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SUBROUTINE CSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, 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 UPLO
INTEGER INFO, N
REAL ANORM, RCOND
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX AP( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CSPCON estimates the reciprocal of the condition number (in the
* 1-norm) of a complex symmetric packed matrix A using the
* factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF.
*
* 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.
*
* AP (input) COMPLEX array, dimension (N*(N+1)/2)
* The block diagonal matrix D and the multipliers used to
* obtain the factor U or L as computed by CSPTRF, stored as a
* packed triangular matrix.
*
* IPIV (input) INTEGER array, dimension (N)
* Details of the interchanges and the block structure of D
* as determined by CSPTRF.
*
* ANORM (input) REAL
* The 1-norm of the original matrix A.
*
* RCOND (output) REAL
* 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) COMPLEX array, dimension (2*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 UPPER
INTEGER I, IP, KASE
REAL AINVNM
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLACON, CSPTRS, XERBLA
* ..
* .. 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( ANORM.LT.ZERO ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CSPCON', -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
*
IP = N*( N+1 ) / 2
DO 10 I = N, 1, -1
IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
$ RETURN
IP = IP - I
10 CONTINUE
ELSE
*
* Lower triangular storage: examine D from top to bottom.
*
IP = 1
DO 20 I = 1, N
IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
$ RETURN
IP = IP + N - I + 1
20 CONTINUE
END IF
*
* Estimate the 1-norm of the inverse.
*
KASE = 0
30 CONTINUE
CALL CLACON( N, WORK( N+1 ), WORK, AINVNM, KASE )
IF( KASE.NE.0 ) THEN
*
* Multiply by inv(L*D*L') or inv(U*D*U').
*
CALL CSPTRS( UPLO, N, 1, AP, 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 CSPCON
*
END
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