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OpenBLAS

reference

ctrtrif.f

ctrtrif.f 5.17 KB

SUBROUTINE CTRTRIF( UPLO, DIAG, 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
* September 30, 1994
*
* .. Scalar Arguments ..
 CHARACTER DIAG, UPLO
 INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
 COMPLEX A( LDA, * )
* ..
*
* Purpose
* =======
*
* CTRTRI computes the inverse of a complex upper or lower triangular
* matrix A.
*
* This is the Level 3 BLAS version of the algorithm.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': A is upper triangular;
* = 'L': A is lower triangular.
*
* DIAG (input) CHARACTER*1
* = 'N': A is non-unit triangular;
* = 'U': A is unit triangular.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) COMPLEX array, dimension (LDA,N)
* On entry, the triangular matrix A. If UPLO = 'U', the
* leading N-by-N upper triangular part of the array A contains
* the upper triangular matrix, and the strictly lower
* triangular part of A is not referenced. If UPLO = 'L', the
* leading N-by-N lower triangular part of the array A contains
* the lower triangular matrix, and the strictly upper
* triangular part of A is not referenced. If DIAG = 'U', the
* diagonal elements of A are also not referenced and are
* assumed to be 1.
* On exit, the (triangular) inverse of the original matrix, in
* the same storage format.
*
* 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, A(i,i) is exactly zero. The triangular
* matrix is singular and its inverse can not be computed.
*
* =====================================================================
*
* .. Parameters ..
 COMPLEX ONE, ZERO
 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
 $ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
 LOGICAL NOUNIT, UPPER
 INTEGER J, JB, NB, NN
* ..
* .. External Functions ..
 LOGICAL LSAME
 EXTERNAL LSAME
* ..
* .. External Subroutines ..
 EXTERNAL CTRMM, CTRSM, CTRTI2, XERBLA
* ..
* .. Intrinsic Functions ..
 INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
 INFO = 0
 UPPER = LSAME( UPLO, 'U' )
 NOUNIT = LSAME( DIAG, 'N' )
 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
 INFO = -1
 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
 INFO = -2
 ELSE IF( N.LT.0 ) THEN
 INFO = -3
 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
 INFO = -5
 END IF
 IF( INFO.NE.0 ) THEN
 CALL XERBLA( 'CTRTRI', -INFO )
 RETURN
 END IF
*
* Quick return if possible
*
 IF( N.EQ.0 )
 $ RETURN
*
* Check for singularity if non-unit.
*
 IF( NOUNIT ) THEN
 DO 10 INFO = 1, N
 IF( A( INFO, INFO ).EQ.ZERO )
 $ RETURN
 10 CONTINUE
 INFO = 0
 END IF
*
* Determine the block size for this environment.
*
 NB = 128
 IF( NB.LE.1 .OR. NB.GE.N ) THEN
*
* Use unblocked code
*
 CALL CTRTI2( UPLO, DIAG, N, A, LDA, INFO )
 ELSE
*
* Use blocked code
*
 IF( UPPER ) THEN
*
* Compute inverse of upper triangular matrix
*
 DO 20 J = 1, N, NB
 JB = MIN( NB, N-J+1 )
*
* Compute rows 1:j-1 of current block column
*
 CALL CTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
 $ JB, ONE, A, LDA, A( 1, J ), LDA )
 CALL CTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
 $ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
*
* Compute inverse of current diagonal block
*
 CALL CTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
 20 CONTINUE
 ELSE
*
* Compute inverse of lower triangular matrix
*
 NN = ( ( N-1 ) / NB )*NB + 1
 DO 30 J = NN, 1, -NB
 JB = MIN( NB, N-J+1 )
 IF( J+JB.LE.N ) THEN
*
* Compute rows j+jb:n of current block column
*
 CALL CTRMM( 'Left', 'Lower', 'No transpose', DIAG,
 $ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
 $ A( J+JB, J ), LDA )
 CALL CTRSM( 'Right', 'Lower', 'No transpose', DIAG,
 $ N-J-JB+1, JB, -ONE, A( J, J ), LDA,
 $ A( J+JB, J ), LDA )
 END IF
*
* Compute inverse of current diagonal block
*
 CALL CTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
 30 CONTINUE
 END IF
 END IF
*
 RETURN
*
* End of CTRTRI
*
 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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SUBROUTINECTRTRIF(UPLO,DIAG,N,A,LDA,INFO)
*
*--LAPACKroutine(version3.0)--
*Univ.ofTennessee,Univ.ofCaliforniaBerkeley,NAGLtd.,
*CourantInstitute,ArgonneNationalLab,andRiceUniversity
*September30,1994
*
*..ScalarArguments..
CHARACTERDIAG,UPLO
INTEGERINFO,LDA,N
*..
*..ArrayArguments..
COMPLEXA(LDA,*)
*..
*
*Purpose
*=======
*
*CTRTRIcomputestheinverseofacomplexupperorlowertriangular
*matrixA.
*
*ThisistheLevel3BLASversionofthealgorithm.
*
*Arguments
*=========
*
*UPLO(input)CHARACTER*1
*='U':Aisuppertriangular;
*='L':Aislowertriangular.
*
*DIAG(input)CHARACTER*1
*='N':Aisnon-unittriangular;
*='U':Aisunittriangular.
*
*N(input)INTEGER
*TheorderofthematrixA.N>=0.
*
*A(input/output)COMPLEXarray,dimension(LDA,N)
*Onentry,thetriangularmatrixA.IfUPLO='U',the
*leadingN-by-NuppertriangularpartofthearrayAcontains
*theuppertriangularmatrix,andthestrictlylower
*triangularpartofAisnotreferenced.IfUPLO='L',the
*leadingN-by-NlowertriangularpartofthearrayAcontains
*thelowertriangularmatrix,andthestrictlyupper
*triangularpartofAisnotreferenced.IfDIAG='U',the
*diagonalelementsofAarealsonotreferencedandare
*assumedtobe1.
*Onexit,the(triangular)inverseoftheoriginalmatrix,in
*thesamestorageformat.
*
*LDA(input)INTEGER
*TheleadingdimensionofthearrayA.LDA>=max(1,N).
*
*INFO(output)INTEGER
*=0:successfulexit
*<0:ifINFO=-i,thei-thargumenthadanillegalvalue
*>0:ifINFO=i,A(i,i)isexactlyzero.Thetriangular
*matrixissingularanditsinversecannotbecomputed.
*
*=====================================================================
*
*..Parameters..
COMPLEXONE,ZERO
PARAMETER(ONE=(1.0E+0,0.0E+0),
$ZERO=(0.0E+0,0.0E+0))
*..
*..LocalScalars..
LOGICALNOUNIT,UPPER
INTEGERJ,JB,NB,NN
*..
*..ExternalFunctions..
LOGICALLSAME
EXTERNALLSAME
*..
*..ExternalSubroutines..
EXTERNALCTRMM,CTRSM,CTRTI2,XERBLA
*..
*..IntrinsicFunctions..
INTRINSICMAX,MIN
*..
*..ExecutableStatements..
*
*Testtheinputparameters.
*
INFO=0
UPPER=LSAME(UPLO,'U')
NOUNIT=LSAME(DIAG,'N')
IF(.NOT.UPPER.AND..NOT.LSAME(UPLO,'L'))THEN
INFO=-1
ELSEIF(.NOT.NOUNIT.AND..NOT.LSAME(DIAG,'U'))THEN
INFO=-2
ELSEIF(N.LT.0)THEN
INFO=-3
ELSEIF(LDA.LT.MAX(1,N))THEN
INFO=-5
ENDIF
IF(INFO.NE.0)THEN
CALLXERBLA('CTRTRI',-INFO)
RETURN
ENDIF
*
*Quickreturnifpossible
*
IF(N.EQ.0)
$RETURN
*
*Checkforsingularityifnon-unit.
*
IF(NOUNIT)THEN
DO10INFO=1,N
IF(A(INFO,INFO).EQ.ZERO)
$RETURN
10CONTINUE
INFO=0
ENDIF
*
*Determinetheblocksizeforthisenvironment.
*
NB=128
IF(NB.LE.1.OR.NB.GE.N)THEN
*
*Useunblockedcode
*
CALLCTRTI2(UPLO,DIAG,N,A,LDA,INFO)
ELSE
*
*Useblockedcode
*
IF(UPPER)THEN
*
*Computeinverseofuppertriangularmatrix
*
DO20J=1,N,NB
JB=MIN(NB,N-J+1)
*
*Computerows1:j-1ofcurrentblockcolumn
*
CALLCTRMM('Left','Upper','No transpose',DIAG,J-1,
$JB,ONE,A,LDA,A(1,J),LDA)
CALLCTRSM('Right','Upper','No transpose',DIAG,J-1,
$JB,-ONE,A(J,J),LDA,A(1,J),LDA)
*
*Computeinverseofcurrentdiagonalblock
*
CALLCTRTI2('Upper',DIAG,JB,A(J,J),LDA,INFO)
20CONTINUE
ELSE
*
*Computeinverseoflowertriangularmatrix
*
NN=((N-1)/NB)*NB+1
DO30J=NN,1,-NB
JB=MIN(NB,N-J+1)
IF(J+JB.LE.N)THEN
*
*Computerowsj+jb:nofcurrentblockcolumn
*
CALLCTRMM('Left','Lower','No transpose',DIAG,
$N-J-JB+1,JB,ONE,A(J+JB,J+JB),LDA,
$A(J+JB,J),LDA)
CALLCTRSM('Right','Lower','No transpose',DIAG,
$N-J-JB+1,JB,-ONE,A(J,J),LDA,
$A(J+JB,J),LDA)
ENDIF
*
*Computeinverseofcurrentdiagonalblock
*
CALLCTRTI2('Lower',DIAG,JB,A(J,J),LDA,INFO)
30CONTINUE
ENDIF
ENDIF
*
RETURN
*
*EndofCTRTRI
*
END