LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ 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*
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
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
subroutine slassq(n, x, incx, scale, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition slassq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
Here is the call graph for this function:
Here is the caller graph for this function: