LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zlanhs()

double precision function zlanhs ( character  NORM,
integer  N,
complex*16, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  WORK 
)

ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

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

Purpose:
 ZLANHS  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 Hessenberg matrix A.
Returns
ZLANHS
    ZLANHS = ( 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 ZLANHS as described
          above.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, ZLANHS is
          set to zero.
[in]A
          A is COMPLEX*16 array, dimension (LDA,N)
          The n by n upper Hessenberg matrix A; the part of A below the
          first sub-diagonal is not referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,1).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
          referenced.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 111 of file zlanhs.f.

111 *
112 * -- LAPACK auxiliary routine (version 3.7.0) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 * December 2016
116 *
117 * .. Scalar Arguments ..
118  CHARACTER norm
119  INTEGER lda, n
120 * ..
121 * .. Array Arguments ..
122  DOUBLE PRECISION work( * )
123  COMPLEX*16 a( lda, * )
124 * ..
125 *
126 * =====================================================================
127 *
128 * .. Parameters ..
129  DOUBLE PRECISION one, zero
130  parameter( one = 1.0d+0, zero = 0.0d+0 )
131 * ..
132 * .. Local Scalars ..
133  INTEGER i, j
134  DOUBLE PRECISION scale, sum, value
135 * ..
136 * .. External Functions ..
137  LOGICAL lsame, disnan
138  EXTERNAL lsame, disnan
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL zlassq
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC abs, min, sqrt
145 * ..
146 * .. Executable Statements ..
147 *
148  IF( n.EQ.0 ) THEN
149  VALUE = zero
150  ELSE IF( lsame( norm, 'M' ) ) THEN
151 *
152 * Find max(abs(A(i,j))).
153 *
154  VALUE = zero
155  DO 20 j = 1, n
156  DO 10 i = 1, min( n, j+1 )
157  sum = abs( a( i, j ) )
158  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
159  10 CONTINUE
160  20 CONTINUE
161  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
162 *
163 * Find norm1(A).
164 *
165  VALUE = zero
166  DO 40 j = 1, n
167  sum = zero
168  DO 30 i = 1, min( n, j+1 )
169  sum = sum + abs( a( i, j ) )
170  30 CONTINUE
171  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
172  40 CONTINUE
173  ELSE IF( lsame( norm, 'I' ) ) THEN
174 *
175 * Find normI(A).
176 *
177  DO 50 i = 1, n
178  work( i ) = zero
179  50 CONTINUE
180  DO 70 j = 1, n
181  DO 60 i = 1, min( n, j+1 )
182  work( i ) = work( i ) + abs( a( i, j ) )
183  60 CONTINUE
184  70 CONTINUE
185  VALUE = zero
186  DO 80 i = 1, n
187  sum = work( i )
188  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
189  80 CONTINUE
190  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
191 *
192 * Find normF(A).
193 *
194  scale = zero
195  sum = one
196  DO 90 j = 1, n
197  CALL zlassq( min( n, j+1 ), a( 1, j ), 1, scale, sum )
198  90 CONTINUE
199  VALUE = scale*sqrt( sum )
200  END IF
201 *
202  zlanhs = VALUE
203  RETURN
204 *
205 * End of ZLANHS
206 *
subroutine zlassq(N, X, INCX, SCALE, SUMSQ)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f:108
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:61
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function zlanhs(NORM, N, A, LDA, WORK)
ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlanhs.f:111
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