ZTPRFS(3F) ZTPRFS(3F)
ZTPRFS - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix
SUBROUTINE ZTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR,
BERR, WORK, RWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
ZTPRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix.
The solution matrix X must be computed by ZTPTRS or some other means
before entering this routine. ZTPRFS does not do iterative refinement
because doing so cannot improve the backward error.
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS (input) 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)
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in a
linear array. The j-th column of A is stored in the array AP as
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ZTPRFS(3F) ZTPRFS(3F)
follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If
DIAG = 'U', the diagonal elements of A are not referenced and are
assumed to be 1.
B (input) COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input) COMPLEX*16 array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
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 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). The
estimate is as reliable as the estimate for RCOND, and is almost
always a slight overestimate of the true error.
BERR (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution vector
X(j) (i.e., the smallest relative change in any element of A or B
that makes X(j) an exact solution).
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
ZTPRFS(3F) ZTPRFS(3F)
ZTPRFS - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix
SUBROUTINE ZTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR,
BERR, WORK, RWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
ZTPRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix.
The solution matrix X must be computed by ZTPTRS or some other means
before entering this routine. ZTPRFS does not do iterative refinement
because doing so cannot improve the backward error.
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS (input) 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)
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in a
linear array. The j-th column of A is stored in the array AP as
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ZTPRFS(3F) ZTPRFS(3F)
follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If
DIAG = 'U', the diagonal elements of A are not referenced and are
assumed to be 1.
B (input) COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input) COMPLEX*16 array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
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 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). The
estimate is as reliable as the estimate for RCOND, and is almost
always a slight overestimate of the true error.
BERR (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution vector
X(j) (i.e., the smallest relative change in any element of A or B
that makes X(j) an exact solution).
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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