163 lines
4.7 KiB
FortranFixed
163 lines
4.7 KiB
FortranFixed
SUBROUTINE DTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
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$ 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 DIAG, TRANS, 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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DOUBLE PRECISION 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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* DTBTRS solves a triangular system of the form
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*
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* A * X = B or A**T * X = B,
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*
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* where A is a triangular band matrix of order N, and B is an
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* N-by NRHS matrix. A check is made to verify that A is nonsingular.
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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': A is upper triangular;
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* = 'L': A is lower triangular.
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*
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* TRANS (input) CHARACTER*1
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* Specifies the form the system of equations:
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* = 'N': A * X = B (No transpose)
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* = 'T': A**T * X = B (Transpose)
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* = 'C': A**H * X = B (Conjugate transpose = Transpose)
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*
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* DIAG (input) CHARACTER*1
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* = 'N': A is non-unit triangular;
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* = 'U': A is unit triangular.
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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 or subdiagonals of the
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* triangular band matrix A. 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) DOUBLE PRECISION array, dimension (LDAB,N)
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* The upper or lower triangular band matrix A, stored in the
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* first kd+1 rows of AB. The j-th column of A is stored
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* in the j-th column of the array AB as follows:
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* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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* If DIAG = 'U', the diagonal elements of A are not referenced
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* and are assumed to be 1.
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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) DOUBLE PRECISION array, dimension (LDB,NRHS)
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* On entry, the right hand side matrix B.
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* On exit, if INFO = 0, 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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* > 0: if INFO = i, the i-th diagonal element of A is zero,
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* indicating that the matrix is singular and the
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* solutions X have not been computed.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL NOUNIT, 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 DTBSV, 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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NOUNIT = LSAME( DIAG, 'N' )
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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( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
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$ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( KD.LT.0 ) THEN
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INFO = -5
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -6
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ELSE IF( LDAB.LT.KD+1 ) THEN
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INFO = -8
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -10
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DTBTRS', -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 )
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$ RETURN
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*
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* Check for singularity.
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*
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IF( NOUNIT ) THEN
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IF( UPPER ) THEN
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DO 10 INFO = 1, N
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IF( AB( KD+1, INFO ).EQ.ZERO )
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$ RETURN
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10 CONTINUE
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ELSE
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DO 20 INFO = 1, N
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IF( AB( 1, INFO ).EQ.ZERO )
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$ RETURN
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20 CONTINUE
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END IF
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END IF
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INFO = 0
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*
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* Solve A * X = B or A' * X = B.
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*
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DO 30 J = 1, NRHS
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CALL DTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, B( 1, J ), 1 )
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30 CONTINUE
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*
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RETURN
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*
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* End of DTBTRS
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*
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END
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