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REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
$ LDAFB, IPIV, C, CAPPLY, INFO, WORK,
$ RWORK )
*
* -- LAPACK routine (version 3.2.1) --
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
* -- Jason Riedy of Univ. of California Berkeley. --
* -- April 2009 --
*
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley and NAG Ltd. --
*
IMPLICIT NONE
* ..
* .. Scalar Arguments ..
CHARACTER TRANS
LOGICAL CAPPLY
INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
REAL C( * ), RWORK( * )
* ..
*
* Purpose
* =======
*
* CLA_GBRCOND_C Computes the infinity norm condition number of
* op(A) * inv(diag(C)) where C is a REAL vector.
*
* Arguments
* =========
*
* TRANS (input) CHARACTER*1
* Specifies the form of the system of equations:
* = 'N': A * X = B (No transpose)
* = 'T': A**T * X = B (Transpose)
* = 'C': A**H * X = B (Conjugate Transpose = Transpose)
*
* N (input) INTEGER
* The number of linear equations, i.e., 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)
* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
* The j-th column of A is stored in the j-th column of the
* array AB as follows:
* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KL+KU+1.
*
* AFB (input) COMPLEX array, dimension (LDAFB,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.
*
* LDAFB (input) INTEGER
* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*
* IPIV (input) INTEGER array, dimension (N)
* The pivot indices from the factorization A = P*L*U
* as computed by CGBTRF; row i of the matrix was interchanged
* with row IPIV(i).
*
* C (input) REAL array, dimension (N)
* The vector C in the formula op(A) * inv(diag(C)).
*
* CAPPLY (input) LOGICAL
* If .TRUE. then access the vector C in the formula above.
*
* INFO (output) INTEGER
* = 0: Successful exit.
* i > 0: The ith argument is invalid.
*
* WORK (input) COMPLEX array, dimension (2*N).
* Workspace.
*
* RWORK (input) REAL array, dimension (N).
* Workspace.
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL NOTRANS
INTEGER KASE, I, J
REAL AINVNM, ANORM, TMP
COMPLEX ZDUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLACN2, CGBTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function Definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
CLA_GBRCOND_C = 0.0E+0
*
INFO = 0
NOTRANS = LSAME( TRANS, 'N' )
IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
$ LSAME( TRANS, 'C' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
INFO = -3
ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KL+KU+1 ) THEN
INFO = -6
ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLA_GBRCOND_C', -INFO )
RETURN
END IF
*
* Compute norm of op(A)*op2(C).
*
ANORM = 0.0E+0
KD = KU + 1
KE = KL + 1
IF ( NOTRANS ) THEN
DO I = 1, N
TMP = 0.0E+0
IF ( CAPPLY ) THEN
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KD+I-J, J ) ) / C( J )
END DO
ELSE
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KD+I-J, J ) )
END DO
END IF
RWORK( I ) = TMP
ANORM = MAX( ANORM, TMP )
END DO
ELSE
DO I = 1, N
TMP = 0.0E+0
IF ( CAPPLY ) THEN
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KE-I+J, I ) ) / C( J )
END DO
ELSE
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KE-I+J, I ) )
END DO
END IF
RWORK( I ) = TMP
ANORM = MAX( ANORM, TMP )
END DO
END IF
*
* Quick return if possible.
*
IF( N.EQ.0 ) THEN
CLA_GBRCOND_C = 1.0E+0
RETURN
ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
RETURN
END IF
*
* Estimate the norm of inv(op(A)).
*
AINVNM = 0.0E+0
*
KASE = 0
10 CONTINUE
CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.2 ) THEN
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * RWORK( I )
END DO
*
IF ( NOTRANS ) THEN
CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
$ IPIV, WORK, N, INFO )
ELSE
CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
$ LDAFB, IPIV, WORK, N, INFO )
ENDIF
*
* Multiply by inv(C).
*
IF ( CAPPLY ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
ELSE
*
* Multiply by inv(C**H).
*
IF ( CAPPLY ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
*
IF ( NOTRANS ) THEN
CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
$ LDAFB, IPIV, WORK, N, INFO )
ELSE
CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
$ IPIV, WORK, N, INFO )
END IF
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * RWORK( I )
END DO
END IF
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM .NE. 0.0E+0 )
$ CLA_GBRCOND_C = 1.0E+0 / AINVNM
*
RETURN
*
END
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