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SUBROUTINE SPOTF2( UPLO, N, A, LDA, INFO )
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* .. Scalar Arguments ..
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* .. Array Arguments ..
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* SPOTF2 computes the Cholesky factorization of a real symmetric
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* positive definite matrix A.
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* The factorization has the form
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* A = U' * U , if UPLO = 'U', or
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* A = L * L', if UPLO = 'L',
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* where U is an upper triangular matrix and L is lower triangular.
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* This is the unblocked version of the algorithm, calling Level 2 BLAS.
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* UPLO (input) CHARACTER*1
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* Specifies whether the upper or lower triangular part of the
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* symmetric matrix A is stored.
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* = 'U': Upper triangular
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* = 'L': Lower triangular
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* The order of the matrix A. N >= 0.
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* A (input/output) REAL array, dimension (LDA,N)
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* On entry, the symmetric matrix A. If UPLO = 'U', the leading
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* n by n upper triangular part of A contains the upper
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* triangular part of the matrix A, and the strictly lower
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* triangular part of A is not referenced. If UPLO = 'L', the
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* leading n by n lower triangular part of A contains the lower
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* triangular part of the matrix A, and the strictly upper
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* triangular part of A is not referenced.
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* On exit, if INFO = 0, the factor U or L from the Cholesky
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* factorization A = U'*U or A = L*L'.
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* The leading dimension of the array A. LDA >= max(1,N).
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -k, the k-th argument had an illegal value
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* > 0: if INFO = k, the leading minor of order k is not
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* positive definite, and the factorization could not be
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* =====================================================================
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* .. External Functions ..
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* .. External Subroutines ..
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EXTERNAL SGEMV, SSCAL, XERBLA
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* .. Intrinsic Functions ..
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* .. Executable Statements ..
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* Test the input parameters.
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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ELSE IF( N.LT.0 ) THEN
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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CALL XERBLA( 'SPOTF2', -INFO )
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* Quick return if possible
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* Compute the Cholesky factorization A = U'*U.
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* Compute U(J,J) and test for non-positive-definiteness.
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AJJ = A( J, J ) - SDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
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IF( AJJ.LE.ZERO ) THEN
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* Compute elements J+1:N of row J.
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CALL SGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
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$ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
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CALL SSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
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* Compute the Cholesky factorization A = L*L'.
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* Compute L(J,J) and test for non-positive-definiteness.
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AJJ = A( J, J ) - SDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
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IF( AJJ.LE.ZERO ) THEN
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* Compute elements J+1:N of column J.
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CALL SGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
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$ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
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CALL SSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
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libcruft/lapack/spotf2.f
