SUBROUTINE SGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
$ RESID )
*
* -- LAPACK test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER KL, KU, LDA, LDAFAC, M, N
REAL RESID
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* SGBT01 reconstructs a band matrix A from its L*U factorization and
* computes the residual:
* norm(L*U - A) / ( N * norm(A) * EPS ),
* where EPS is the machine epsilon.
*
* The expression L*U - A is computed one column at a time, so A and
* AFAC are not modified.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= 0.
*
* KL (input) INTEGER
* The number of subdiagonals within the band of A. KL >= 0.
*
* KU (input) INTEGER
* The number of superdiagonals within the band of A. KU >= 0.
*
* A (input/output) REAL array, dimension (LDA,N)
* The original matrix A in band storage, stored in rows 1 to
* KL+KU+1.
*
* LDA (input) INTEGER.
* The leading dimension of the array A. LDA >= max(1,KL+KU+1).
*
* AFAC (input) REAL array, dimension (LDAFAC,N)
* The factored form of the matrix A. AFAC contains the banded
* factors L and U from the L*U factorization, as computed by
* SGBTRF. U is stored as an upper triangular band matrix with
* KL+KU superdiagonals in rows 1 to KL+KU+1, and the
* multipliers used during the factorization are stored in rows
* KL+KU+2 to 2*KL+KU+1. See SGBTRF for further details.
*
* LDAFAC (input) INTEGER
* The leading dimension of the array AFAC.
* LDAFAC >= max(1,2*KL*KU+1).
*
* IPIV (input) INTEGER array, dimension (min(M,N))
* The pivot indices from SGBTRF.
*
* WORK (workspace) REAL array, dimension (2*KL+KU+1)
*
* RESID (output) REAL
* norm(L*U - A) / ( N * norm(A) * EPS )
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, I1, I2, IL, IP, IW, J, JL, JU, JUA, KD, LENJ
REAL ANORM, EPS, T
* ..
* .. External Functions ..
REAL SASUM, SLAMCH
EXTERNAL SASUM, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL SAXPY, SCOPY
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
* Quick exit if M = 0 or N = 0.
*
RESID = ZERO
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* Determine EPS and the norm of A.
*
EPS = SLAMCH( 'Epsilon' )
KD = KU + 1
ANORM = ZERO
DO 10 J = 1, N
I1 = MAX( KD+1-J, 1 )
I2 = MIN( KD+M-J, KL+KD )
IF( I2.GE.I1 )
$ ANORM = MAX( ANORM, SASUM( I2-I1+1, A( I1, J ), 1 ) )
10 CONTINUE
*
* Compute one column at a time of L*U - A.
*
KD = KL + KU + 1
DO 40 J = 1, N
*
* Copy the J-th column of U to WORK.
*
JU = MIN( KL+KU, J-1 )
JL = MIN( KL, M-J )
LENJ = MIN( M, J ) - J + JU + 1
IF( LENJ.GT.0 ) THEN
CALL SCOPY( LENJ, AFAC( KD-JU, J ), 1, WORK, 1 )
DO 20 I = LENJ + 1, JU + JL + 1
WORK( I ) = ZERO
20 CONTINUE
*
* Multiply by the unit lower triangular matrix L. Note that L
* is stored as a product of transformations and permutations.
*
DO 30 I = MIN( M-1, J ), J - JU, -1
IL = MIN( KL, M-I )
IF( IL.GT.0 ) THEN
IW = I - J + JU + 1
T = WORK( IW )
CALL SAXPY( IL, T, AFAC( KD+1, I ), 1, WORK( IW+1 ),
$ 1 )
IP = IPIV( I )
IF( I.NE.IP ) THEN
IP = IP - J + JU + 1
WORK( IW ) = WORK( IP )
WORK( IP ) = T
END IF
END IF
30 CONTINUE
*
* Subtract the corresponding column of A.
*
JUA = MIN( JU, KU )
IF( JUA+JL+1.GT.0 )
$ CALL SAXPY( JUA+JL+1, -ONE, A( KU+1-JUA, J ), 1,
$ WORK( JU+1-JUA ), 1 )
*
* Compute the 1-norm of the column.
*
RESID = MAX( RESID, SASUM( JU+JL+1, WORK, 1 ) )
END IF
40 CONTINUE
*
* Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
IF( ANORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
END IF
*
RETURN
*
* End of SGBT01
*
END