zsysvx - tion to a complex system of linear equations A*X = B, where A is an N- by-N symmetric matrix and X and B are N-by-NRHS matrices
SUBROUTINE ZSYSVX(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LDWORK, WORK2, INFO) CHARACTER*1 FACT, UPLO DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDA, LDAF, LDB, LDX, LDWORK, INFO INTEGER IPIVOT(*) DOUBLE PRECISION RCOND DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZSYSVX_64(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LDWORK, WORK2, INFO) CHARACTER*1 FACT, UPLO DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, LDWORK, INFO INTEGER*8 IPIVOT(*) DOUBLE PRECISION RCOND DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE SYSVX(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LDWORK, WORK2, INFO) CHARACTER(LEN=1) :: FACT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, LDWORK, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8) :: RCOND REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE SYSVX_64(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LDWORK, WORK2, INFO) CHARACTER(LEN=1) :: FACT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, LDWORK, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8) :: RCOND REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zsysvx(char fact, char uplo, int n, int nrhs, doublecomplex *a, int lda, doublecomplex *af, int ldaf, int *ipivot, doublecom- plex *b, int ldb, doublecomplex *x, int ldx, double *rcond, double *ferr, double *berr, int *info); void zsysvx_64(char fact, char uplo, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, doublecomplex *b, long ldb, doublecomplex *x, long ldx, dou- ble *rcond, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library zsysvx(3P)
NAME
zsysvx - use the diagonal pivoting factorization to compute the solu-
tion to a complex system of linear equations A*X = B, where A is an N-
by-N symmetric matrix and X and B are N-by-NRHS matrices
SYNOPSIS
SUBROUTINE ZSYSVX(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B,
LDB, X, LDX, RCOND, FERR, BERR, WORK, LDWORK, WORK2, INFO)
CHARACTER*1 FACT, UPLO
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDA, LDAF, LDB, LDX, LDWORK, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION RCOND
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZSYSVX_64(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT,
B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LDWORK, WORK2, INFO)
CHARACTER*1 FACT, UPLO
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, LDWORK, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION RCOND
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE SYSVX(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT,
B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LDWORK, WORK2,
INFO)
CHARACTER(LEN=1) :: FACT, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, LDWORK, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8) :: RCOND
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE SYSVX_64(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF,
IPIVOT, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LDWORK,
WORK2, INFO)
CHARACTER(LEN=1) :: FACT, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8) :: RCOND
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zsysvx(char fact, char uplo, int n, int nrhs, doublecomplex *a,
int lda, doublecomplex *af, int ldaf, int *ipivot, doublecom-
plex *b, int ldb, doublecomplex *x, int ldx, double *rcond,
double *ferr, double *berr, int *info);
void zsysvx_64(char fact, char uplo, long n, long nrhs, doublecomplex
*a, long lda, doublecomplex *af, long ldaf, long *ipivot,
doublecomplex *b, long ldb, doublecomplex *x, long ldx, dou-
ble *rcond, double *ferr, double *berr, long *info);
PURPOSE
zsysvx uses the diagonal pivoting factorization to compute the solution
to a complex system of linear equations A * X = B, where A is an N-by-N
symmetric 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 diagonal pivoting method is used to factor A.
The form of the factorization is
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, 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 A has been sup-
plied on entry. = 'F': On entry, AF and IPIVOT contain the
factored form of A. A, AF and IPIVOT will not be modified.
= 'N': The matrix A will be copied to AF and factored.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The number of linear equations, i.e., 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.
A (input) The symmetric matrix A. If UPLO = 'U', the leading N-by-N
upper triangular part of A contains the upper triangular part
of the matrix A, and the strictly lower triangular part of A
is not referenced. If UPLO = 'L', the leading N-by-N lower
triangular part of A contains the lower triangular part of
the matrix A, and the strictly upper triangular part of A is
not referenced.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
AF (input or output)
If FACT = 'F', then AF is an input argument and on entry con-
tains the block diagonal matrix D and the multipliers used to
obtain the factor U or L from the factorization A = U*D*U**T
or A = L*D*L**T as computed by ZSYTRF.
If FACT = 'N', then AF is an output argument and on exit
returns the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization A =
U*D*U**T or A = L*D*L**T.
LDAF (input)
The leading dimension of the array AF. LDAF >= max(1,N).
IPIVOT (input or output)
If FACT = 'F', then IPIVOT is an input argument and on entry
contains details of the interchanges and the block structure
of D, as determined by ZSYTRF. If IPIVOT(k) > 0, then rows
and columns k and IPIVOT(k) were interchanged and D(k,k) is a
1-by-1 diagonal block. If UPLO = 'U' and IPIVOT(k) =
IPIVOT(k-1) < 0, then rows and columns k-1 and -IPIVOT(k)
were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal
block. If UPLO = 'L' and IPIVOT(k) = IPIVOT(k+1) < 0, then
rows and columns k+1 and -IPIVOT(k) were interchanged and
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
If FACT = 'N', then IPIVOT is an output argument and on exit
contains details of the interchanges and the block structure
of D, as determined by ZSYTRF.
B (input) The N-by-NRHS right hand side matrix B.
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 estimate of the reciprocal condition number of the matrix
A. If RCOND is less than the machine precision (in particu-
lar, if RCOND = 0), the matrix is singular to working preci-
sion. This condition is indicated by a return code of INFO >
0.
FERR (output)
The estimated 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 esti-
mated upper bound for the magnitude of the largest element in
(X(j) - XTRUE) divided by the magnitude of the largest ele-
ment in X(j). The estimate is as reliable as the estimate
for RCOND, and is almost always a slight overestimate of the
true error.
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)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The length of WORK. LDWORK >= 2*N, and for best performance
LDWORK >= N*NB, where NB is the optimal blocksize for ZSYTRF.
If LDWORK = -1, then a workspace query is assumed; the rou-
tine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LDWORK is issued by XERBLA.
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: D(i,i) is exactly zero. The factorization has been
completed but the factor D is exactly singular, so the solu-
tion and error bounds could not be computed. RCOND = 0 is
returned. = N+1: D is nonsingular, but RCOND is less than
machine precision, meaning that the matrix is singular to
working precision. Nevertheless, the solution and error
bounds are computed because there are a number of situations
where the computed solution can be more accurate than the
value of RCOND would suggest.
7 Nov 2015 zsysvx(3P)