LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zlanht()

double precision function zlanht ( character  NORM,
integer  N,
double precision, dimension( * )  D,
complex*16, dimension( * )  E 
)

ZLANHT 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 ZLANHT + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZLANHT  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
ZLANHT
    ZLANHT = ( 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 ZLANHT as described
          above.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, ZLANHT is
          set to zero.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal elements of A.
[in]E
          E is COMPLEX*16 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.
Date
December 2016

Definition at line 103 of file zlanht.f.

103 *
104 * -- LAPACK auxiliary routine (version 3.7.0) --
105 * -- LAPACK is a software package provided by Univ. of Tennessee, --
106 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
107 * December 2016
108 *
109 * .. Scalar Arguments ..
110  CHARACTER norm
111  INTEGER n
112 * ..
113 * .. Array Arguments ..
114  DOUBLE PRECISION d( * )
115  COMPLEX*16 e( * )
116 * ..
117 *
118 * =====================================================================
119 *
120 * .. Parameters ..
121  DOUBLE PRECISION one, zero
122  parameter( one = 1.0d+0, zero = 0.0d+0 )
123 * ..
124 * .. Local Scalars ..
125  INTEGER i
126  DOUBLE PRECISION anorm, scale, sum
127 * ..
128 * .. External Functions ..
129  LOGICAL lsame, disnan
130  EXTERNAL lsame, disnan
131 * ..
132 * .. External Subroutines ..
133  EXTERNAL dlassq, zlassq
134 * ..
135 * .. Intrinsic Functions ..
136  INTRINSIC abs, max, sqrt
137 * ..
138 * .. Executable Statements ..
139 *
140  IF( n.LE.0 ) THEN
141  anorm = zero
142  ELSE IF( lsame( norm, 'M' ) ) THEN
143 *
144 * Find max(abs(A(i,j))).
145 *
146  anorm = abs( d( n ) )
147  DO 10 i = 1, n - 1
148  sum = abs( d( i ) )
149  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
150  sum = abs( e( i ) )
151  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
152  10 CONTINUE
153  ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' .OR.
154  $ lsame( norm, 'I' ) ) THEN
155 *
156 * Find norm1(A).
157 *
158  IF( n.EQ.1 ) THEN
159  anorm = abs( d( 1 ) )
160  ELSE
161  anorm = abs( d( 1 ) )+abs( e( 1 ) )
162  sum = abs( e( n-1 ) )+abs( d( n ) )
163  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
164  DO 20 i = 2, n - 1
165  sum = abs( d( i ) )+abs( e( i ) )+abs( e( i-1 ) )
166  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
167  20 CONTINUE
168  END IF
169  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
170 *
171 * Find normF(A).
172 *
173  scale = zero
174  sum = one
175  IF( n.GT.1 ) THEN
176  CALL zlassq( n-1, e, 1, scale, sum )
177  sum = 2*sum
178  END IF
179  CALL dlassq( n, d, 1, scale, sum )
180  anorm = scale*sqrt( sum )
181  END IF
182 *
183  zlanht = anorm
184  RETURN
185 *
186 * End of ZLANHT
187 *
subroutine dlassq(N, X, INCX, SCALE, SUMSQ)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f:105
double precision function zlanht(NORM, N, D, E)
ZLANHT 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.
Definition: zlanht.f:103
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
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