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OpenBLAS

reference

dpotf2f.f

dpotf2f.f 4.76 KB

SUBROUTINE DPOTF2F( 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
* 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

一键复制编辑原始数据按行查看历史

Zhang Xianyi 提交于 2011年01月24日 22:54 +08:00 . Import GotoBLAS2 1.13 BSD version codes.

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SUBROUTINEDPOTF2F(UPLO,N,A,LDA,INFO)
*
*--LAPACKroutine(version3.0)--
*Univ.ofTennessee,Univ.ofCaliforniaBerkeley,NAGLtd.,
*CourantInstitute,ArgonneNationalLab,andRiceUniversity
*February29,1992
*
*..ScalarArguments..
CHARACTERUPLO
INTEGERINFO,LDA,N
*..
*..ArrayArguments..
DOUBLE PRECISIONA(LDA,*)
*..
*
*Purpose
*=======
*
*DPOTF2computestheCholeskyfactorizationofarealsymmetric
*positivedefinitematrixA.
*
*Thefactorizationhastheform
*A=U' * U , if UPLO = 'U', or
* A = L * L',ifUPLO='L',
*whereUisanuppertriangularmatrixandLislowertriangular.
*
*Thisistheunblockedversionofthealgorithm,callingLevel2BLAS.
*
*Arguments
*=========
*
*UPLO(input)CHARACTER*1
*Specifieswhethertheupperorlowertriangularpartofthe
*symmetricmatrixAisstored.
*='U':Uppertriangular
*='L':Lowertriangular
*
*N(input)INTEGER
*TheorderofthematrixA.N>=0.
*
*A(input/output)DOUBLE PRECISIONarray,dimension(LDA,N)
*Onentry,thesymmetricmatrixA.IfUPLO='U',theleading
*nbynuppertriangularpartofAcontainstheupper
*triangularpartofthematrixA,andthestrictlylower
*triangularpartofAisnotreferenced.IfUPLO='L',the
*leadingnbynlowertriangularpartofAcontainsthelower
*triangularpartofthematrixA,andthestrictlyupper
*triangularpartofAisnotreferenced.
*
*Onexit,ifINFO=0,thefactorUorLfromtheCholesky
*factorizationA=U'*U or A = L*L'.
*
*LDA(input)INTEGER
*TheleadingdimensionofthearrayA.LDA>=max(1,N).
*
*INFO(output)INTEGER
*=0:successfulexit
*<0:ifINFO=-k,thek-thargumenthadanillegalvalue
*>0:ifINFO=k,theleadingminoroforderkisnot
*positivedefinite,andthefactorizationcouldnotbe
*completed.
*
*=====================================================================
*
*..Parameters..
DOUBLE PRECISIONONE,ZERO
PARAMETER(ONE=1.0D+0,ZERO=0.0D+0)
*..
*..LocalScalars..
LOGICALUPPER
INTEGERJ
DOUBLE PRECISIONAJJ
*..
*..ExternalFunctions..
LOGICALLSAME
DOUBLE PRECISIONDDOT
EXTERNALLSAME,DDOT
*..
*..ExternalSubroutines..
EXTERNALDGEMV,DSCAL,XERBLA
*..
*..IntrinsicFunctions..
INTRINSICMAX,SQRT
*..
*..ExecutableStatements..
*
*Testtheinputparameters.
*
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
ENDIF
IF(INFO.NE.0)THEN
CALLXERBLA('DPOTF2',-INFO)
RETURN
ENDIF
*
*Quickreturnifpossible
*
IF(N.EQ.0)
$RETURN
*
IF(UPPER)THEN
*
*ComputetheCholeskyfactorizationA=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'.
*
DO20J=1,N
*
*ComputeL(J,J)andtestfornon-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 TO30
ENDIF
AJJ=SQRT(AJJ)
A(J,J)=AJJ
*
*ComputeelementsJ+1:NofcolumnJ.
*
IF(J.LT.N)THEN
CALLDGEMV('No transpose',N-J,J-1,-ONE,A(J+1,1),
$LDA,A(J,1),LDA,ONE,A(J+1,J),1)
CALLDSCAL(N-J,ONE/AJJ,A(J+1,J),1)
ENDIF
20CONTINUE
ENDIF
GO TO40
*
30CONTINUE
INFO=J
*
40CONTINUE
RETURN
*
*EndofDPOTF2
*
END