168 lines
4.8 KiB
Fortran
168 lines
4.8 KiB
Fortran
SUBROUTINE DPOTF2F( UPLO, N, A, LDA, INFO )
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*
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* -- LAPACK routine (version 3.0) --
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* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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* Courant Institute, Argonne National Lab, and Rice University
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* February 29, 1992
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * )
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* ..
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*
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* Purpose
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* =======
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*
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* DPOTF2 computes the Cholesky factorization of a real symmetric
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* positive definite matrix A.
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*
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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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*
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* This is the unblocked version of the algorithm, calling Level 2 BLAS.
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*
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* Arguments
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* =========
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*
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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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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* A (input/output) DOUBLE PRECISION 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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*
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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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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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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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* completed.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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INTEGER J
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DOUBLE PRECISION AJJ
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DDOT
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EXTERNAL LSAME, DDOT
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* ..
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* .. External Subroutines ..
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EXTERNAL DGEMV, DSCAL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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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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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DPOTF2', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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IF( UPPER ) THEN
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*
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* Compute the Cholesky factorization A = U'*U.
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*
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DO 10 J = 1, N
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*
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* Compute U(J,J) and test for non-positive-definiteness.
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*
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AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
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IF( AJJ.LE.ZERO ) THEN
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A( J, J ) = AJJ
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GO TO 30
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END IF
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AJJ = SQRT( AJJ )
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A( J, J ) = AJJ
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*
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* Compute elements J+1:N of row J.
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*
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IF( J.LT.N ) THEN
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CALL DGEMV( '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 DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
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END IF
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10 CONTINUE
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ELSE
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*
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* Compute the Cholesky factorization A = L*L'.
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*
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DO 20 J = 1, N
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*
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* Compute L(J,J) and test for non-positive-definiteness.
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*
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AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
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$ LDA )
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IF( AJJ.LE.ZERO ) THEN
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A( J, J ) = AJJ
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GO TO 30
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END IF
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AJJ = SQRT( AJJ )
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A( J, J ) = AJJ
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*
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* Compute elements J+1:N of column J.
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*
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IF( J.LT.N ) THEN
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CALL DGEMV( '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 DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
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END IF
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20 CONTINUE
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END IF
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GO TO 40
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*
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30 CONTINUE
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INFO = J
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*
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40 CONTINUE
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RETURN
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*
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* End of DPOTF2
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*
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END
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