Mercurial > jwe > octave
changeset 3283:604ce3f77788
[project @ 1999-10-13 19:54:06 by jwe]
| author | jwe |
|---|---|
| date | Wed, 13 Oct 1999 19:54:07 +0000 |
| parents | 518ea57df2c4 |
| children | f7e4a95916f2 |
| files | libcruft/dassl/dpotf2.f libcruft/dassl/dpotrf.f |
| diffstat | 2 files changed, 0 insertions(+), 354 deletions(-) [+] |
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--- a/libcruft/dassl/dpotf2.f Wed Oct 13 19:00:38 1999 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,168 +0,0 @@ - SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO ) -* -* -- LAPACK routine (version 1.0) -- -* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -* Courant Institute, Argonne National Lab, and Rice University -* February 29, 1992 -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* Purpose -* ======= -* -* DPOTF2 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) 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'*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 .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER J - DOUBLE PRECISION AJJ -* .. -* .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DDOT - EXTERNAL LSAME, DDOT -* .. -* .. External Subroutines .. - EXTERNAL DGEMV, DSCAL, 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( 'DPOTF2', -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 ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 ) - IF( AJJ.LE.ZERO ) 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 DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ), - $ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA ) - CALL DSCAL( 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 ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ), - $ LDA ) - IF( AJJ.LE.ZERO ) 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 DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ), - $ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 ) - CALL DSCAL( 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 DPOTF2 -* - END
--- a/libcruft/dassl/dpotrf.f Wed Oct 13 19:00:38 1999 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,186 +0,0 @@ - SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO ) -* -* -- LAPACK routine (version 1.0) -- -* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -* Courant Institute, Argonne National Lab, and Rice University -* February 29, 1992 -* -* .. 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' * 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 block version of the algorithm, calling Level 3 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) 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'*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 .. - 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