1DTBSV(1) BLAS routine DTBSV(1)
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6 DTBSV - one of the systems of equations A*x = b, or A'*x = b,
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9 SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
10 INTEGER INCX,K,LDA,N
12 CHARACTER DIAG,TRANS,UPLO
14 DOUBLE PRECISION
16 A(LDA,*),X(*)
17
19 DTBSV solves one of the systems of equations
20 where b and x are n element vectors and A is an n by n unit, or non-
22 unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.
23 No test for singularity or near-singularity is included in this rou‐
25 tine. Such tests must be performed before calling this routine.
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29 UPLO - CHARACTER*1.
30 On entry, UPLO specifies whether the matrix is an upper or lower
31 triangular matrix as follows:
32 UPLO = 'U' or 'u' A is an upper triangular matrix.
34 UPLO = 'L' or 'l' A is a lower triangular matrix.
36 Unchanged on exit.
38 TRANS - CHARACTER*1.
40 On entry, TRANS specifies the equations to be solved as follows:
41 TRANS = 'N' or 'n' A*x = b.
43 TRANS = 'T' or 't' A'*x = b.
45 TRANS = 'C' or 'c' A'*x = b.
47 Unchanged on exit.
49 DIAG - CHARACTER*1.
51 On entry, DIAG specifies whether or not A is unit triangular as
52 follows:
53 DIAG = 'U' or 'u' A is assumed to be unit triangular.
55 DIAG = 'N' or 'n' A is not assumed to be unit triangular.
57 Unchanged on exit.
59 N - INTEGER.
61 On entry, N specifies the order of the matrix A. N must be at
62 least zero. Unchanged on exit.
63 K - INTEGER.
65 On entry with UPLO = 'U' or 'u', K specifies the number of
66 super-diagonals of the matrix A. On entry with UPLO = 'L' or
67 'l', K specifies the number of sub-diagonals of the matrix A. K
68 must satisfy 0 .le. K. Unchanged on exit.
69 A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
71 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n
72 part of the array A must contain the upper triangular band part
73 of the matrix of coefficients, supplied column by column, with
74 the leading diagonal of the matrix in row ( k + 1 ) of the
75 array, the first super-diagonal starting at position 2 in row k,
76 and so on. The top left k by k triangle of the array A is not
77 referenced. The following program segment will transfer an
78 upper triangular band matrix from conventional full matrix stor‐
79 age to band storage:
80 DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M
82 + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
83 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n
85 part of the array A must contain the lower triangular band part
86 of the matrix of coefficients, supplied column by column, with
87 the leading diagonal of the matrix in row 1 of the array, the
88 first sub-diagonal starting at position 1 in row 2, and so on.
89 The bottom right k by k triangle of the array A is not refer‐
90 enced. The following program segment will transfer a lower tri‐
91 angular band matrix from conventional full matrix storage to
92 band storage:
93 DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M +
95 I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
96 Note that when DIAG = 'U' or 'u' the elements of the array A
98 corresponding to the diagonal elements of the matrix are not
99 referenced, but are assumed to be unity. Unchanged on exit.
100 LDA - INTEGER.
102 On entry, LDA specifies the first dimension of A as declared in
103 the calling (sub) program. LDA must be at least ( k + 1 ).
104 Unchanged on exit.
105 X - DOUBLE PRECISION array of dimension at least
107 ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
108 array X must contain the n element right-hand side vector b. On
109 exit, X is overwritten with the solution vector x.
110 INCX - INTEGER.
112 On entry, INCX specifies the increment for the elements of X.
113 INCX must not be zero. Unchanged on exit.
114 Level 2 Blas routine.
116 -- Written on 22-October-1986. Jack Dongarra, Argonne National
118 Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
119 Central Office. Richard Hanson, Sandia National Labs.
120BLAS routine November 2006 DTBSV(1)