Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?latbs
Solves a triangular banded system of equations.
Syntax
call slatbs ( uplo , trans , diag , normin , n , kd , ab , ldab , x , scale , cnorm , info )
call dlatbs ( uplo , trans , diag , normin , n , kd , ab , ldab , x , scale , cnorm , info )
call clatbs ( uplo , trans , diag , normin , n , kd , ab , ldab , x , scale , cnorm , info )
call zlatbs ( uplo , trans , diag , normin , n , kd , ab , ldab , x , scale , cnorm , info )
Include Files
mkl.fi
Description
slatbs dlatbs clatbs zlatbs
The routine solves one of the triangular systems
A*x = s*b, or A^{T}*x = s*b, or A^{H}*x = s*b (for complex flavors)
with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here A:code:`T` denotes the transpose of A , A:code:`H` denotes the conjugate transpose of A , x and b are n -element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine ?tbsv is called. If the matrix A is singular (A(j, j)=0 for some j ), then s is set to 0 and a non-trivial solution to A*x = 0 is returned.
Input Parameters
- uplo
-
CHARACTER*1 . Specifies whether the matrix A is upper or lower triangular. = ‘U’ : upper triangular = ‘L’ : lower triangular
- trans
-
CHARACTER*1 . Specifies the operation applied to A . = ‘N’ : solve A*x = s * b (no transpose) = ‘T’ : solve A:code:`T`*x = s * b (transpose) = ‘C’ : solve A:code:`H`*x = s * b (conjugate transpose)
- diag
-
CHARACTER*1 . Specifies whether the matrix A is unit triangular = ‘N’ : non-unit triangular = ‘U’ : unit triangular
- normin
-
CHARACTER*1 . Specifies whether cnorm is set. = ‘Y’ : cnorm contains the column norms on entry; = ‘N’ : cnorm is not set on entry. On exit, the norms is computed and stored in cnorm .
- n
-
INTEGER . The order of the matrix A . n≥ 0 .
- kd
-
INTEGER . The number of subdiagonals or superdiagonals in the triangular matrix A . kb≥ 0 .
- ab
-
REAL for slatbs DOUBLE PRECISION for dlatbs COMPLEX for clatbs DOUBLE COMPLEX for zlatbs . Array, DIMENSION ( ldab , n ). The upper or lower triangular band matrix A , stored in the first kb +1 rows of the array. The j -th column of A is stored in the j -th column of the array ab as follows: if uplo = 'U' , ab(kd+1+i-j,j) = A(i,j) for max(1, j-kd) ≤ i ≤ j ; if uplo = 'L' , ab(1+i-j,j) = A(i,j) for j ≤ i ≤ min(n, j+kd) .
- ldab
-
INTEGER . The leading dimension of the array ab . ldab≥kb+1 .
- x
-
REAL for slatbs DOUBLE PRECISION for dlatbs COMPLEX for clatbs DOUBLE COMPLEX for zlatbs . Array, DIMENSION ( n ). On entry, the right hand side b of the triangular system.
- cnorm
-
REAL for slatbs / clatbs DOUBLE PRECISION for dlatbs / zlatbs . Array, DIMENSION ( n ). If NORMIN = 'Y' , cnorm is an input argument and cnorm(j) contains the norm of the off-diagonal part of the j -th column of A . If trans = 'N' , cnorm(j) must be greater than or equal to the infinity-norm, and if trans = 'T' or ‘C’ , cnorm(j) must be greater than or equal to the 1-norm.
Output Parameters
- scale
-
REAL for slatbs / clatbs DOUBLE PRECISION for dlatbs / zlatbs . The scaling factor s for the triangular system as described above. If scale = 0 , the matrix A is singular or badly scaled, and the vector x is an exact or approximate solution to Ax = 0 .
- cnorm
-
If normin = 'N' , cnorm is an output argument and cnorm(j) returns the 1-norm of the off-diagonal part of the j -th column of A .
info
INTEGER .
= 0: successful exit
< 0: if info = -k , the k -th argument had an illegal value