phynexis-deps/lapack
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
f86d08bae6c46685e0f759850e82dc0a8fa00a21
lapack/SRC/dpbtrf.f
T
Julie e18d437924 Making LAPACK's code eternal... no more version and date in source files. 
GitHub is now enabling us to track accurately version and date.
No need for this anymore.
2021-03-25 10:16:58 -07:00

433 lines
13 KiB
FortranFixed
Raw Blame History

*> \brief \b DPBTRF
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DPBTRF + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbtrf.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbtrf.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbtrf.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, KD, LDAB, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AB( LDAB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DPBTRF computes the Cholesky factorization of a real symmetric
*> positive definite band 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] KD
*> \verbatim
*> KD is INTEGER
*> The number of superdiagonals of the matrix A if UPLO = 'U',
*> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*> \endverbatim
*>
*> \param[in,out] AB
*> \verbatim
*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
*> On entry, the upper or lower triangle of the symmetric band
*> matrix A, stored in the first KD+1 rows of the array. The
*> j-th column of A is stored in the j-th column of the array AB
*> as follows:
*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
*>
*> On exit, if INFO = 0, the triangular factor U or L from the
*> Cholesky factorization A = U**T*U or A = L*L**T of the band
*> matrix A, in the same storage format as A.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KD+1.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> N = 6, KD = 2, and UPLO = 'U':
*>
*> On entry: On exit:
*>
*> * * a13 a24 a35 a46 * * u13 u24 u35 u46
*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
*>
*> Similarly, if UPLO = 'L' the format of A is as follows:
*>
*> On entry: On exit:
*>
*> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
*> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
*> \endverbatim
*
*> \par Contributors:
* ==================
*>
*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
*
* =====================================================================
SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, KD, LDAB, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AB( LDAB, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
INTEGER NBMAX, LDWORK
PARAMETER ( NBMAX = 32, LDWORK = NBMAX+1 )
* ..
* .. Local Scalars ..
INTEGER I, I2, I3, IB, II, J, JJ, NB
* ..
* .. Local Arrays ..
DOUBLE PRECISION WORK( LDWORK, NBMAX )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DPBTF2, DPOTF2, DSYRK, DTRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( ( .NOT.LSAME( UPLO, 'U' ) ) .AND.
$ ( .NOT.LSAME( UPLO, 'L' ) ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KD.LT.0 ) THEN
INFO = -3
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DPBTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Determine the block size for this environment
*
NB = ILAENV( 1, 'DPBTRF', UPLO, N, KD, -1, -1 )
*
* The block size must not exceed the semi-bandwidth KD, and must not
* exceed the limit set by the size of the local array WORK.
*
NB = MIN( NB, NBMAX )
*
IF( NB.LE.1 .OR. NB.GT.KD ) THEN
*
* Use unblocked code
*
CALL DPBTF2( UPLO, N, KD, AB, LDAB, INFO )
ELSE
*
* Use blocked code
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Compute the Cholesky factorization of a symmetric band
* matrix, given the upper triangle of the matrix in band
* storage.
*
* Zero the upper triangle of the work array.
*
DO 20 J = 1, NB
DO 10 I = 1, J - 1
WORK( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
*
* Process the band matrix one diagonal block at a time.
*
DO 70 I = 1, N, NB
IB = MIN( NB, N-I+1 )
*
* Factorize the diagonal block
*
CALL DPOTF2( UPLO, IB, AB( KD+1, I ), LDAB-1, II )
IF( II.NE.0 ) THEN
INFO = I + II - 1
GO TO 150
END IF
IF( I+IB.LE.N ) THEN
*
* Update the relevant part of the trailing submatrix.
* If A11 denotes the diagonal block which has just been
* factorized, then we need to update the remaining
* blocks in the diagram:
*
* A11 A12 A13
* A22 A23
* A33
*
* The numbers of rows and columns in the partitioning
* are IB, I2, I3 respectively. The blocks A12, A22 and
* A23 are empty if IB = KD. The upper triangle of A13
* lies outside the band.
*
I2 = MIN( KD-IB, N-I-IB+1 )
I3 = MIN( IB, N-I-KD+1 )
*
IF( I2.GT.0 ) THEN
*
* Update A12
*
CALL DTRSM( 'Left', 'Upper', 'Transpose',
$ 'Non-unit', IB, I2, ONE, AB( KD+1, I ),
$ LDAB-1, AB( KD+1-IB, I+IB ), LDAB-1 )
*
* Update A22
*
CALL DSYRK( 'Upper', 'Transpose', I2, IB, -ONE,
$ AB( KD+1-IB, I+IB ), LDAB-1, ONE,
$ AB( KD+1, I+IB ), LDAB-1 )
END IF
*
IF( I3.GT.0 ) THEN
*
* Copy the lower triangle of A13 into the work array.
*
DO 40 JJ = 1, I3
DO 30 II = JJ, IB
WORK( II, JJ ) = AB( II-JJ+1, JJ+I+KD-1 )
30 CONTINUE
40 CONTINUE
*
* Update A13 (in the work array).
*
CALL DTRSM( 'Left', 'Upper', 'Transpose',
$ 'Non-unit', IB, I3, ONE, AB( KD+1, I ),
$ LDAB-1, WORK, LDWORK )
*
* Update A23
*
IF( I2.GT.0 )
$ CALL DGEMM( 'Transpose', 'No Transpose', I2, I3,
$ IB, -ONE, AB( KD+1-IB, I+IB ),
$ LDAB-1, WORK, LDWORK, ONE,
$ AB( 1+IB, I+KD ), LDAB-1 )
*
* Update A33
*
CALL DSYRK( 'Upper', 'Transpose', I3, IB, -ONE,
$ WORK, LDWORK, ONE, AB( KD+1, I+KD ),
$ LDAB-1 )
*
* Copy the lower triangle of A13 back into place.
*
DO 60 JJ = 1, I3
DO 50 II = JJ, IB
AB( II-JJ+1, JJ+I+KD-1 ) = WORK( II, JJ )
50 CONTINUE
60 CONTINUE
END IF
END IF
70 CONTINUE
ELSE
*
* Compute the Cholesky factorization of a symmetric band
* matrix, given the lower triangle of the matrix in band
* storage.
*
* Zero the lower triangle of the work array.
*
DO 90 J = 1, NB
DO 80 I = J + 1, NB
WORK( I, J ) = ZERO
80 CONTINUE
90 CONTINUE
*
* Process the band matrix one diagonal block at a time.
*
DO 140 I = 1, N, NB
IB = MIN( NB, N-I+1 )
*
* Factorize the diagonal block
*
CALL DPOTF2( UPLO, IB, AB( 1, I ), LDAB-1, II )
IF( II.NE.0 ) THEN
INFO = I + II - 1
GO TO 150
END IF
IF( I+IB.LE.N ) THEN
*
* Update the relevant part of the trailing submatrix.
* If A11 denotes the diagonal block which has just been
* factorized, then we need to update the remaining
* blocks in the diagram:
*
* A11
* A21 A22
* A31 A32 A33
*
* The numbers of rows and columns in the partitioning
* are IB, I2, I3 respectively. The blocks A21, A22 and
* A32 are empty if IB = KD. The lower triangle of A31
* lies outside the band.
*
I2 = MIN( KD-IB, N-I-IB+1 )
I3 = MIN( IB, N-I-KD+1 )
*
IF( I2.GT.0 ) THEN
*
* Update A21
*
CALL DTRSM( 'Right', 'Lower', 'Transpose',
$ 'Non-unit', I2, IB, ONE, AB( 1, I ),
$ LDAB-1, AB( 1+IB, I ), LDAB-1 )
*
* Update A22
*
CALL DSYRK( 'Lower', 'No Transpose', I2, IB, -ONE,
$ AB( 1+IB, I ), LDAB-1, ONE,
$ AB( 1, I+IB ), LDAB-1 )
END IF
*
IF( I3.GT.0 ) THEN
*
* Copy the upper triangle of A31 into the work array.
*
DO 110 JJ = 1, IB
DO 100 II = 1, MIN( JJ, I3 )
WORK( II, JJ ) = AB( KD+1-JJ+II, JJ+I-1 )
100 CONTINUE
110 CONTINUE
*
* Update A31 (in the work array).
*
CALL DTRSM( 'Right', 'Lower', 'Transpose',
$ 'Non-unit', I3, IB, ONE, AB( 1, I ),
$ LDAB-1, WORK, LDWORK )
*
* Update A32
*
IF( I2.GT.0 )
$ CALL DGEMM( 'No transpose', 'Transpose', I3, I2,
$ IB, -ONE, WORK, LDWORK,
$ AB( 1+IB, I ), LDAB-1, ONE,
$ AB( 1+KD-IB, I+IB ), LDAB-1 )
*
* Update A33
*
CALL DSYRK( 'Lower', 'No Transpose', I3, IB, -ONE,
$ WORK, LDWORK, ONE, AB( 1, I+KD ),
$ LDAB-1 )
*
* Copy the upper triangle of A31 back into place.
*
DO 130 JJ = 1, IB
DO 120 II = 1, MIN( JJ, I3 )
AB( KD+1-JJ+II, JJ+I-1 ) = WORK( II, JJ )
120 CONTINUE
130 CONTINUE
END IF
END IF
140 CONTINUE
END IF
END IF
RETURN
*
150 CONTINUE
RETURN
*
* End of DPBTRF
*
END
Reference in New Issue View Git Blame Copy Permalink