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SUBROUTINE CGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
$ WORK, RWORK, INFO )
*
* -- LAPACK routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER NORM
INTEGER INFO, KL, KU, LDAB, N
REAL ANORM, RCOND
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL RWORK( * )
COMPLEX AB( LDAB, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CGBCON estimates the reciprocal of the condition number of a complex
* general band matrix A, in either the 1-norm or the infinity-norm,
* using the LU factorization computed by CGBTRF.
*
* 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) COMPLEX array, dimension (LDAB,N)
* Details of the LU factorization of the band matrix A, as
* computed by CGBTRF. 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) REAL
* 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) REAL
* The reciprocal of the condition number of the matrix A,
* computed as RCOND = 1/(norm(A) * norm(inv(A))).
*
* WORK (workspace) COMPLEX array, dimension (2*N)
*
* RWORK (workspace) REAL array, dimension (N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL LNOTI, ONENRM
CHARACTER NORMIN
INTEGER IX, J, JP, KASE, KASE1, KD, LM
REAL AINVNM, SCALE, SMLNUM
COMPLEX T, ZDUM
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICAMAX
REAL SLAMCH
COMPLEX CDOTC
EXTERNAL LSAME, ICAMAX, SLAMCH, CDOTC
* ..
* .. External Subroutines ..
EXTERNAL CAXPY, CLACON, CLATBS, CSRSCL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, AIMAG, MIN, REAL
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. 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( 'CGBCON', -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 = SLAMCH( '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 CLACON( N, WORK( N+1 ), WORK, AINVNM, KASE )
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 CAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
20 CONTINUE
END IF
*
* Multiply by inv(U).
*
CALL CLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
$ KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
ELSE
*
* Multiply by inv(U').
*
CALL CLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
$ NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
$ INFO )
*
* Multiply by inv(L').
*
IF( LNOTI ) THEN
DO 30 J = N - 1, 1, -1
LM = MIN( KL, N-J )
WORK( J ) = WORK( J ) - CDOTC( 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 = ICAMAX( N, WORK, 1 )
IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 40
CALL CSRSCL( 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 CGBCON
*
END
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