LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ stbt02()

subroutine stbt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  KD,
integer  NRHS,
real, dimension( ldab, * )  AB,
integer  LDAB,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  WORK,
real  RESID 
)

STBT02

Purpose:
 STBT02 computes the residual for the computed solution to a
 triangular system of linear equations op(A)*X = B when A is a
 triangular band matrix.  The test ratio is the maximum over the
 number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.
 The norm used is the 1-norm.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A    * X = B  (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.
[in]AB
          AB is REAL array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in]X
          X is REAL array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]B
          B is REAL array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 152 of file stbt02.f.

154 *
155 * -- LAPACK test routine --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 *
159 * .. Scalar Arguments ..
160  CHARACTER DIAG, TRANS, UPLO
161  INTEGER KD, LDAB, LDB, LDX, N, NRHS
162  REAL RESID
163 * ..
164 * .. Array Arguments ..
165  REAL AB( LDAB, * ), B( LDB, * ), WORK( * ),
166  $ X( LDX, * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  REAL ZERO, ONE
173  parameter( zero = 0.0e+0, one = 1.0e+0 )
174 * ..
175 * .. Local Scalars ..
176  INTEGER J
177  REAL ANORM, BNORM, EPS, XNORM
178 * ..
179 * .. External Functions ..
180  LOGICAL LSAME
181  REAL SASUM, SLAMCH, SLANTB
182  EXTERNAL lsame, sasum, slamch, slantb
183 * ..
184 * .. External Subroutines ..
185  EXTERNAL saxpy, scopy, stbmv
186 * ..
187 * .. Intrinsic Functions ..
188  INTRINSIC max
189 * ..
190 * .. Executable Statements ..
191 *
192 * Quick exit if N = 0 or NRHS = 0
193 *
194  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
195  resid = zero
196  RETURN
197  END IF
198 *
199 * Compute the 1-norm of op(A).
200 *
201  IF( lsame( trans, 'N' ) ) THEN
202  anorm = slantb( '1', uplo, diag, n, kd, ab, ldab, work )
203  ELSE
204  anorm = slantb( 'I', uplo, diag, n, kd, ab, ldab, work )
205  END IF
206 *
207 * Exit with RESID = 1/EPS if ANORM = 0.
208 *
209  eps = slamch( 'Epsilon' )
210  IF( anorm.LE.zero ) THEN
211  resid = one / eps
212  RETURN
213  END IF
214 *
215 * Compute the maximum over the number of right hand sides of
216 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
217 *
218  resid = zero
219  DO 10 j = 1, nrhs
220  CALL scopy( n, x( 1, j ), 1, work, 1 )
221  CALL stbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
222  CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
223  bnorm = sasum( n, work, 1 )
224  xnorm = sasum( n, x( 1, j ), 1 )
225  IF( xnorm.LE.zero ) THEN
226  resid = one / eps
227  ELSE
228  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
229  END IF
230  10 CONTINUE
231 *
232  RETURN
233 *
234 * End of STBT02
235 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slantb.f:140
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine stbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBMV
Definition: stbmv.f:186
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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