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SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
$ IWORK, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION ANORM, RCOND
* ..
* .. Array Arguments ..
INTEGER IPIV( * ), IWORK( * )
DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DSYCON estimates the reciprocal of the condition number (in the
* 1-norm) of a real symmetric matrix A using the factorization
* A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
*
* An estimate is obtained for norm(inv(A)), and the reciprocal of the
* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the details of the factorization are stored
* as an upper or lower triangular matrix.
* = 'U': Upper triangular, form is A = U*D*U**T;
* = 'L': Lower triangular, form is A = L*D*L**T.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,N)
* The block diagonal matrix D and the multipliers used to
* obtain the factor U or L as computed by DSYTRF.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* IPIV (input) INTEGER array, dimension (N)
* Details of the interchanges and the block structure of D
* as determined by DSYTRF.
*
* ANORM (input) DOUBLE PRECISION
* The 1-norm of the original matrix A.
*
* RCOND (output) DOUBLE PRECISION
* The reciprocal of the condition number of the matrix A,
* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
* estimate of the 1-norm of inv(A) computed in this routine.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (2*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 UPPER
INTEGER I, KASE
DOUBLE PRECISION AINVNM
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DLACON, DSYTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( ANORM.LT.ZERO ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSYCON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
RCOND = ZERO
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
ELSE IF( ANORM.LE.ZERO ) THEN
RETURN
END IF
*
* Check that the diagonal matrix D is nonsingular.
*
IF( UPPER ) THEN
*
* Upper triangular storage: examine D from bottom to top
*
DO 10 I = N, 1, -1
IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
$ RETURN
10 CONTINUE
ELSE
*
* Lower triangular storage: examine D from top to bottom.
*
DO 20 I = 1, N
IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
$ RETURN
20 CONTINUE
END IF
*
* Estimate the 1-norm of the inverse.
*
KASE = 0
30 CONTINUE
CALL DLACON( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE )
IF( KASE.NE.0 ) THEN
*
* Multiply by inv(L*D*L') or inv(U*D*U').
*
CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
GO TO 30
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM.NE.ZERO )
$ RCOND = ( ONE / AINVNM ) / ANORM
*
RETURN
*
* End of DSYCON
*
END
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