Solves a triangular banded system of equations.
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 )
The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).
The routine solves one of the triangular systems
A*x = s*b, or AT*x = s*b, or AH*x = s*b (for complex flavors)
with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here AT denotes the transpose of A, AH 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.
CHARACTER*1.
Specifies whether the matrix A is upper or lower triangular.
= 'U': upper triangular
= 'L': lower triangular
CHARACTER*1.
Specifies the operation applied to A.
= 'N': solve A*x = s*b (no transpose)
= 'T': solve AT*x = s*b (transpose)
= 'C': solve AH*x = s*b (conjugate transpose)
CHARACTER*1.
Specifies whether the matrix A is unit triangular
= 'N': non-unit triangular
= 'U': unit triangular
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.
INTEGER. The order of the matrix A. n ≥ 0.
INTEGER. The number of subdiagonals or superdiagonals in the triangular matrix A. kb ≥ 0.
REAL for slatbs
DOUBLE PRECISION for dlatbs
COMPLEX for clatbs
COMPLEX*16 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).
INTEGER. The leading dimension of the array ab. ldab ≥ kb+1.
REAL for slatbs
DOUBLE PRECISION for dlatbs
COMPLEX for clatbs
COMPLEX*16 for zlatbs.
Array, DIMENSION (n).
On entry, the right hand side b of the triangular system.
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.
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.
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.
INTEGER.
= 0: successful exit
< 0: if info = -k, the k-th argument had an illegal value
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