pttrs(3) Library Functions Manual pttrs(3) NAME pttrs - pttrs: triangular solve using factor SYNOPSIS Functions subroutine cpttrs (uplo, n, nrhs, d, e, b, ldb, info) CPTTRS subroutine dpttrs (n, nrhs, d, e, b, ldb, info) DPTTRS subroutine spttrs (n, nrhs, d, e, b, ldb, info) SPTTRS subroutine zpttrs (uplo, n, nrhs, d, e, b, ldb, info) ZPTTRS Detailed Description Function Documentation subroutine cpttrs (character uplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer info) CPTTRS Purpose: CPTTRS solves a tridiagonal system of the form A * X = B using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF. D is a diagonal matrix specified in the vector D, U (or L) is a unit bidiagonal matrix whose superdiagonal (subdiagonal) is specified in the vector E, and X and B are N by NRHS matrices. Parameters UPLO UPLO is CHARACTER*1 Specifies the form of the factorization and whether the vector E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L. = 'U': A = U**H*D*U, E is the superdiagonal of U = 'L': A = L*D*L**H, E is the subdiagonal of L N N is INTEGER The order of the tridiagonal matrix A. N >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. D D is REAL array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization A = U**H*D*U or A = L*D*L**H. E E is COMPLEX array, dimension (N-1) If UPLO = 'U', the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U**H*D*U. If UPLO = 'L', the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization A = L*D*L**H. B B is COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, 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 = -k, the k-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 120 of file cpttrs.f. subroutine dpttrs (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, integer info) DPTTRS Purpose: DPTTRS solves a tridiagonal system of the form A * X = B using the L*D*L**T factorization of A computed by DPTTRF. D is a diagonal matrix specified in the vector D, L is a unit bidiagonal matrix whose subdiagonal is specified in the vector E, and X and B are N by NRHS matrices. Parameters N N is INTEGER The order of the tridiagonal matrix A. N >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. D D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A. E E is DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the factorization A = U**T*D*U. B B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, 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 = -k, the k-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 108 of file dpttrs.f. subroutine spttrs (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer info) SPTTRS Purpose: SPTTRS solves a tridiagonal system of the form A * X = B using the L*D*L**T factorization of A computed by SPTTRF. D is a diagonal matrix specified in the vector D, L is a unit bidiagonal matrix whose subdiagonal is specified in the vector E, and X and B are N by NRHS matrices. Parameters N N is INTEGER The order of the tridiagonal matrix A. N >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. D D is REAL array, dimension (N) The n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A. E E is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the factorization A = U**T*D*U. B B is REAL array, dimension (LDB,NRHS) On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, 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 = -k, the k-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 108 of file spttrs.f. subroutine zpttrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, integer info) ZPTTRS Purpose: ZPTTRS solves a tridiagonal system of the form A * X = B using the factorization A = U**H *D* U or A = L*D*L**H computed by ZPTTRF. D is a diagonal matrix specified in the vector D, U (or L) is a unit bidiagonal matrix whose superdiagonal (subdiagonal) is specified in the vector E, and X and B are N by NRHS matrices. Parameters UPLO UPLO is CHARACTER*1 Specifies the form of the factorization and whether the vector E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L. = 'U': A = U**H *D*U, E is the superdiagonal of U = 'L': A = L*D*L**H, E is the subdiagonal of L N N is INTEGER The order of the tridiagonal matrix A. N >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. D D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization A = U**H *D*U or A = L*D*L**H. E E is COMPLEX*16 array, dimension (N-1) If UPLO = 'U', the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U**H*D*U. If UPLO = 'L', the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization A = L*D*L**H. B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, 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 = -k, the k-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 120 of file zpttrs.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 pttrs(3)