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340 lines
11 KiB
Fortran
340 lines
11 KiB
Fortran
SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
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* .. Scalar Arguments ..
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INTEGER INCX,K,LDA,N
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CHARACTER DIAG,TRANS,UPLO
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*),X(*)
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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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* DTBSV solves one of the systems of equations
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*
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* A*x = b, or A'*x = b,
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*
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* where b and x are n element vectors and A is an n by n unit, or
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* non-unit, upper or lower triangular band matrix, with ( k + 1 )
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* diagonals.
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*
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* No test for singularity or near-singularity is included in this
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* routine. Such tests must be performed before calling this routine.
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*
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* Arguments
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* ==========
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*
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* UPLO - CHARACTER*1.
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* On entry, UPLO specifies whether the matrix is an upper or
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* lower triangular matrix as follows:
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*
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* UPLO = 'U' or 'u' A is an upper triangular matrix.
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*
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* UPLO = 'L' or 'l' A is a lower triangular matrix.
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*
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* Unchanged on exit.
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*
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* TRANS - CHARACTER*1.
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* On entry, TRANS specifies the equations to be solved as
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* follows:
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*
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* TRANS = 'N' or 'n' A*x = b.
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*
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* TRANS = 'T' or 't' A'*x = b.
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*
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* TRANS = 'C' or 'c' A'*x = b.
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*
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* Unchanged on exit.
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*
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* DIAG - CHARACTER*1.
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* On entry, DIAG specifies whether or not A is unit
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* triangular as follows:
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*
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* DIAG = 'U' or 'u' A is assumed to be unit triangular.
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*
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* DIAG = 'N' or 'n' A is not assumed to be unit
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* triangular.
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*
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* Unchanged on exit.
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*
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* N - INTEGER.
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* On entry, N specifies the order of the matrix A.
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* N must be at least zero.
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* Unchanged on exit.
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*
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* K - INTEGER.
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* On entry with UPLO = 'U' or 'u', K specifies the number of
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* super-diagonals of the matrix A.
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* On entry with UPLO = 'L' or 'l', K specifies the number of
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* sub-diagonals of the matrix A.
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* K must satisfy 0 .le. K.
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* Unchanged on exit.
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*
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* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
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* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
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* by n part of the array A must contain the upper triangular
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* band part of the matrix of coefficients, supplied column by
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* column, with the leading diagonal of the matrix in row
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* ( k + 1 ) of the array, the first super-diagonal starting at
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* position 2 in row k, and so on. The top left k by k triangle
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* of the array A is not referenced.
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* The following program segment will transfer an upper
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* triangular band matrix from conventional full matrix storage
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* to band storage:
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*
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* DO 20, J = 1, N
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* M = K + 1 - J
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* DO 10, I = MAX( 1, J - K ), J
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* A( M + I, J ) = matrix( I, J )
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* 10 CONTINUE
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* 20 CONTINUE
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*
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* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
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* by n part of the array A must contain the lower triangular
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* band part of the matrix of coefficients, supplied column by
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* column, with the leading diagonal of the matrix in row 1 of
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* the array, the first sub-diagonal starting at position 1 in
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* row 2, and so on. The bottom right k by k triangle of the
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* array A is not referenced.
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* The following program segment will transfer a lower
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* triangular band matrix from conventional full matrix storage
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* to band storage:
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*
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* DO 20, J = 1, N
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* M = 1 - J
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* DO 10, I = J, MIN( N, J + K )
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* A( M + I, J ) = matrix( I, J )
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* 10 CONTINUE
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* 20 CONTINUE
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*
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* Note that when DIAG = 'U' or 'u' the elements of the array A
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* corresponding to the diagonal elements of the matrix are not
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* referenced, but are assumed to be unity.
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* Unchanged on exit.
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*
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* LDA - INTEGER.
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* On entry, LDA specifies the first dimension of A as declared
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* in the calling (sub) program. LDA must be at least
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* ( k + 1 ).
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* Unchanged on exit.
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*
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* X - DOUBLE PRECISION array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCX ) ).
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* Before entry, the incremented array X must contain the n
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* element right-hand side vector b. On exit, X is overwritten
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* with the solution vector x.
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*
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* INCX - INTEGER.
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* On entry, INCX specifies the increment for the elements of
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* X. INCX must not be zero.
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* Unchanged on exit.
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*
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* Further Details
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* ===============
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*
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* Level 2 Blas routine.
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*
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* -- Written on 22-October-1986.
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* Jack Dongarra, Argonne National Lab.
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* Jeremy Du Croz, Nag Central Office.
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* Sven Hammarling, Nag Central Office.
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* Richard Hanson, Sandia National Labs.
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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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DOUBLE PRECISION TEMP
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INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
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LOGICAL NOUNIT
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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 XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX,MIN
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* ..
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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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IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
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INFO = 1
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ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
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+ .NOT.LSAME(TRANS,'C')) THEN
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INFO = 2
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ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) 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 (K.LT.0) THEN
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INFO = 5
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ELSE IF (LDA.LT. (K+1)) THEN
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INFO = 7
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ELSE IF (INCX.EQ.0) THEN
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INFO = 9
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('DTBSV ',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) RETURN
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*
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NOUNIT = LSAME(DIAG,'N')
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*
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* Set up the start point in X if the increment is not unity. This
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* will be ( N - 1 )*INCX too small for descending loops.
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*
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IF (INCX.LE.0) THEN
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KX = 1 - (N-1)*INCX
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ELSE IF (INCX.NE.1) THEN
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KX = 1
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END IF
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*
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* Start the operations. In this version the elements of A are
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* accessed by sequentially with one pass through A.
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*
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IF (LSAME(TRANS,'N')) THEN
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*
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* Form x := inv( A )*x.
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*
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IF (LSAME(UPLO,'U')) THEN
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KPLUS1 = K + 1
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IF (INCX.EQ.1) THEN
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DO 20 J = N,1,-1
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IF (X(J).NE.ZERO) THEN
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L = KPLUS1 - J
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IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
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TEMP = X(J)
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DO 10 I = J - 1,MAX(1,J-K),-1
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X(I) = X(I) - TEMP*A(L+I,J)
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10 CONTINUE
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END IF
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20 CONTINUE
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ELSE
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KX = KX + (N-1)*INCX
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JX = KX
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DO 40 J = N,1,-1
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KX = KX - INCX
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IF (X(JX).NE.ZERO) THEN
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IX = KX
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L = KPLUS1 - J
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IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
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TEMP = X(JX)
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DO 30 I = J - 1,MAX(1,J-K),-1
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X(IX) = X(IX) - TEMP*A(L+I,J)
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IX = IX - INCX
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30 CONTINUE
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END IF
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JX = JX - INCX
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40 CONTINUE
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END IF
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ELSE
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IF (INCX.EQ.1) THEN
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DO 60 J = 1,N
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IF (X(J).NE.ZERO) THEN
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L = 1 - J
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IF (NOUNIT) X(J) = X(J)/A(1,J)
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TEMP = X(J)
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DO 50 I = J + 1,MIN(N,J+K)
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X(I) = X(I) - TEMP*A(L+I,J)
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50 CONTINUE
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END IF
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60 CONTINUE
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ELSE
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JX = KX
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DO 80 J = 1,N
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KX = KX + INCX
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IF (X(JX).NE.ZERO) THEN
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IX = KX
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L = 1 - J
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IF (NOUNIT) X(JX) = X(JX)/A(1,J)
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TEMP = X(JX)
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DO 70 I = J + 1,MIN(N,J+K)
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X(IX) = X(IX) - TEMP*A(L+I,J)
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IX = IX + INCX
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70 CONTINUE
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END IF
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JX = JX + INCX
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80 CONTINUE
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END IF
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END IF
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ELSE
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*
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* Form x := inv( A')*x.
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*
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IF (LSAME(UPLO,'U')) THEN
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KPLUS1 = K + 1
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IF (INCX.EQ.1) THEN
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DO 100 J = 1,N
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TEMP = X(J)
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L = KPLUS1 - J
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DO 90 I = MAX(1,J-K),J - 1
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TEMP = TEMP - A(L+I,J)*X(I)
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90 CONTINUE
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IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
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X(J) = TEMP
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100 CONTINUE
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ELSE
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JX = KX
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DO 120 J = 1,N
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TEMP = X(JX)
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IX = KX
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L = KPLUS1 - J
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DO 110 I = MAX(1,J-K),J - 1
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TEMP = TEMP - A(L+I,J)*X(IX)
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IX = IX + INCX
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110 CONTINUE
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IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
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X(JX) = TEMP
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JX = JX + INCX
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IF (J.GT.K) KX = KX + INCX
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120 CONTINUE
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END IF
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ELSE
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IF (INCX.EQ.1) THEN
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DO 140 J = N,1,-1
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TEMP = X(J)
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L = 1 - J
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DO 130 I = MIN(N,J+K),J + 1,-1
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TEMP = TEMP - A(L+I,J)*X(I)
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130 CONTINUE
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IF (NOUNIT) TEMP = TEMP/A(1,J)
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X(J) = TEMP
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140 CONTINUE
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ELSE
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KX = KX + (N-1)*INCX
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JX = KX
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DO 160 J = N,1,-1
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TEMP = X(JX)
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IX = KX
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L = 1 - J
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DO 150 I = MIN(N,J+K),J + 1,-1
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TEMP = TEMP - A(L+I,J)*X(IX)
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IX = IX - INCX
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150 CONTINUE
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IF (NOUNIT) TEMP = TEMP/A(1,J)
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X(JX) = TEMP
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JX = JX - INCX
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IF ((N-J).GE.K) KX = KX - INCX
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160 CONTINUE
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END IF
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END IF
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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 DTBSV .
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*
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END
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