*DECK DTBSV
SUBROUTINE DTBSV (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
C***BEGIN PROLOGUE DTBSV
C***PURPOSE Solve one of the systems of equations.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B4
C***TYPE DOUBLE PRECISION (STBSV-S, DTBSV-D, CTBSV-C)
C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J. J., (ANL)
C Du Croz, J., (NAG)
C Hammarling, S., (NAG)
C Hanson, R. J., (SNLA)
C***DESCRIPTION
C
C DTBSV solves one of the systems of equations
C
C A*x = b, or A'*x = b,
C
C where b and x are n element vectors and A is an n by n unit, or
C non-unit, upper or lower triangular band matrix, with ( k + 1)
C diagonals.
C
C No test for singularity or near-singularity is included in this
C routine. Such tests must be performed before calling this routine.
C
C Parameters
C ==========
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the matrix is an upper or
C lower triangular matrix as follows:
C
C UPLO = 'U' or 'u' A is an upper triangular matrix.
C
C UPLO = 'L' or 'l' A is a lower triangular matrix.
C
C Unchanged on exit.
C
C TRANS - CHARACTER*1.
C On entry, TRANS specifies the equations to be solved as
C follows:
C
C TRANS = 'N' or 'n' A*x = b.
C
C TRANS = 'T' or 't' A'*x = b.
C
C TRANS = 'C' or 'c' A'*x = b.
C
C Unchanged on exit.
C
C DIAG - CHARACTER*1.
C On entry, DIAG specifies whether or not A is unit
C triangular as follows:
C
C DIAG = 'U' or 'u' A is assumed to be unit triangular.
C
C DIAG = 'N' or 'n' A is not assumed to be unit
C triangular.
C
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the order of the matrix A.
C N must be at least zero.
C Unchanged on exit.
C
C K - INTEGER.
C On entry with UPLO = 'U' or 'u', K specifies the number of
C super-diagonals of the matrix A.
C On entry with UPLO = 'L' or 'l', K specifies the number of
C sub-diagonals of the matrix A.
C K must satisfy 0 .le. K.
C Unchanged on exit.
C
C A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
C Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
C by n part of the array A must contain the upper triangular
C band part of the matrix of coefficients, supplied column by
C column, with the leading diagonal of the matrix in row
C ( k + 1 ) of the array, the first super-diagonal starting at
C position 2 in row k, and so on. The top left k by k triangle
C of the array A is not referenced.
C The following program segment will transfer an upper
C triangular band matrix from conventional full matrix storage
C to band storage:
C
C DO 20, J = 1, N
C M = K + 1 - J
C DO 10, I = MAX( 1, J - K ), J
C A( M + I, J ) = matrix( I, J )
C 10 CONTINUE
C 20 CONTINUE
C
C Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
C by n part of the array A must contain the lower triangular
C band part of the matrix of coefficients, supplied column by
C column, with the leading diagonal of the matrix in row 1 of
C the array, the first sub-diagonal starting at position 1 in
C row 2, and so on. The bottom right k by k triangle of the
C array A is not referenced.
C The following program segment will transfer a lower
C triangular band matrix from conventional full matrix storage
C to band storage:
C
C DO 20, J = 1, N
C M = 1 - J
C DO 10, I = J, MIN( N, J + K )
C A( M + I, J ) = matrix( I, J )
C 10 CONTINUE
C 20 CONTINUE
C
C Note that when DIAG = 'U' or 'u' the elements of the array A
C corresponding to the diagonal elements of the matrix are not
C referenced, but are assumed to be unity.
C Unchanged on exit.
C
C LDA - INTEGER.
C On entry, LDA specifies the first dimension of A as declared
C in the calling (sub) program. LDA must be at least
C ( k + 1 ).
C Unchanged on exit.
C
C X - DOUBLE PRECISION array of dimension at least
C ( 1 + ( n - 1 )*abs( INCX ) ).
C Before entry, the incremented array X must contain the n
C element right-hand side vector b. On exit, X is overwritten
C with the solution vector x.
C
C INCX - INTEGER.
C On entry, INCX specifies the increment for the elements of
C X. INCX must not be zero.
C Unchanged on exit.
C
C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and
C Hanson, R. J. An extended set of Fortran basic linear
C algebra subprograms. ACM TOMS, Vol. 14, No. 1,
C pp. 1-17, March 1988.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 861022 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE DTBSV
C .. Scalar Arguments ..
INTEGER INCX, K, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), X( * )
C .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
C .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L
LOGICAL NOUNIT
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX, MIN
C***FIRST EXECUTABLE STATEMENT DTBSV
C
C Test the input parameters.
C
INFO = 0
IF ( .NOT.LSAME( UPLO , 'U' ).AND.
$ .NOT.LSAME( UPLO , 'L' ) )THEN
INFO = 1
ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
$ .NOT.LSAME( TRANS, 'T' ).AND.
$ .NOT.LSAME( TRANS, 'C' ) )THEN
INFO = 2
ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
$ .NOT.LSAME( DIAG , 'N' ) )THEN
INFO = 3
ELSE IF( N.LT.0 )THEN
INFO = 4
ELSE IF( K.LT.0 )THEN
INFO = 5
ELSE IF( LDA.LT.( K + 1 ) )THEN
INFO = 7
ELSE IF( INCX.EQ.0 )THEN
INFO = 9
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DTBSV ', INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( N.EQ.0 )
$ RETURN
C
NOUNIT = LSAME( DIAG, 'N' )
C
C Set up the start point in X if the increment is not unity. This
C will be ( N - 1 )*INCX too small for descending loops.
C
IF( INCX.LE.0 )THEN
KX = 1 - ( N - 1 )*INCX
ELSE IF( INCX.NE.1 )THEN
KX = 1
END IF
C
C Start the operations. In this version the elements of A are
C accessed by sequentially with one pass through A.
C
IF( LSAME( TRANS, 'N' ) )THEN
C
C Form x := inv( A )*x.
C
IF( LSAME( UPLO, 'U' ) )THEN
KPLUS1 = K + 1
IF( INCX.EQ.1 )THEN
DO 20, J = N, 1, -1
IF( X( J ).NE.ZERO )THEN
L = KPLUS1 - J
IF( NOUNIT )
$ X( J ) = X( J )/A( KPLUS1, J )
TEMP = X( J )
DO 10, I = J - 1, MAX( 1, J - K ), -1
X( I ) = X( I ) - TEMP*A( L + I, J )
10 CONTINUE
END IF
20 CONTINUE
ELSE
KX = KX + ( N - 1 )*INCX
JX = KX
DO 40, J = N, 1, -1
KX = KX - INCX
IF( X( JX ).NE.ZERO )THEN
IX = KX
L = KPLUS1 - J
IF( NOUNIT )
$ X( JX ) = X( JX )/A( KPLUS1, J )
TEMP = X( JX )
DO 30, I = J - 1, MAX( 1, J - K ), -1
X( IX ) = X( IX ) - TEMP*A( L + I, J )
IX = IX - INCX
30 CONTINUE
END IF
JX = JX - INCX
40 CONTINUE
END IF
ELSE
IF( INCX.EQ.1 )THEN
DO 60, J = 1, N
IF( X( J ).NE.ZERO )THEN
L = 1 - J
IF( NOUNIT )
$ X( J ) = X( J )/A( 1, J )
TEMP = X( J )
DO 50, I = J + 1, MIN( N, J + K )
X( I ) = X( I ) - TEMP*A( L + I, J )
50 CONTINUE
END IF
60 CONTINUE
ELSE
JX = KX
DO 80, J = 1, N
KX = KX + INCX
IF( X( JX ).NE.ZERO )THEN
IX = KX
L = 1 - J
IF( NOUNIT )
$ X( JX ) = X( JX )/A( 1, J )
TEMP = X( JX )
DO 70, I = J + 1, MIN( N, J + K )
X( IX ) = X( IX ) - TEMP*A( L + I, J )
IX = IX + INCX
70 CONTINUE
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
ELSE
C
C Form x := inv( A')*x.
C
IF( LSAME( UPLO, 'U' ) )THEN
KPLUS1 = K + 1
IF( INCX.EQ.1 )THEN
DO 100, J = 1, N
TEMP = X( J )
L = KPLUS1 - J
DO 90, I = MAX( 1, J - K ), J - 1
TEMP = TEMP - A( L + I, J )*X( I )
90 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( KPLUS1, J )
X( J ) = TEMP
100 CONTINUE
ELSE
JX = KX
DO 120, J = 1, N
TEMP = X( JX )
IX = KX
L = KPLUS1 - J
DO 110, I = MAX( 1, J - K ), J - 1
TEMP = TEMP - A( L + I, J )*X( IX )
IX = IX + INCX
110 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( KPLUS1, J )
X( JX ) = TEMP
JX = JX + INCX
IF( J.GT.K )
$ KX = KX + INCX
120 CONTINUE
END IF
ELSE
IF( INCX.EQ.1 )THEN
DO 140, J = N, 1, -1
TEMP = X( J )
L = 1 - J
DO 130, I = MIN( N, J + K ), J + 1, -1
TEMP = TEMP - A( L + I, J )*X( I )
130 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( 1, J )
X( J ) = TEMP
140 CONTINUE
ELSE
KX = KX + ( N - 1 )*INCX
JX = KX
DO 160, J = N, 1, -1
TEMP = X( JX )
IX = KX
L = 1 - J
DO 150, I = MIN( N, J + K ), J + 1, -1
TEMP = TEMP - A( L + I, J )*X( IX )
IX = IX - INCX
150 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( 1, J )
X( JX ) = TEMP
JX = JX - INCX
IF( ( N - J ).GE.K )
$ KX = KX - INCX
160 CONTINUE
END IF
END IF
END IF
C
RETURN
C
C End of DTBSV .
C
END