tbtrs - tbtrs: triangular solve

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 tbtrs(3)

subroutinectbtrs(characteruplo,charactertrans,characterdiag,integern,integerkd,integernrhs,complex,dimension(ldab,*)ab,integerldab,complex,dimension(ldb,*)b,integerldb,integerinfo)CTBTRSPurpose: CTBTRS solves a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. This subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error. If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine. ParametersUPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. TRANS TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose) DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. KD KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. AB AB is COMPLEX array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of AB. 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). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. B B is COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedtbtrs(characteruplo,charactertrans,characterdiag,integern,integerkd,integernrhs,doubleprecision,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(ldb,*)b,integerldb,integerinfo)DTBTRSPurpose: DTBTRS solves a triangular system of the form A * X = B or A**T * X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. This subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error. If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine. ParametersUPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. TRANS TRANS is CHARACTER*1 Specifies the form the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose) DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. KD KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. AB AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of AB. 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). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. B B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinestbtrs(characteruplo,charactertrans,characterdiag,integern,integerkd,integernrhs,real,dimension(ldab,*)ab,integerldab,real,dimension(ldb,*)b,integerldb,integerinfo)STBTRSPurpose: STBTRS solves a triangular system of the form A * X = B or A**T * X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. This subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error. If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine. ParametersUPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. TRANS TRANS is CHARACTER*1 Specifies the form the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose) DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. KD KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. AB AB is REAL array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of AB. 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). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. B B is REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutineztbtrs(characteruplo,charactertrans,characterdiag,integern,integerkd,integernrhs,complex*16,dimension(ldab,*)ab,integerldab,complex*16,dimension(ldb,*)b,integerldb,integerinfo)ZTBTRSPurpose: ZTBTRS solves a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. This subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error. If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine. ParametersUPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. TRANS TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose) DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. KD KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. AB AB is COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of AB. 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). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

tbtrs - tbtrs: triangular solve

Functions subroutine ctbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info) CTBTRS subroutine dtbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info) DTBTRS subroutine stbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info) STBTRS subroutine ztbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info) ZTBTRS