146 lines
4.1 KiB
FortranFixed
146 lines
4.1 KiB
FortranFixed
SUBROUTINE CPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, KD, LDAB, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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COMPLEX AB( LDAB, * ), B( LDB, * )
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* ..
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*
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* Purpose
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* =======
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*
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* CPBTRS solves a system of linear equations A*X = B with a Hermitian
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* positive definite band matrix A using the Cholesky factorization
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* A = U**H*U or A = L*L**H computed by CPBTRF.
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*
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* Arguments
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* =========
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*
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* UPLO (input) CHARACTER*1
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* = 'U': Upper triangular factor stored in AB;
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* = 'L': Lower triangular factor stored in AB.
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* KD (input) INTEGER
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* The number of superdiagonals of the matrix A if UPLO = 'U',
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* or the number of subdiagonals if UPLO = 'L'. KD >= 0.
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*
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* NRHS (input) INTEGER
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* The number of right hand sides, i.e., the number of columns
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* of the matrix B. NRHS >= 0.
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*
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* AB (input) COMPLEX array, dimension (LDAB,N)
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* The triangular factor U or L from the Cholesky factorization
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* A = U**H*U or A = L*L**H of the band matrix A, stored in the
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* first KD+1 rows of the array. The j-th column of U or L is
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* stored in the j-th column of the array AB as follows:
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* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
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* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
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*
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* LDAB (input) INTEGER
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* The leading dimension of the array AB. LDAB >= KD+1.
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*
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* B (input/output) COMPLEX array, dimension (LDB,NRHS)
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* On entry, the right hand side matrix B.
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* On exit, the solution matrix X.
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*
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* LDB (input) INTEGER
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* The leading dimension of the array B. LDB >= max(1,N).
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL UPPER
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INTEGER J
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL CTBSV, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( KD.LT.0 ) THEN
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INFO = -3
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDAB.LT.KD+1 ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CPBTRS', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 .OR. NRHS.EQ.0 )
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$ RETURN
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*
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IF( UPPER ) THEN
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*
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* Solve A*X = B where A = U'*U.
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*
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DO 10 J = 1, NRHS
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*
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* Solve U'*X = B, overwriting B with X.
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*
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CALL CTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
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$ KD, AB, LDAB, B( 1, J ), 1 )
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*
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* Solve U*X = B, overwriting B with X.
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*
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CALL CTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
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$ LDAB, B( 1, J ), 1 )
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10 CONTINUE
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ELSE
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*
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* Solve A*X = B where A = L*L'.
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*
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DO 20 J = 1, NRHS
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*
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* Solve L*X = B, overwriting B with X.
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*
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CALL CTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
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$ LDAB, B( 1, J ), 1 )
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*
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* Solve L'*X = B, overwriting B with X.
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*
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CALL CTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
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$ KD, AB, LDAB, B( 1, J ), 1 )
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20 CONTINUE
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END IF
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*
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RETURN
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*
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* End of CPBTRS
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*
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END
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