 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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.

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.```

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  IMPLICIT NONE
120 * .. Scalar Arguments ..
121  CHARACTER NORM
122  INTEGER LDA, M, N
123 * ..
124 * .. Array Arguments ..
125  DOUBLE PRECISION A( LDA, * ), WORK( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  DOUBLE PRECISION ONE, ZERO
132  parameter( one = 1.0d+0, zero = 0.0d+0 )
133 * ..
134 * .. Local Scalars ..
135  INTEGER I, J
136  DOUBLE PRECISION SUM, VALUE, TEMP
137 * ..
138 * .. Local Arrays ..
139  DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL dlassq, dcombssq
143 * ..
144 * .. External Functions ..
145  LOGICAL LSAME, DISNAN
146  EXTERNAL lsame, disnan
147 * ..
148 * .. Intrinsic Functions ..
149  INTRINSIC abs, min, sqrt
150 * ..
151 * .. Executable Statements ..
152 *
153  IF( min( m, n ).EQ.0 ) THEN
154  VALUE = zero
155  ELSE IF( lsame( norm, 'M' ) ) THEN
156 *
157 * Find max(abs(A(i,j))).
158 *
159  VALUE = zero
160  DO 20 j = 1, n
161  DO 10 i = 1, m
162  temp = abs( a( i, j ) )
163  IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
164  10 CONTINUE
165  20 CONTINUE
166  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
167 *
168 * Find norm1(A).
169 *
170  VALUE = zero
171  DO 40 j = 1, n
172  sum = zero
173  DO 30 i = 1, m
174  sum = sum + abs( a( i, j ) )
175  30 CONTINUE
176  IF( VALUE.LT.sum .OR. disnan( sum ) ) VALUE = sum
177  40 CONTINUE
178  ELSE IF( lsame( norm, 'I' ) ) THEN
179 *
180 * Find normI(A).
181 *
182  DO 50 i = 1, m
183  work( i ) = zero
184  50 CONTINUE
185  DO 70 j = 1, n
186  DO 60 i = 1, m
187  work( i ) = work( i ) + abs( a( i, j ) )
188  60 CONTINUE
189  70 CONTINUE
190  VALUE = zero
191  DO 80 i = 1, m
192  temp = work( i )
193  IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
194  80 CONTINUE
195  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
196 *
197 * Find normF(A).
198 * SSQ(1) is scale
199 * SSQ(2) is sum-of-squares
200 * For better accuracy, sum each column separately.
201 *
202  ssq( 1 ) = zero
203  ssq( 2 ) = one
204  DO 90 j = 1, n
205  colssq( 1 ) = zero
206  colssq( 2 ) = one
207  CALL dlassq( m, a( 1, j ), 1, colssq( 1 ), colssq( 2 ) )
208  CALL dcombssq( ssq, colssq )
209  90 CONTINUE
210  VALUE = ssq( 1 )*sqrt( ssq( 2 ) )
211  END IF
212 *
213  dlange = VALUE
214  RETURN
215 *
216 * End of DLANGE
217 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine dlassq(n, x, incx, scl, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f90:126
subroutine dcombssq(V1, V2)
DCOMBSSQ adds two scaled sum of squares quantities.
Definition: dcombssq.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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