julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
185 lines
5.6 KiB
FortranFixed
185 lines
5.6 KiB
FortranFixed
SUBROUTINE DPOTRF( 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 ..
|
|
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
|
|
INTEGER ILAENV
|
|
EXTERNAL LSAME, ILAENV
|
|
* ..
|
|
* .. 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
|
|
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( 'DPOTRF', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
* Determine the block size for this environment.
|
|
*
|
|
NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
|
|
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.
|
|
*
|
|
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 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 TO 30
|
|
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
|
|
10 CONTINUE
|
|
*
|
|
ELSE
|
|
*
|
|
* Compute the Cholesky factorization A = L*L'.
|
|
*
|
|
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 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 TO 30
|
|
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
|
|
20 CONTINUE
|
|
END IF
|
|
END IF
|
|
GO TO 40
|
|
*
|
|
30 CONTINUE
|
|
INFO = INFO + J - 1
|
|
*
|
|
40 CONTINUE
|
|
RETURN
|
|
*
|
|
* End of DPOTRF
|
|
*
|
|
END
|