LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dlangt()

double precision function dlangt ( character  NORM,
integer  N,
double precision, dimension( * )  DL,
double precision, dimension( * )  D,
double precision, dimension( * )  DU 
)

DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

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

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

Definition at line 105 of file dlangt.f.

106 *
107 * -- LAPACK auxiliary routine --
108 * -- LAPACK is a software package provided by Univ. of Tennessee, --
109 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110 *
111 * .. Scalar Arguments ..
112  CHARACTER NORM
113  INTEGER N
114 * ..
115 * .. Array Arguments ..
116  DOUBLE PRECISION D( * ), DL( * ), DU( * )
117 * ..
118 *
119 * =====================================================================
120 *
121 * .. Parameters ..
122  DOUBLE PRECISION ONE, ZERO
123  parameter( one = 1.0d+0, zero = 0.0d+0 )
124 * ..
125 * .. Local Scalars ..
126  INTEGER I
127  DOUBLE PRECISION ANORM, SCALE, SUM, TEMP
128 * ..
129 * .. External Functions ..
130  LOGICAL LSAME, DISNAN
131  EXTERNAL lsame, disnan
132 * ..
133 * .. External Subroutines ..
134  EXTERNAL dlassq
135 * ..
136 * .. Intrinsic Functions ..
137  INTRINSIC abs, sqrt
138 * ..
139 * .. Executable Statements ..
140 *
141  IF( n.LE.0 ) THEN
142  anorm = zero
143  ELSE IF( lsame( norm, 'M' ) ) THEN
144 *
145 * Find max(abs(A(i,j))).
146 *
147  anorm = abs( d( n ) )
148  DO 10 i = 1, n - 1
149  IF( anorm.LT.abs( dl( i ) ) .OR. disnan( abs( dl( i ) ) ) )
150  $ anorm = abs(dl(i))
151  IF( anorm.LT.abs( d( i ) ) .OR. disnan( abs( d( i ) ) ) )
152  $ anorm = abs(d(i))
153  IF( anorm.LT.abs( du( i ) ) .OR. disnan(abs( du( i ) ) ) )
154  $ anorm = abs(du(i))
155  10 CONTINUE
156  ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' ) THEN
157 *
158 * Find norm1(A).
159 *
160  IF( n.EQ.1 ) THEN
161  anorm = abs( d( 1 ) )
162  ELSE
163  anorm = abs( d( 1 ) )+abs( dl( 1 ) )
164  temp = abs( d( n ) )+abs( du( n-1 ) )
165  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
166  DO 20 i = 2, n - 1
167  temp = abs( d( i ) )+abs( dl( i ) )+abs( du( i-1 ) )
168  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
169  20 CONTINUE
170  END IF
171  ELSE IF( lsame( norm, 'I' ) ) THEN
172 *
173 * Find normI(A).
174 *
175  IF( n.EQ.1 ) THEN
176  anorm = abs( d( 1 ) )
177  ELSE
178  anorm = abs( d( 1 ) )+abs( du( 1 ) )
179  temp = abs( d( n ) )+abs( dl( n-1 ) )
180  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
181  DO 30 i = 2, n - 1
182  temp = abs( d( i ) )+abs( du( i ) )+abs( dl( i-1 ) )
183  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
184  30 CONTINUE
185  END IF
186  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
187 *
188 * Find normF(A).
189 *
190  scale = zero
191  sum = one
192  CALL dlassq( n, d, 1, scale, sum )
193  IF( n.GT.1 ) THEN
194  CALL dlassq( n-1, dl, 1, scale, sum )
195  CALL dlassq( n-1, du, 1, scale, sum )
196  END IF
197  anorm = scale*sqrt( sum )
198  END IF
199 *
200  dlangt = anorm
201  RETURN
202 *
203 * End of DLANGT
204 *
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
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function dlangt(NORM, N, DL, D, DU)
DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlangt.f:106
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