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SUBROUTINE <a name="DPOCON.1"></a><a href="dpocon.f.html#DPOCON.1">DPOCON</a>( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
$ INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Modified to call <a name="DLACN2.8"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a> in place of <a name="DLACON.8"></a><a href="dlacon.f.html#DLACON.1">DLACON</a>, 5 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION ANORM, RCOND
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DPOCON.23"></a><a href="dpocon.f.html#DPOCON.1">DPOCON</a> estimates the reciprocal of the condition number (in the
</span><span class="comment">*</span><span class="comment"> 1-norm) of a real symmetric positive definite matrix using the
</span><span class="comment">*</span><span class="comment"> Cholesky factorization A = U**T*U or A = L*L**T computed by <a name="DPOTRF.25"></a><a href="dpotrf.f.html#DPOTRF.1">DPOTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> An estimate is obtained for norm(inv(A)), and the reciprocal of the
</span><span class="comment">*</span><span class="comment"> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input) DOUBLE PRECISION array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> The triangular factor U or L from the Cholesky factorization
</span><span class="comment">*</span><span class="comment"> A = U**T*U or A = L*L**T, as computed by <a name="DPOTRF.42"></a><a href="dpotrf.f.html#DPOTRF.1">DPOTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ANORM (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> The 1-norm (or infinity-norm) of the symmetric matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RCOND (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> The reciprocal of the condition number of the matrix A,
</span><span class="comment">*</span><span class="comment"> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
</span><span class="comment">*</span><span class="comment"> estimate of the 1-norm of inv(A) computed in this routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UPPER
CHARACTER NORMIN
INTEGER IX, KASE
DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> INTEGER ISAVE( 3 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.79"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
INTEGER IDAMAX
DOUBLE PRECISION <a name="DLAMCH.81"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
EXTERNAL <a name="LSAME.82"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, IDAMAX, <a name="DLAMCH.82"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="DLACN2.85"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a>, <a name="DLATRS.85"></a><a href="dlatrs.f.html#DLATRS.1">DLATRS</a>, <a name="DRSCL.85"></a><a href="drscl.f.html#DRSCL.1">DRSCL</a>, <a name="XERBLA.85"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, MAX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
UPPER = <a name="LSAME.95"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) 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 = -5
END IF
IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.106"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DPOCON.106"></a><a href="dpocon.f.html#DPOCON.1">DPOCON</a>'</span>, -INFO )
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> RCOND = ZERO
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
ELSE IF( ANORM.EQ.ZERO ) THEN
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span> SMLNUM = <a name="DLAMCH.120"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'Safe minimum'</span> )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Estimate the 1-norm of inv(A).
</span><span class="comment">*</span><span class="comment">
</span> KASE = 0
NORMIN = <span class="string">'N'</span>
10 CONTINUE
CALL <a name="DLACN2.127"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a>( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Multiply by inv(U').
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="DLATRS.133"></a><a href="dlatrs.f.html#DLATRS.1">DLATRS</a>( <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N, A,
$ LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
NORMIN = <span class="string">'Y'</span>
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Multiply by inv(U).
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="DLATRS.139"></a><a href="dlatrs.f.html#DLATRS.1">DLATRS</a>( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N,
$ A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Multiply by inv(L).
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="DLATRS.145"></a><a href="dlatrs.f.html#DLATRS.1">DLATRS</a>( <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N,
$ A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
NORMIN = <span class="string">'Y'</span>
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Multiply by inv(L').
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="DLATRS.151"></a><a href="dlatrs.f.html#DLATRS.1">DLATRS</a>( <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N, A,
$ LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Multiply by 1/SCALE if doing so will not cause overflow.
</span><span class="comment">*</span><span class="comment">
</span> SCALE = SCALEL*SCALEU
IF( SCALE.NE.ONE ) THEN
IX = IDAMAX( N, WORK, 1 )
IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 20
CALL <a name="DRSCL.162"></a><a href="drscl.f.html#DRSCL.1">DRSCL</a>( N, SCALE, WORK, 1 )
END IF
GO TO 10
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the estimate of the reciprocal condition number.
</span><span class="comment">*</span><span class="comment">
</span> IF( AINVNM.NE.ZERO )
$ RCOND = ( ONE / AINVNM ) / ANORM
<span class="comment">*</span><span class="comment">
</span> 20 CONTINUE
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="DPOCON.175"></a><a href="dpocon.f.html#DPOCON.1">DPOCON</a>
</span><span class="comment">*</span><span class="comment">
</span> END
</pre>
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