Developer Reference for Intel® oneAPI Math Kernel Library for C
?tbsv
Solves a system of linear equations whose coefficients are in a triangular band matrix.
Syntax
void cblas_stbsv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
const MKL_INT k, const float *a, const MKL_INT lda, float *x,
const MKL_INT incx);
void cblas_dtbsv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
const MKL_INT k, const double *a, const MKL_INT lda, double *x,
const MKL_INT incx);
void cblas_ctbsv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
const MKL_INT k, const void *a, const MKL_INT lda, void *x,
const MKL_INT incx);
void cblas_ztbsv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
const MKL_INT k, const void *a, const MKL_INT lda, void *x,
const MKL_INT incx);Include Files
mkl.h
Description
The ?tbsv routines solve one of the following systems of equations:
A * x = b , or A ‘* x = b , or conjg( A ‘)* x = b ,
where:
b and x are n -element vectors,
A is an n -by- n unit, or non-unit, upper or lower triangular band matrix, with (k + 1) diagonals.
The routine does not test for singularity or near-singularity.
Such tests must be performed before calling this routine.
Input Parameters
- Layout
-
Specifies whether two-dimensional array storage is row-major ( CblasRowMajor ) or column-major ( CblasColMajor ).
uplo
Specifies whether the matrix A is an upper or lower triangular matrix:
if uplo = CblasUpper the matrix is upper triangular;
if uplo = CblasLower , the matrix is low triangular.
trans
Specifies the system of equations:
if trans = CblasNoTrans , then A*x = b ;
if trans = CblasTrans , then A'*x = b ;
if trans = CblasConjTrans , then conjg(A')*x = b .
diag
Specifies whether the matrix A is unit triangular:
if diag = CblasUnit then the matrix is unit triangular;
if diag = CblasNonUnit , then the matrix is not unit triangular.
- n
-
Specifies the order of the matrix A . The value of n must be at least zero.
k
On entry with uplo = CblasUpper , k specifies the number of super-diagonals of the matrix A . On entry with uplo = CblasLower , k specifies the number of sub-diagonals of the matrix A .
The value of k must satisfy 0 ≤ k .
- a
-
REAL for stbsv DOUBLE PRECISION for dtbsv COMPLEX for ctbsv DOUBLE COMPLEX for ztbsv Array, size (lda, n)lda*n .
Layout = CblasColMajor :
Before entry with uplo = CblasUpper , the leading (k + 1) by n part of the array a must contain the upper triangular band part of the matrix of coefficients, supplied column-by-column, with the leading diagonal of the matrix in row k of the array, the first super-diagonal starting at position 1 in row (k - 1) , and so on. The top left k by k triangle of the array a is not referenced.
The following program segment transfers an upper triangular band matrix from conventional full matrix storage ( matrix , with leading dimension ldm ) to band storage ( a , with leading dimension lda ):
Before entry with uplo = CblasLower , the leading (k + 1) by n part of the array a must contain the lower triangular band part of the matrix of coefficients, supplied column-by-column, with the leading diagonal of the matrix in row 0 of the array, the first sub-diagonal starting at position 0 in row 1 , and so on. The bottom right k by k triangle of the array a is not referenced.
The following program segment transfers a lower triangular band matrix from conventional full matrix storage ( matrix , with leading dimension ldm ) to band storage ( a , with leading dimension lda ):
When diag = CblasUnit , the elements of the array a corresponding to the diagonal elements of the matrix are not referenced, but are assumed to be unity.
Layout = CblasRowMajor: Before entry with uplo = CblasUpper , the leading ( k + 1)-by- n part of array a must contain the upper triangular band part of the matrix of coefficients. The matrix must be supplied row-by-row, with the leading diagonal of the matrix in column 0 of the array, the first super-diagonal starting at position 0 in column 1, and so on. The bottom right k -by- k triangle of array a is not referenced. The following program segment transfers the upper triangular part of a Hermitian band matrix from row-major full matrix storage ( matrix with leading dimension ldm ) to row-major band storage ( a , with leading dimension lda ): Before entry with uplo = CblasLower , the leading ( k + 1)-by- n part of array a must contain the lower triangular band part of the matrix of coefficients, supplied row-by-row, with the leading diagonal of the matrix in column k of the array, the first sub-diagonal starting at position 1 in column k -1, and so on. The top left k -by- k triangle of array a is not referenced. The following program segment transfers the lower triangular part of a Hermitian row-major band matrix from row-major full matrix storage ( matrix , with leading dimension ldm ) to row-major band storage ( a , with leading dimension lda ):
- lda
-
Specifies the leading dimension of a as declared in the calling (sub)program. The value of lda must be at least (k + 1) .
- x
-
REAL for stbsv DOUBLE PRECISION for dtbsv COMPLEX for ctbsv DOUBLE COMPLEX for ztbsv Array, size at least (1 + (n - 1)*abs(incx)) . Before entry, the incremented array x must contain the n -element right-hand side vector b .
- incx
-
Specifies the increment for the elements of x .
The value of incx must not be zero.
Output Parameters
- x
-
Overwritten with the solution vector x .
BLAS 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.