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SUBROUTINE <a name="SPPCON.1"></a><a href="sppcon.f.html#SPPCON.1">SPPCON</a>( UPLO, N, AP, 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="SLACN2.7"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a> in place of <a name="SLACON.7"></a><a href="slacon.f.html#SLACON.1">SLACON</a>, 7 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, N
REAL ANORM, RCOND
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
REAL AP( * ), 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="SPPCON.22"></a><a href="sppcon.f.html#SPPCON.1">SPPCON</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 packed matrix using
</span><span class="comment">*</span><span class="comment"> the Cholesky factorization A = U**T*U or A = L*L**T computed by
</span><span class="comment">*</span><span class="comment"> <a name="SPPTRF.25"></a><a href="spptrf.f.html#SPPTRF.1">SPPTRF</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"> AP (input) REAL array, dimension (N*(N+1)/2)
</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, packed columnwise in a linear
</span><span class="comment">*</span><span class="comment"> array. The j-th column of U or L is stored in the array AP
</span><span class="comment">*</span><span class="comment"> as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ANORM (input) REAL
</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) REAL
</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) REAL 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> REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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
REAL 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.80"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
INTEGER ISAMAX
REAL <a name="SLAMCH.82"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
EXTERNAL <a name="LSAME.83"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, ISAMAX, <a name="SLAMCH.83"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SLACN2.86"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a>, <a name="SLATPS.86"></a><a href="slatps.f.html#SLATPS.1">SLATPS</a>, <a name="SRSCL.86"></a><a href="srscl.f.html#SRSCL.1">SRSCL</a>, <a name="XERBLA.86"></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
<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.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.97"></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( ANORM.LT.ZERO ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.105"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SPPCON.105"></a><a href="sppcon.f.html#SPPCON.1">SPPCON</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="SLAMCH.119"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</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 the inverse.
</span><span class="comment">*</span><span class="comment">
</span> KASE = 0
NORMIN = <span class="string">'N'</span>
10 CONTINUE
CALL <a name="SLACN2.126"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</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="SLATPS.132"></a><a href="slatps.f.html#SLATPS.1">SLATPS</a>( <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N,
$ AP, 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="SLATPS.138"></a><a href="slatps.f.html#SLATPS.1">SLATPS</a>( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N,
$ AP, 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="SLATPS.144"></a><a href="slatps.f.html#SLATPS.1">SLATPS</a>( <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N,
$ AP, 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="SLATPS.150"></a><a href="slatps.f.html#SLATPS.1">SLATPS</a>( <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N,
$ AP, 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 = ISAMAX( N, WORK, 1 )
IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 20
CALL <a name="SRSCL.161"></a><a href="srscl.f.html#SRSCL.1">SRSCL</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="SPPCON.174"></a><a href="sppcon.f.html#SPPCON.1">SPPCON</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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