zptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Her- mitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
SUBROUTINE ZPTSVX(FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 FACT DOUBLE COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO DOUBLE PRECISION RCOND DOUBLE PRECISION D(*), DF(*), FERR(*), BERR(*), WORK2(*) SUBROUTINE ZPTSVX_64(FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 FACT DOUBLE COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO DOUBLE PRECISION RCOND DOUBLE PRECISION D(*), DF(*), FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE PTSVX(FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: FACT COMPLEX(8), DIMENSION(:) :: E, EF, WORK COMPLEX(8), DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO REAL(8) :: RCOND REAL(8), DIMENSION(:) :: D, DF, FERR, BERR, WORK2 SUBROUTINE PTSVX_64(FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: FACT COMPLEX(8), DIMENSION(:) :: E, EF, WORK COMPLEX(8), DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO REAL(8) :: RCOND REAL(8), DIMENSION(:) :: D, DF, FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zptsvx(char fact, int n, int nrhs, double *d, doublecomplex *e, double *df, doublecomplex *ef, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *rcond, double *ferr, dou- ble *berr, int *info); void zptsvx_64(char fact, long n, long nrhs, double *d, doublecomplex *e, double *df, doublecomplex *ef, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *rcond, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library zptsvx(3P) NAME zptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Her- mitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices SYNOPSIS SUBROUTINE ZPTSVX(FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 FACT DOUBLE COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO DOUBLE PRECISION RCOND DOUBLE PRECISION D(*), DF(*), FERR(*), BERR(*), WORK2(*) SUBROUTINE ZPTSVX_64(FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 FACT DOUBLE COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO DOUBLE PRECISION RCOND DOUBLE PRECISION D(*), DF(*), FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE PTSVX(FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: FACT COMPLEX(8), DIMENSION(:) :: E, EF, WORK COMPLEX(8), DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO REAL(8) :: RCOND REAL(8), DIMENSION(:) :: D, DF, FERR, BERR, WORK2 SUBROUTINE PTSVX_64(FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: FACT COMPLEX(8), DIMENSION(:) :: E, EF, WORK COMPLEX(8), DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO REAL(8) :: RCOND REAL(8), DIMENSION(:) :: D, DF, FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zptsvx(char fact, int n, int nrhs, double *d, doublecomplex *e, double *df, doublecomplex *ef, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *rcond, double *ferr, dou- ble *berr, int *info); void zptsvx_64(char fact, long n, long nrhs, double *d, doublecomplex *e, double *df, doublecomplex *ef, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *rcond, double *ferr, double *berr, long *info); PURPOSE zptsvx uses the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermi- tian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also pro- vided. The following steps are performed: 1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L is a unit lower bidiagonal matrix and D is diagonal. The factorization can also be regarded as having the form A = U**H*D*U. 2. If the leading i-by-i principal minor is not positive definite, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below. 3. The system of equations is solved for X using the factored form of A. 4. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it. ARGUMENTS FACT (input) Specifies whether or not the factored form of the matrix A is supplied on entry. = 'F': On entry, DF and EF contain the factored form of A. D, E, DF, and EF will not be modified. = 'N': The matrix A will be copied to DF and EF and fac- tored. N (input) The order of the matrix A. N >= 0. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. D (input) The n diagonal elements of the tridiagonal matrix A. E (input) The (n-1) subdiagonal elements of the tridiagonal matrix A. DF (input or output) If FACT = 'F', then DF is an input argument and on entry con- tains the n diagonal elements of the diagonal matrix D from the L*D*L**H factorization of A. If FACT = 'N', then DF is an output argument and on exit contains the n diagonal ele- ments of the diagonal matrix D from the L*D*L**H factoriza- tion of A. EF (input or output) If FACT = 'F', then EF is an input argument and on entry con- tains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. If FACT = 'N', then EF is an output argument and on exit contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. B (input) On entry, the N-by-NRHS right hand side matrix B. Unchanged on exit. LDB (input) The leading dimension of the array B. LDB >= max(1,N). X (output) If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. LDX (input) The leading dimension of the array X. LDX >= max(1,N). RCOND (output) The reciprocal condition number of the matrix A. If RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. This condi- tion is indicated by a return code of INFO > 0. FERR (output) The forward error bound for each solution vector X(j) (the j- th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). BERR (output) The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any ele- ment of A or B that makes X(j) an exact solution). WORK (workspace) dimension(N) WORK2 (workspace) dimension(N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, and i is <= N: the leading minor of order i of A is not positive def- inite, so the factorization could not be completed, and the solution has not been computed. RCOND = 0 is returned. = N+1: U is nonsingular, but RCOND is less than machine preci- sion, meaning that the matrix is singular to working preci- sion. Nevertheless, the solution and error bounds are com- puted because there are a number of situations where the com- puted solution can be more accurate than the value of RCOND would suggest. 7 Nov 2015 zptsvx(3P)