SUBROUTINE SPOTF2( UPLO, N, A, LDA, INFO ) * * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SPOTF2 computes the Cholesky factorization of a real symmetric * positive definite matrix A. * * The factorization has the form * A = U' * U , if UPLO = 'U', or * A = L * L', if UPLO = 'L', * where U is an upper triangular matrix and L is lower triangular. * * This is the unblocked version of the algorithm, calling Level 2 BLAS. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * symmetric matrix A is stored. * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * A (input/output) 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'*U or A = L*L'. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order k is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J REAL AJJ * .. * .. External Functions .. LOGICAL LSAME, SISNAN REAL SDOT EXTERNAL LSAME, SDOT, SISNAN * .. * .. External Subroutines .. EXTERNAL SGEMV, SSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, 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 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SPOTF2', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * IF( UPPER ) THEN * * Compute the Cholesky factorization A = U'*U. * DO 10 J = 1, N * * Compute U(J,J) and test for non-positive-definiteness. * AJJ = A( J, J ) - SDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 ) IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN A( J, J ) = AJJ GO TO 30 END IF AJJ = SQRT( AJJ ) A( J, J ) = AJJ * * Compute elements J+1:N of row J. * IF( J.LT.N ) THEN CALL SGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ), \$ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA ) CALL SSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA ) END IF 10 CONTINUE ELSE * * Compute the Cholesky factorization A = L*L'. * DO 20 J = 1, N * * Compute L(J,J) and test for non-positive-definiteness. * AJJ = A( J, J ) - SDOT( J-1, A( J, 1 ), LDA, A( J, 1 ), \$ LDA ) IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN A( J, J ) = AJJ GO TO 30 END IF AJJ = SQRT( AJJ ) A( J, J ) = AJJ * * Compute elements J+1:N of column J. * IF( J.LT.N ) THEN CALL SGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ), \$ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 ) CALL SSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 ) END IF 20 CONTINUE END IF GO TO 40 * 30 CONTINUE INFO = J * 40 CONTINUE RETURN * * End of SPOTF2 * END