*> \brief \b SPOTRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SPOTRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * REAL A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SPOTRF computes the Cholesky factorization of a real symmetric *> positive definite matrix A. *> *> 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. *> *> This is the block version of the algorithm, calling Level 3 BLAS. *> \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] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \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 realPOcomputational * * ===================================================================== SUBROUTINE SPOTRF( UPLO, N, A, LDA, 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, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, JB, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL SGEMM, SPOTRF2, SSYRK, STRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. 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( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SPOTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'SPOTRF', UPLO, N, -1, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code. * CALL SPOTRF2( UPLO, N, A, LDA, INFO ) ELSE * * Use blocked code. * IF( UPPER ) THEN * * Compute the Cholesky factorization A = U**T*U. * DO 10 J = 1, N, NB * * Update and factorize the current diagonal block and test * for non-positive-definiteness. * JB = MIN( NB, N-J+1 ) CALL SSYRK( 'Upper', 'Transpose', JB, J-1, -ONE, \$ A( 1, J ), LDA, ONE, A( J, J ), LDA ) CALL SPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 30 IF( J+JB.LE.N ) THEN * * Compute the current block row. * CALL SGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1, \$ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ), \$ LDA, ONE, A( J, J+JB ), LDA ) CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', \$ JB, N-J-JB+1, ONE, A( J, J ), LDA, \$ A( J, J+JB ), LDA ) END IF 10 CONTINUE * ELSE * * Compute the Cholesky factorization A = L*L**T. * DO 20 J = 1, N, NB * * Update and factorize the current diagonal block and test * for non-positive-definiteness. * JB = MIN( NB, N-J+1 ) CALL SSYRK( 'Lower', 'No transpose', JB, J-1, -ONE, \$ A( J, 1 ), LDA, ONE, A( J, J ), LDA ) CALL SPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 30 IF( J+JB.LE.N ) THEN * * Compute the current block column. * CALL SGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, \$ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), \$ LDA, ONE, A( J+JB, J ), LDA ) CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', \$ N-J-JB+1, JB, ONE, A( J, J ), LDA, \$ A( J+JB, J ), LDA ) END IF 20 CONTINUE END IF END IF GO TO 40 * 30 CONTINUE INFO = INFO + J - 1 * 40 CONTINUE RETURN * * End of SPOTRF * END