j ) )
182 60 CONTINUE
183 70 CONTINUE
184 VALUE = zero
185 DO 80 i = 1, m
186 temp = work( i )
187 IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
188 80 CONTINUE
189 ELSE IF( ( lsame( norm, 'F' ) ) .OR.
190 $ ( lsame( norm, 'E' ) ) ) THEN
191*
192* Find normF(A).
193*
194 scale = zero
195 sum = one
196 DO 90 j = 1, n
197 CALL slassq( m, a( 1, j ), 1, scale, sum )
198 90 CONTINUE
199 VALUE = scale*sqrt( sum )
200 END IF
201*
202 slange = VALUE
203 RETURN
204*
205* End of SLANGE
206*
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:57
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:112
subroutine slassq(n, x, incx, scale, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition slassq.f90:122
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: