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SUBROUTINE CTRCON( NORM, UPLO, DIAG, N, A, LDA, 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
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, LDA, N
REAL RCOND
* ..
* .. Array Arguments ..
REAL RWORK( * )
COMPLEX A( LDA, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CTRCON estimates the reciprocal of the condition number of a
* triangular matrix A, in either the 1-norm or the infinity-norm.
*
* The norm of A is computed and an estimate is obtained for
* norm(inv(A)), then 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.
*
* UPLO (input) CHARACTER*1
* = 'U': A is upper triangular;
* = 'L': A is lower triangular.
*
* DIAG (input) CHARACTER*1
* = 'N': A is non-unit triangular;
* = 'U': A is unit triangular.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input) COMPLEX array, dimension (LDA,N)
* The triangular matrix A. If UPLO = 'U', the leading N-by-N
* upper triangular part of the array A contains the upper
* triangular matrix, and the strictly lower triangular part of
* A is not referenced. If UPLO = 'L', the leading N-by-N lower
* triangular part of the array A contains the lower triangular
* matrix, and the strictly upper triangular part of A is not
* referenced. If DIAG = 'U', the diagonal elements of A are
* also not referenced and are assumed to be 1.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* 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 NOUNIT, ONENRM, UPPER
CHARACTER NORMIN
INTEGER IX, KASE, KASE1
REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
COMPLEX ZDUM
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICAMAX
REAL CLANTR, SLAMCH
EXTERNAL LSAME, ICAMAX, CLANTR, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CLACON, CLATRS, CSRSCL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, AIMAG, MAX, REAL
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
NOUNIT = LSAME( DIAG, 'N' )
*
IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
INFO = -1
ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTRCON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
END IF
*
RCOND = ZERO
SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) )
*
* Compute the norm of the triangular matrix A.
*
ANORM = CLANTR( NORM, UPLO, DIAG, N, N, A, LDA, RWORK )
*
* Continue only if ANORM > 0.
*
IF( ANORM.GT.ZERO ) THEN
*
* Estimate the norm of the inverse of A.
*
AINVNM = ZERO
NORMIN = 'N'
IF( ONENRM ) THEN
KASE1 = 1
ELSE
KASE1 = 2
END IF
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(A).
*
CALL CLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
$ LDA, WORK, SCALE, RWORK, INFO )
ELSE
*
* Multiply by inv(A').
*
CALL CLATRS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
$ N, A, LDA, WORK, SCALE, RWORK, INFO )
END IF
NORMIN = 'Y'
*
* Multiply by 1/SCALE if doing so will not cause overflow.
*
IF( SCALE.NE.ONE ) THEN
IX = ICAMAX( N, WORK, 1 )
XNORM = CABS1( WORK( IX ) )
IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 20
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 / ANORM ) / AINVNM
END IF
*
20 CONTINUE
RETURN
*
* End of CTRCON
*
END
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