gbtrs - gbtrs: triangular solve using factor

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 gbtrs(3)

subroutinecgbtrs(charactertrans,integern,integerkl,integerku,integernrhs,complex,dimension(ldab,*)ab,integerldab,integer,dimension(*)ipiv,complex,dimension(ldb,*)b,integerldb,integerinfo)CGBTRSPurpose: CGBTRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by CGBTRF. ParametersTRANS 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) N N is INTEGER The order of the matrix A. N >= 0. KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. KU KU is INTEGER The number of superdiagonals within the band of A. KU >= 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) Details of the LU factorization of the band matrix A, as computed by CGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1. IPIV IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i). B B is COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, 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 Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedgbtrs(charactertrans,integern,integerkl,integerku,integernrhs,doubleprecision,dimension(ldab,*)ab,integerldab,integer,dimension(*)ipiv,doubleprecision,dimension(ldb,*)b,integerldb,integerinfo)DGBTRSPurpose: DGBTRS solves a system of linear equations A * X = B or A**T * X = B with a general band matrix A using the LU factorization computed by DGBTRF. ParametersTRANS 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**T* X = B (Conjugate transpose = Transpose) N N is INTEGER The order of the matrix A. N >= 0. KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. KU KU is INTEGER The number of superdiagonals within the band of A. KU >= 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) Details of the LU factorization of the band matrix A, as computed by DGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1. IPIV IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i). B B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, 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 Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinesgbtrs(charactertrans,integern,integerkl,integerku,integernrhs,real,dimension(ldab,*)ab,integerldab,integer,dimension(*)ipiv,real,dimension(ldb,*)b,integerldb,integerinfo)SGBTRSPurpose: SGBTRS solves a system of linear equations A * X = B or A**T * X = B with a general band matrix A using the LU factorization computed by SGBTRF. ParametersTRANS 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**T* X = B (Conjugate transpose = Transpose) N N is INTEGER The order of the matrix A. N >= 0. KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. KU KU is INTEGER The number of superdiagonals within the band of A. KU >= 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) Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1. IPIV IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i). B B is REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, 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 Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezgbtrs(charactertrans,integern,integerkl,integerku,integernrhs,complex*16,dimension(ldab,*)ab,integerldab,integer,dimension(*)ipiv,complex*16,dimension(ldb,*)b,integerldb,integerinfo)ZGBTRSPurpose: ZGBTRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by ZGBTRF. ParametersTRANS 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) N N is INTEGER The order of the matrix A. N >= 0. KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. KU KU is INTEGER The number of superdiagonals within the band of A. KU >= 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) Details of the LU factorization of the band matrix A, as computed by ZGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1. IPIV IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i). B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, 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 Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

gbtrs - gbtrs: triangular solve using factor

Functions subroutine cgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) CGBTRS subroutine dgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) DGBTRS subroutine sgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) SGBTRS subroutine zgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) ZGBTRS