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

 double precision function zlange ( character norm, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work )

ZLANGE 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:
``` ZLANGE  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value  of a
complex matrix A.```
Returns
ZLANGE
```    ZLANGE = ( 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 ZLANGE as described above.``` [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0. When M = 0, ZLANGE is set to zero.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0. When N = 0, ZLANGE is set to zero.``` [in] A ``` A is COMPLEX*16 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 114 of file zlange.f.

115*
116* -- LAPACK auxiliary routine --
117* -- LAPACK is a software package provided by Univ. of Tennessee, --
118* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119*
120* .. Scalar Arguments ..
121 CHARACTER NORM
122 INTEGER LDA, M, N
123* ..
124* .. Array Arguments ..
125 DOUBLE PRECISION WORK( * )
126 COMPLEX*16 A( LDA, * )
127* ..
128*
129* =====================================================================
130*
131* .. Parameters ..
132 DOUBLE PRECISION ONE, ZERO
133 parameter( one = 1.0d+0, zero = 0.0d+0 )
134* ..
135* .. Local Scalars ..
136 INTEGER I, J
137 DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
138* ..
139* .. External Functions ..
140 LOGICAL LSAME, DISNAN
141 EXTERNAL lsame, disnan
142* ..
143* .. External Subroutines ..
144 EXTERNAL zlassq
145* ..
146* .. Intrinsic Functions ..
147 INTRINSIC abs, min, sqrt
148* ..
149* .. Executable Statements ..
150*
151 IF( min( m, n ).EQ.0 ) THEN
152 VALUE = zero
153 ELSE IF( lsame( norm, 'M' ) ) THEN
154*
155* Find max(abs(A(i,j))).
156*
157 VALUE = zero
158 DO 20 j = 1, n
159 DO 10 i = 1, m
160 temp = abs( a( i, j ) )
161 IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
162 10 CONTINUE
163 20 CONTINUE
164 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
165*
166* Find norm1(A).
167*
168 VALUE = zero
169 DO 40 j = 1, n
170 sum = zero
171 DO 30 i = 1, m
172 sum = sum + abs( a( i, j ) )
173 30 CONTINUE
174 IF( VALUE.LT.sum .OR. disnan( sum ) ) VALUE = sum
175 40 CONTINUE
176 ELSE IF( lsame( norm, 'I' ) ) THEN
177*
178* Find normI(A).
179*
180 DO 50 i = 1, m
181 work( i ) = zero
182 50 CONTINUE
183 DO 70 j = 1, n
184 DO 60 i = 1, m
185 work( i ) = work( i ) + abs( a( i, j ) )
186 60 CONTINUE
187 70 CONTINUE
188 VALUE = zero
189 DO 80 i = 1, m
190 temp = work( i )
191 IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
192 80 CONTINUE
193 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
194*
195* Find normF(A).
196*
197 scale = zero
198 sum = one
199 DO 90 j = 1, n
200 CALL zlassq( m, a( 1, j ), 1, scale, sum )
201 90 CONTINUE
202 VALUE = scale*sqrt( sum )
203 END IF
204*
205 zlange = VALUE
206 RETURN
207*
208* End of ZLANGE
209*
logical function disnan(din)
DISNAN tests input for NaN.
Definition disnan.f:59
double precision function zlange(norm, m, n, a, lda, work)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition zlange.f:115
subroutine zlassq(n, x, incx, scale, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition zlassq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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