LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ clanht()

real function clanht ( character  NORM,
integer  N,
real, dimension( * )  D,
complex, dimension( * )  E 
)

CLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.

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

Purpose:
 CLANHT  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 Hermitian tridiagonal matrix A.
Returns
CLANHT
    CLANHT = ( 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 CLANHT as described
          above.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, CLANHT is
          set to zero.
[in]D
          D is REAL array, dimension (N)
          The diagonal elements of A.
[in]E
          E is COMPLEX array, dimension (N-1)
          The (n-1) sub-diagonal or super-diagonal elements of A.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 100 of file clanht.f.

101 *
102 * -- LAPACK auxiliary routine --
103 * -- LAPACK is a software package provided by Univ. of Tennessee, --
104 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
105 *
106 * .. Scalar Arguments ..
107  CHARACTER NORM
108  INTEGER N
109 * ..
110 * .. Array Arguments ..
111  REAL D( * )
112  COMPLEX E( * )
113 * ..
114 *
115 * =====================================================================
116 *
117 * .. Parameters ..
118  REAL ONE, ZERO
119  parameter( one = 1.0e+0, zero = 0.0e+0 )
120 * ..
121 * .. Local Scalars ..
122  INTEGER I
123  REAL ANORM, SCALE, SUM
124 * ..
125 * .. External Functions ..
126  LOGICAL LSAME, SISNAN
127  EXTERNAL lsame, sisnan
128 * ..
129 * .. External Subroutines ..
130  EXTERNAL classq, slassq
131 * ..
132 * .. Intrinsic Functions ..
133  INTRINSIC abs, sqrt
134 * ..
135 * .. Executable Statements ..
136 *
137  IF( n.LE.0 ) THEN
138  anorm = zero
139  ELSE IF( lsame( norm, 'M' ) ) THEN
140 *
141 * Find max(abs(A(i,j))).
142 *
143  anorm = abs( d( n ) )
144  DO 10 i = 1, n - 1
145  sum = abs( d( i ) )
146  IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
147  sum = abs( e( i ) )
148  IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
149  10 CONTINUE
150  ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' .OR.
151  $ lsame( norm, 'I' ) ) THEN
152 *
153 * Find norm1(A).
154 *
155  IF( n.EQ.1 ) THEN
156  anorm = abs( d( 1 ) )
157  ELSE
158  anorm = abs( d( 1 ) )+abs( e( 1 ) )
159  sum = abs( e( n-1 ) )+abs( d( n ) )
160  IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
161  DO 20 i = 2, n - 1
162  sum = abs( d( i ) )+abs( e( i ) )+abs( e( i-1 ) )
163  IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
164  20 CONTINUE
165  END IF
166  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
167 *
168 * Find normF(A).
169 *
170  scale = zero
171  sum = one
172  IF( n.GT.1 ) THEN
173  CALL classq( n-1, e, 1, scale, sum )
174  sum = 2*sum
175  END IF
176  CALL slassq( n, d, 1, scale, sum )
177  anorm = scale*sqrt( sum )
178  END IF
179 *
180  clanht = anorm
181  RETURN
182 *
183 * End of CLANHT
184 *
subroutine slassq(n, x, incx, scl, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f90:126
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f90:126
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function clanht(NORM, N, D, E)
CLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanht.f:101
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