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