LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ slangb()

real function slangb ( character  NORM,
integer  N,
integer  KL,
integer  KU,
real, dimension( ldab, * )  AB,
integer  LDAB,
real, dimension( * )  WORK 
)

SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

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

Purpose:
 SLANGB  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the element of  largest absolute value  of an
 n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
Returns
SLANGB
    SLANGB = ( 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 SLANGB as described
          above.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, SLANGB is
          set to zero.
[in]KL
          KL is INTEGER
          The number of sub-diagonals of the matrix A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of super-diagonals of the matrix A.  KU >= 0.
[in]AB
          AB is REAL array, dimension (LDAB,N)
          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
          column of A is stored in the j-th column of the array AB as
          follows:
          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KL+KU+1.
[out]WORK
          WORK is REAL 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.

Definition at line 122 of file slangb.f.

124 *
125 * -- LAPACK auxiliary routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER NORM
131  INTEGER KL, KU, LDAB, N
132 * ..
133 * .. Array Arguments ..
134  REAL AB( LDAB, * ), WORK( * )
135 * ..
136 *
137 * =====================================================================
138 *
139 *
140 * .. Parameters ..
141  REAL ONE, ZERO
142  parameter( one = 1.0e+0, zero = 0.0e+0 )
143 * ..
144 * .. Local Scalars ..
145  INTEGER I, J, K, L
146  REAL SCALE, SUM, VALUE, TEMP
147 * ..
148 * .. External Subroutines ..
149  EXTERNAL slassq
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME, SISNAN
153  EXTERNAL lsame, sisnan
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC abs, max, min, sqrt
157 * ..
158 * .. Executable Statements ..
159 *
160  IF( n.EQ.0 ) THEN
161  VALUE = zero
162  ELSE IF( lsame( norm, 'M' ) ) THEN
163 *
164 * Find max(abs(A(i,j))).
165 *
166  VALUE = zero
167  DO 20 j = 1, n
168  DO 10 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
169  temp = abs( ab( i, j ) )
170  IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
171  10 CONTINUE
172  20 CONTINUE
173  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
174 *
175 * Find norm1(A).
176 *
177  VALUE = zero
178  DO 40 j = 1, n
179  sum = zero
180  DO 30 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
181  sum = sum + abs( ab( i, j ) )
182  30 CONTINUE
183  IF( VALUE.LT.sum .OR. sisnan( sum ) ) VALUE = sum
184  40 CONTINUE
185  ELSE IF( lsame( norm, 'I' ) ) THEN
186 *
187 * Find normI(A).
188 *
189  DO 50 i = 1, n
190  work( i ) = zero
191  50 CONTINUE
192  DO 70 j = 1, n
193  k = ku + 1 - j
194  DO 60 i = max( 1, j-ku ), min( n, j+kl )
195  work( i ) = work( i ) + abs( ab( k+i, j ) )
196  60 CONTINUE
197  70 CONTINUE
198  VALUE = zero
199  DO 80 i = 1, n
200  temp = work( i )
201  IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
202  80 CONTINUE
203  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
204 *
205 * Find normF(A).
206 *
207  scale = zero
208  sum = one
209  DO 90 j = 1, n
210  l = max( 1, j-ku )
211  k = ku + 1 - j + l
212  CALL slassq( min( n, j+kl )-l+1, ab( k, j ), 1, scale, sum )
213  90 CONTINUE
214  VALUE = scale*sqrt( sum )
215  END IF
216 *
217  slangb = VALUE
218  RETURN
219 *
220 * End of SLANGB
221 *
subroutine slassq(n, x, incx, scl, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f90:137
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 slangb(NORM, N, KL, KU, AB, LDAB, WORK)
SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slangb.f:124
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