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SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
*
* -- LAPACK routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, N
DOUBLE PRECISION ANORM, RCOND
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 AP( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* ZPPCON estimates the reciprocal of the condition number (in the
* 1-norm) of a complex Hermitian positive definite packed matrix using
* the Cholesky factorization A = U**H*U or A = L*L**H computed by
* ZPPTRF.
*
* 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
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
* The triangular factor U or L from the Cholesky factorization
* A = U**H*U or A = L*L**H, packed columnwise in a linear
* array. The j-th column of U or L is stored in the array AP
* as follows:
* if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
*
* ANORM (input) DOUBLE PRECISION
* The 1-norm (or infinity-norm) of the Hermitian 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) COMPLEX*16 array, dimension (2*N)
*
* RWORK (workspace) DOUBLE PRECISION 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
CHARACTER NORMIN
INTEGER IX, KASE
DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
COMPLEX*16 ZDUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IZAMAX
DOUBLE PRECISION DLAMCH
EXTERNAL LSAME, IZAMAX, DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATPS
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DIMAG
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
* ..
* .. 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 = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZPPCON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
RCOND = ZERO
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
ELSE IF( ANORM.EQ.ZERO ) THEN
RETURN
END IF
*
SMLNUM = DLAMCH( 'Safe minimum' )
*
* Estimate the 1-norm of the inverse.
*
KASE = 0
NORMIN = 'N'
10 CONTINUE
CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( UPPER ) THEN
*
* Multiply by inv(U').
*
CALL ZLATPS( 'Upper', 'Conjugate transpose', 'Non-unit',
$ NORMIN, N, AP, WORK, SCALEL, RWORK, INFO )
NORMIN = 'Y'
*
* Multiply by inv(U).
*
CALL ZLATPS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
$ AP, WORK, SCALEU, RWORK, INFO )
ELSE
*
* Multiply by inv(L).
*
CALL ZLATPS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
$ AP, WORK, SCALEL, RWORK, INFO )
NORMIN = 'Y'
*
* Multiply by inv(L').
*
CALL ZLATPS( 'Lower', 'Conjugate transpose', 'Non-unit',
$ NORMIN, N, AP, WORK, SCALEU, RWORK, INFO )
END IF
*
* Multiply by 1/SCALE if doing so will not cause overflow.
*
SCALE = SCALEL*SCALEU
IF( SCALE.NE.ONE ) THEN
IX = IZAMAX( N, WORK, 1 )
IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 20
CALL ZDRSCL( 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 / AINVNM ) / ANORM
*
20 CONTINUE
RETURN
*
* End of ZPPCON
*
END
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