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SUBROUTINE DGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
$ WORK, IWORK, INFO ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. * * .. Scalar Arguments .. CHARACTER NORM INTEGER INFO, KL, KU, LDAB, N DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. INTEGER IPIV( * ), IWORK( * ) DOUBLE PRECISION AB( LDAB, * ), WORK( * ) * .. * * Purpose * ======= * * DGBCON estimates the reciprocal of the condition number of a real * general band matrix A, in either the 1-norm or the infinity-norm, * using the LU factorization computed by DGBTRF. * * An estimate is obtained for norm(inv(A)), and the reciprocal of the * condition number is computed as * RCOND = 1 / ( norm(A) * norm(inv(A)) ). * * Arguments * ========= * * NORM (input) CHARACTER*1 * Specifies whether the 1-norm condition number or the * infinity-norm condition number is required: * = '1' or 'O': 1-norm; * = 'I': Infinity-norm. * * N (input) INTEGER * The order 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. * * AB (input) DOUBLE PRECISION array, dimension (LDAB,N) * Details of the LU factorization of the band matrix A, as * computed by DGBTRF. 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. * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= 2*KL+KU+1. * * IPIV (input) INTEGER array, dimension (N) * The pivot indices; for 1 <= i <= N, row i of the matrix was * interchanged with row IPIV(i). * * ANORM (input) DOUBLE PRECISION * If NORM = '1' or 'O', the 1-norm of the original matrix A. * If NORM = 'I', the infinity-norm of the original matrix A. * * RCOND (output) DOUBLE PRECISION * The reciprocal of the condition number of the matrix A, * computed as RCOND = 1/(norm(A) * norm(inv(A))). * * WORK (workspace) DOUBLE PRECISION array, dimension (3*N) * * IWORK (workspace) INTEGER array, dimension (N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL LNOTI, ONENRM CHARACTER NORMIN INTEGER IX, J, JP, KASE, KASE1, KD, LM DOUBLE PRECISION AINVNM, SCALE, SMLNUM, T * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX DOUBLE PRECISION DDOT, DLAMCH EXTERNAL LSAME, IDAMAX, DDOT, DLAMCH * .. * .. External Subroutines .. EXTERNAL DAXPY, DLACN2, DLATBS, DRSCL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( KL.LT.0 ) THEN INFO = -3 ELSE IF( KU.LT.0 ) THEN INFO = -4 ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN INFO = -6 ELSE IF( ANORM.LT.ZERO ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGBCON', -INFO ) RETURN END IF * * Quick return if possible * RCOND = ZERO IF( N.EQ.0 ) THEN RCOND = ONE RETURN ELSE IF( ANORM.EQ.ZERO ) THEN RETURN END IF * SMLNUM = DLAMCH( 'Safe minimum' ) * * Estimate the norm of inv(A). * AINVNM = ZERO NORMIN = 'N' IF( ONENRM ) THEN KASE1 = 1 ELSE KASE1 = 2 END IF KD = KL + KU + 1 LNOTI = KL.GT.0 KASE = 0 10 CONTINUE CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.KASE1 ) THEN * * Multiply by inv(L). * IF( LNOTI ) THEN DO 20 J = 1, N - 1 LM = MIN( KL, N-J ) JP = IPIV( J ) T = WORK( JP ) IF( JP.NE.J ) THEN WORK( JP ) = WORK( J ) WORK( J ) = T END IF CALL DAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 ) 20 CONTINUE END IF * * Multiply by inv(U). * CALL DLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, $ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), $ INFO ) ELSE * * Multiply by inv(U**T). * CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, $ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), $ INFO ) * * Multiply by inv(L**T). * IF( LNOTI ) THEN DO 30 J = N - 1, 1, -1 LM = MIN( KL, N-J ) WORK( J ) = WORK( J ) - DDOT( LM, AB( KD+1, J ), 1, $ WORK( J+1 ), 1 ) JP = IPIV( J ) IF( JP.NE.J ) THEN T = WORK( JP ) WORK( JP ) = WORK( J ) WORK( J ) = T END IF 30 CONTINUE END IF END IF * * Divide X by 1/SCALE if doing so will not cause overflow. * NORMIN = 'Y' IF( SCALE.NE.ONE ) THEN IX = IDAMAX( N, WORK, 1 ) IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) $ GO TO 40 CALL DRSCL( N, SCALE, WORK, 1 ) END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) $ RCOND = ( ONE / AINVNM ) / ANORM * 40 CONTINUE RETURN * * End of DGBCON * END |