dpotrff.f

SUBROUTINEDPOTRFF( UPLO, N, A, LDA, INFO )
*
* -- LAPACK routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * )
* ..
*
* Purpose
* =======
*
* DPOTRF 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.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) DOUBLE PRECISION 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.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* INFO (output) 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.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE =1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, JB, NB
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DPOTF2, DSYRK, DTRSM, 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
ELSEIF( N.LT.0 ) THEN
 INFO =-2
ELSEIF( LDA.LT.MAX( 1, N ) ) THEN
 INFO =-4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DPOTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
 $ RETURN
*
* Determine the block size for this environment.
*
 NB =224

IF( NB.LE.1.OR. NB.GE.N ) THEN
*
* Use unblocked code.
*
CALL DPOTF2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code.
*
IF( UPPER ) THEN
*
* Compute the Cholesky factorization A = U'*U.
*
DO10 J =1, N, NB
*
* Update and factorize the current diagonal block and test
* for non-positive-definiteness.
*
 JB =MIN( NB, N-J+1 )
CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
 $ A( 1, J ), LDA, ONE, A( J, J ), LDA )
CALL DPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
 $ GO TO30
IF( J+JB.LE.N ) THEN
*
* Compute the current block row.
*
CALL DGEMM( '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 DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
 $ JB, N-J-JB+1, ONE, A( J, J ), LDA,
 $ A( J, J+JB ), LDA )
END IF
10CONTINUE
*
ELSE
*
* Compute the Cholesky factorization A = L*L'.
*
DO20 J =1, N, NB
*
* Update and factorize the current diagonal block and test
* for non-positive-definiteness.
*
 JB =MIN( NB, N-J+1 )
CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
 $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
CALL DPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
 $ GO TO30
IF( J+JB.LE.N ) THEN
*
* Compute the current block column.
*
CALL DGEMM( '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 DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
 $ N-J-JB+1, JB, ONE, A( J, J ), LDA,
 $ A( J+JB, J ), LDA )
END IF
20CONTINUE
END IF
END IF
GO TO40
*
30CONTINUE
 INFO = INFO + J -1
*
40CONTINUE
RETURN
*
* End of DPOTRF
*
END