*> \brief \b SGBT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, * RESID ) * * .. Scalar Arguments .. * INTEGER KL, KU, LDA, LDAFAC, M, N * REAL RESID * .. * .. Array Arguments .. * INTEGER IPIV( * ) * REAL A( LDA, * ), AFAC( LDAFAC, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] KL *> \verbatim *> KL is INTEGER *> The number of subdiagonals within the band of A. KL >= 0. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is INTEGER *> The number of superdiagonals within the band of A. KU >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> The original matrix A in band storage, stored in rows 1 to *> KL+KU+1. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER. *> The leading dimension of the array A. LDA >= max(1,KL+KU+1). *> \endverbatim *> *> \param[in] AFAC *> \verbatim *> AFAC is 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. *> \endverbatim *> *> \param[in] LDAFAC *> \verbatim *> LDAFAC is INTEGER *> The leading dimension of the array AFAC. *> LDAFAC >= max(1,2*KL*KU+1). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (min(M,N)) *> The pivot indices from SGBTRF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (2*KL+KU+1) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is REAL *> norm(L*U - A) / ( N * norm(A) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, $ RESID ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER KL, KU, LDA, LDAFAC, M, N REAL RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) REAL A( LDA, * ), AFAC( LDAFAC, * ), WORK( * ) * .. * * ===================================================================== * * .. 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