LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlange()

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

DLANGE 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 DLANGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLANGE  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
DLANGE
    DLANGE = ( 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 DLANGE as described
          above.
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.  When M = 0,
          DLANGE is set to zero.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.  When N = 0,
          DLANGE is set to zero.
[in]A
          A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 113 of file dlange.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 DOUBLE PRECISION A( LDA, * ), WORK( * )
125* ..
126*
127* =====================================================================
128*
129* .. Parameters ..
130 DOUBLE PRECISION ONE, ZERO
131 parameter( one = 1.0d+0, zero = 0.0d+0 )
132* ..
133* .. Local Scalars ..
134 INTEGER I, J
135 DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
136* ..
137* .. External Subroutines ..
138 EXTERNAL dlassq
139* ..
140* .. External Functions ..
141 LOGICAL LSAME, DISNAN
142 EXTERNAL lsame, disnan
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. disnan( 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. disnan( 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. disnan( 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 dlassq( m, a( 1, j ), 1, scale, sum )
199 90 CONTINUE
200 VALUE = scale*sqrt( sum )
201 END IF
202*
203 dlange = VALUE
204 RETURN
205*
206* End of DLANGE
207*
logical function disnan(din)
DISNAN tests input for NaN.
Definition disnan.f:59
double precision function dlange(norm, m, n, a, lda, work)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition dlange.f:114
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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