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SUBROUTINE SPPTRI( UPLO, N, AP, 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, N
* ..
* .. Array Arguments ..
REAL AP( * )
* ..
*
* Purpose
* =======
*
* SPPTRI computes the inverse of a real symmetric positive definite
* matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
* computed by SPPTRF.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangular factor is stored in AP;
* = 'L': Lower triangular factor is stored in AP.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* AP (input/output) REAL array, dimension (N*(N+1)/2)
* On entry, the triangular factor U or L from the Cholesky
* factorization A = U**T*U or A = L*L**T, packed columnwise as
* 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.
*
* On exit, the upper or lower triangle of the (symmetric)
* inverse of A, overwriting the input factor U or L.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, the (i,i) element of the factor U or L is
* zero, and the inverse could not be computed.
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, JC, JJ, JJN
REAL AJJ
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SDOT
EXTERNAL LSAME, SDOT
* ..
* .. External Subroutines ..
EXTERNAL SSCAL, SSPR, STPMV, STPTRI, 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
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SPPTRI', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Invert the triangular Cholesky factor U or L.
*
CALL STPTRI( UPLO, 'Non-unit', N, AP, INFO )
IF( INFO.GT.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Compute the product inv(U) * inv(U)'.
*
JJ = 0
DO 10 J = 1, N
JC = JJ + 1
JJ = JJ + J
IF( J.GT.1 )
$ CALL SSPR( 'Upper', J-1, ONE, AP( JC ), 1, AP )
AJJ = AP( JJ )
CALL SSCAL( J, AJJ, AP( JC ), 1 )
10 CONTINUE
*
ELSE
*
* Compute the product inv(L)' * inv(L).
*
JJ = 1
DO 20 J = 1, N
JJN = JJ + N - J + 1
AP( JJ ) = SDOT( N-J+1, AP( JJ ), 1, AP( JJ ), 1 )
IF( J.LT.N )
$ CALL STPMV( 'Lower', 'Transpose', 'Non-unit', N-J,
$ AP( JJN ), AP( JJ+1 ), 1 )
JJ = JJN
20 CONTINUE
END IF
*
RETURN
*
* End of SPPTRI
*
END
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