*> \brief \b SPPTRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SPPTRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SPPTRF( UPLO, N, AP, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, N * .. * .. Array Arguments .. * REAL AP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SPPTRF computes the Cholesky factorization of a real symmetric *> positive definite matrix A stored in packed format. *> *> The factorization has the form *> A = U**T * U, if UPLO = 'U', or *> A = L * L**T, if UPLO = 'L', *> where U is an upper triangular matrix and L is lower triangular. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is REAL array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the symmetric matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. *> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T, in the same *> storage format as A. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup realOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The packed storage scheme is illustrated by the following example *> when N = 4, UPLO = 'U': *> *> Two-dimensional storage of the symmetric matrix A: *> *> a11 a12 a13 a14 *> a22 a23 a24 *> a33 a34 (aij = aji) *> a44 *> *> Packed storage of the upper triangle of A: *> *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] *> \endverbatim *> * ===================================================================== SUBROUTINE SPPTRF( UPLO, N, AP, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N * .. * .. Array Arguments .. REAL AP( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, JC, JJ REAL AJJ * .. * .. External Functions .. LOGICAL LSAME REAL SDOT EXTERNAL LSAME, SDOT * .. * .. External Subroutines .. EXTERNAL SSCAL, SSPR, STPSV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. 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( 'SPPTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * IF( UPPER ) THEN * * Compute the Cholesky factorization A = U**T*U. * JJ = 0 DO 10 J = 1, N JC = JJ + 1 JJ = JJ + J * * Compute elements 1:J-1 of column J. * IF( J.GT.1 ) \$ CALL STPSV( 'Upper', 'Transpose', 'Non-unit', J-1, AP, \$ AP( JC ), 1 ) * * Compute U(J,J) and test for non-positive-definiteness. * AJJ = AP( JJ ) - SDOT( J-1, AP( JC ), 1, AP( JC ), 1 ) IF( AJJ.LE.ZERO ) THEN AP( JJ ) = AJJ GO TO 30 END IF AP( JJ ) = SQRT( AJJ ) 10 CONTINUE ELSE * * Compute the Cholesky factorization A = L*L**T. * JJ = 1 DO 20 J = 1, N * * Compute L(J,J) and test for non-positive-definiteness. * AJJ = AP( JJ ) IF( AJJ.LE.ZERO ) THEN AP( JJ ) = AJJ GO TO 30 END IF AJJ = SQRT( AJJ ) AP( JJ ) = AJJ * * Compute elements J+1:N of column J and update the trailing * submatrix. * IF( J.LT.N ) THEN CALL SSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 ) CALL SSPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1, \$ AP( JJ+N-J+1 ) ) JJ = JJ + N - J + 1 END IF 20 CONTINUE END IF GO TO 40 * 30 CONTINUE INFO = J * 40 CONTINUE RETURN * * End of SPPTRF * END