235 lines
6.8 KiB
FortranFixed
235 lines
6.8 KiB
FortranFixed
SUBROUTINE CGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
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$ WORK, RWORK, INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH.
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*
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* .. Scalar Arguments ..
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CHARACTER NORM
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INTEGER INFO, KL, KU, LDAB, N
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REAL ANORM, RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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REAL RWORK( * )
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COMPLEX AB( LDAB, * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CGBCON estimates the reciprocal of the condition number of a complex
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* general band matrix A, in either the 1-norm or the infinity-norm,
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* using the LU factorization computed by CGBTRF.
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*
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* An estimate is obtained for norm(inv(A)), and the reciprocal of the
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* condition number is computed as
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* RCOND = 1 / ( norm(A) * norm(inv(A)) ).
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*
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* Arguments
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* =========
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*
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* NORM (input) CHARACTER*1
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* Specifies whether the 1-norm condition number or the
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* infinity-norm condition number is required:
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* = '1' or 'O': 1-norm;
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* = 'I': Infinity-norm.
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* KL (input) INTEGER
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* The number of subdiagonals within the band of A. KL >= 0.
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*
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* KU (input) INTEGER
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* The number of superdiagonals within the band of A. KU >= 0.
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*
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* AB (input) COMPLEX array, dimension (LDAB,N)
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* Details of the LU factorization of the band matrix A, as
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* computed by CGBTRF. U is stored as an upper triangular band
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* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
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* the multipliers used during the factorization are stored in
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* rows KL+KU+2 to 2*KL+KU+1.
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*
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* LDAB (input) INTEGER
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* The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
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*
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* IPIV (input) INTEGER array, dimension (N)
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* The pivot indices; for 1 <= i <= N, row i of the matrix was
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* interchanged with row IPIV(i).
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*
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* ANORM (input) REAL
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* If NORM = '1' or 'O', the 1-norm of the original matrix A.
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* If NORM = 'I', the infinity-norm of the original matrix A.
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*
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* RCOND (output) REAL
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* The reciprocal of the condition number of the matrix A,
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* computed as RCOND = 1/(norm(A) * norm(inv(A))).
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*
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* WORK (workspace) COMPLEX array, dimension (2*N)
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*
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* RWORK (workspace) REAL array, dimension (N)
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LNOTI, ONENRM
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CHARACTER NORMIN
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INTEGER IX, J, JP, KASE, KASE1, KD, LM
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REAL AINVNM, SCALE, SMLNUM
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COMPLEX T, ZDUM
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* ..
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* .. Local Arrays ..
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INTEGER ISAVE( 3 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ICAMAX
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REAL SLAMCH
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COMPLEX CDOTC
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EXTERNAL LSAME, ICAMAX, SLAMCH, CDOTC
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* ..
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* .. External Subroutines ..
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EXTERNAL CAXPY, CLACN2, CLATBS, CSRSCL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, AIMAG, MIN, REAL
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* ..
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* .. Statement Functions ..
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REAL CABS1
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* ..
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* .. Statement Function definitions ..
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CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
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IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( KL.LT.0 ) THEN
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INFO = -3
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ELSE IF( KU.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
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INFO = -6
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ELSE IF( ANORM.LT.ZERO ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CGBCON', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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RCOND = ZERO
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IF( N.EQ.0 ) THEN
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RCOND = ONE
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RETURN
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ELSE IF( ANORM.EQ.ZERO ) THEN
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RETURN
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END IF
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*
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SMLNUM = SLAMCH( 'Safe minimum' )
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*
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* Estimate the norm of inv(A).
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*
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AINVNM = ZERO
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NORMIN = 'N'
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IF( ONENRM ) THEN
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KASE1 = 1
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ELSE
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KASE1 = 2
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END IF
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KD = KL + KU + 1
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LNOTI = KL.GT.0
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KASE = 0
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10 CONTINUE
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CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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IF( KASE.EQ.KASE1 ) THEN
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*
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* Multiply by inv(L).
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*
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IF( LNOTI ) THEN
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DO 20 J = 1, N - 1
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LM = MIN( KL, N-J )
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JP = IPIV( J )
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T = WORK( JP )
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IF( JP.NE.J ) THEN
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WORK( JP ) = WORK( J )
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WORK( J ) = T
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END IF
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CALL CAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
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20 CONTINUE
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END IF
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*
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* Multiply by inv(U).
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*
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CALL CLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
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$ KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
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ELSE
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*
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* Multiply by inv(U').
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*
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CALL CLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
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$ NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
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$ INFO )
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*
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* Multiply by inv(L').
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*
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IF( LNOTI ) THEN
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DO 30 J = N - 1, 1, -1
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LM = MIN( KL, N-J )
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WORK( J ) = WORK( J ) - CDOTC( LM, AB( KD+1, J ), 1,
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$ WORK( J+1 ), 1 )
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JP = IPIV( J )
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IF( JP.NE.J ) THEN
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T = WORK( JP )
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WORK( JP ) = WORK( J )
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WORK( J ) = T
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END IF
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30 CONTINUE
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END IF
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END IF
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*
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* Divide X by 1/SCALE if doing so will not cause overflow.
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*
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NORMIN = 'Y'
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IF( SCALE.NE.ONE ) THEN
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IX = ICAMAX( N, WORK, 1 )
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IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
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$ GO TO 40
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CALL CSRSCL( N, SCALE, WORK, 1 )
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END IF
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GO TO 10
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END IF
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*
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* Compute the estimate of the reciprocal condition number.
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*
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IF( AINVNM.NE.ZERO )
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$ RCOND = ( ONE / AINVNM ) / ANORM
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*
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40 CONTINUE
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RETURN
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*
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* End of CGBCON
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*
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END
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