ptsv - ptsv: factor and solve

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subroutinecptsv(integern,integernrhs,real,dimension(*)d,complex,dimension(*)e,complex,dimension(ldb,*)b,integerldb,integerinfo)CPTSVcomputesthesolutiontosystemoflinearequationsA*X=BforPTmatricesPurpose: CPTSV computes the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices. A is factored as A = L*D*L**H, and the factored form of A is then used to solve the system of equations. ParametersN N is INTEGER The order of the 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) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**H. E E is COMPLEX array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H*D*U factorization of A. B B is COMPLEX array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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 leading principal minor of order i is not positive, and the solution has not been computed. The factorization has not been completed unless i = N. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedptsv(integern,integernrhs,doubleprecision,dimension(*)d,doubleprecision,dimension(*)e,doubleprecision,dimension(ldb,*)b,integerldb,integerinfo)DPTSVcomputesthesolutiontosystemoflinearequationsA*X=BforPTmatricesPurpose: DPTSV computes the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices. A is factored as A = L*D*L**T, and the factored form of A is then used to solve the system of equations. ParametersN N is INTEGER The order of the 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) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**T. E E is DOUBLE PRECISION array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, 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 U**T*D*U factorization of A.) B B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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 leading principal minor of order i is not positive, and the solution has not been computed. The factorization has not been completed unless i = N. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinesptsv(integern,integernrhs,real,dimension(*)d,real,dimension(*)e,real,dimension(ldb,*)b,integerldb,integerinfo)SPTSVcomputesthesolutiontosystemoflinearequationsA*X=BforPTmatricesPurpose: SPTSV computes the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices. A is factored as A = L*D*L**T, and the factored form of A is then used to solve the system of equations. ParametersN N is INTEGER The order of the 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) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**T. E E is REAL array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, 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 U**T*D*U factorization of A.) B B is REAL array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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 leading principal minor of order i is not positive, and the solution has not been computed. The factorization has not been completed unless i = N. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezptsv(integern,integernrhs,doubleprecision,dimension(*)d,complex*16,dimension(*)e,complex*16,dimension(ldb,*)b,integerldb,integerinfo)ZPTSVcomputesthesolutiontosystemoflinearequationsA*X=BforPTmatricesPurpose: ZPTSV computes the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices. A is factored as A = L*D*L**H, and the factored form of A is then used to solve the system of equations. ParametersN N is INTEGER The order of the 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) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**H. E E is COMPLEX*16 array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H*D*U factorization of A. B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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 leading principal minor of order i is not positive, and the solution has not been computed. The factorization has not been completed unless i = N. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

ptsv - ptsv: factor and solve

Functions subroutine cptsv (n, nrhs, d, e, b, ldb, info) CPTSVcomputesthesolutiontosystemoflinearequationsA*X=BforPTmatrices subroutine dptsv (n, nrhs, d, e, b, ldb, info) DPTSVcomputesthesolutiontosystemoflinearequationsA*X=BforPTmatrices subroutine sptsv (n, nrhs, d, e, b, ldb, info) SPTSVcomputesthesolutiontosystemoflinearequationsA*X=BforPTmatrices subroutine zptsv (n, nrhs, d, e, b, ldb, info) ZPTSVcomputesthesolutiontosystemoflinearequationsA*X=BforPTmatrices