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java.lang.Object | +----org.netlib.lapack.Dppsvx
Following is the description from the original Fortran source. For each array argument, the Java version will include an integer offset parameter, so the arguments may not match the description exactly. Contact seymour@cs.utk.edu with any questions.* .. * * Purpose * ======= * * DPPSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to * compute the solution to a real system of linear equations * A * X = B, * where A is an N-by-N symmetric positive definite matrix stored in * packed format and X and B are N-by-NRHS matrices. * * Error bounds on the solution and a condition estimate are also * provided. * * Description * =========== * * The following steps are performed: * * 1. If FACT = 'E', real scaling factors are computed to equilibrate * the system: * diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B * Whether or not the system will be equilibrated depends on the * scaling of the matrix A, but if equilibration is used, A is * overwritten by diag(S)*A*diag(S) and B by diag(S)*B. * * 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to * factor the matrix A (after equilibration if FACT = 'E') as * A = U**T* U, if UPLO = 'U', or * A = L * L**T, if UPLO = 'L', * where U is an upper triangular matrix and L is a lower triangular * matrix. * * 3. 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, steps 4-6 are skipped. * * 4. The system of equations is solved for X using the factored form * of A. * * 5. Iterative refinement is applied to improve the computed solution * matrix and calculate error bounds and backward error estimates * for it. * * 6. If equilibration was used, the matrix X is premultiplied by * diag(S) so that it solves the original system before * equilibration. * * Arguments * ========= * * FACT (input) CHARACTER*1 * Specifies whether or not the factored form of the matrix A is * supplied on entry, and if not, whether the matrix A should be * equilibrated before it is factored. * = 'F': On entry, AFP contains the factored form of A. * If EQUED = 'Y', the matrix A has been equilibrated * with scaling factors given by S. AP and AFP will not * be modified. * = 'N': The matrix A will be copied to AFP and factored. * = 'E': The matrix A will be equilibrated if necessary, then * copied to AFP and factored. * * UPLO (input) CHARACTER*1 * = 'U': Upper triangle of A is stored; * = 'L': Lower triangle of A is stored. * * N (input) INTEGER * The number of linear equations, i.e., 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/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) * On entry, the upper or lower triangle of the symmetric matrix * A, packed columnwise in a linear array, except if FACT = 'F' * and EQUED = 'Y', then A must contain the equilibrated matrix * diag(S)*A*diag(S). The j-th column of A is stored in the * array AP as 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. * See below for further details. A is not modified if * FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. * * On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by * diag(S)*A*diag(S). * * AFP (input or output) DOUBLE PRECISION array, dimension * (N*(N+1)/2) * If FACT = 'F', then AFP is an input argument and on entry * contains the triangular factor U or L from the Cholesky * factorization A = U'*U or A = L*L', in the same storage * format as A. If EQUED .ne. 'N', then AFP is the factored * form of the equilibrated matrix A. * * If FACT = 'N', then AFP is an output argument and on exit * returns the triangular factor U or L from the Cholesky * factorization A = U'*U or A = L*L' of the original matrix A. * * If FACT = 'E', then AFP is an output argument and on exit * returns the triangular factor U or L from the Cholesky * factorization A = U'*U or A = L*L' of the equilibrated * matrix A (see the description of AP for the form of the * equilibrated matrix). * * EQUED (input or output) CHARACTER*1 * Specifies the form of equilibration that was done. * = 'N': No equilibration (always true if FACT = 'N'). * = 'Y': Equilibration was done, i.e., A has been replaced by * diag(S) * A * diag(S). * EQUED is an input argument if FACT = 'F'; otherwise, it is an * output argument. * * S (input or output) DOUBLE PRECISION array, dimension (N) * The scale factors for A; not accessed if EQUED = 'N'. S is * an input argument if FACT = 'F'; otherwise, S is an output * argument. If FACT = 'F' and EQUED = 'Y', each element of S * must be positive. * * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) * On entry, the N-by-NRHS right hand side matrix B. * On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', * B is overwritten by diag(S) * B. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) * If INFO = 0, the N-by-NRHS solution matrix X to the original * system of equations. Note that if EQUED = 'Y', A and B are * modified on exit, and the solution to the equilibrated system * is inv(diag(S))*X. * * LDX (input) INTEGER * The leading dimension of the array X. LDX >= max(1,N). * * RCOND (output) DOUBLE PRECISION * The estimate of the reciprocal condition number of the matrix * A after equilibration (if done). If RCOND is less than the * machine precision (in particular, if RCOND = 0), the matrix * is singular to working precision. This condition is * indicated by a return code of INFO > 0, and the solution and * error bounds are not computed. * * 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) DOUBLE PRECISION array, dimension (3*N) * * IWORK (workspace) INTEGER array, dimension (N) * * INFO (output) INTEGER * = 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 definite, so the factorization * could not be completed, and the solution and * error bounds could not be computed. * = N+1: RCOND is less than machine precision. The * factorization has been completed, but the matrix * is singular to working precision, and the * solution and error bounds have not been computed. * * Further Details * =============== * * The packed storage scheme is illustrated by the following example * when N = 4, UPLO = 'U': * * Two-dimensional storage of the symmetric matrix A: * * a11 a12 a13 a14 * a22 a23 a24 * a33 a34 (aij = conjg(aji)) * a44 * * Packed storage of the upper triangle of A: * * AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] * * ===================================================================== * * .. Parameters ..
Dppsvx()
dppsvx(String, String, int, int, double[], int, double[], int, StringW, double[], int, double[], int, int, double[], int, int, doubleW, double[], int, double[], int, double[], int, int[], int, intW)
Dppsvx
public Dppsvx()
dppsvx
public static void dppsvx(String fact,
String uplo,
int n,
int nrhs,
double ap[],
int _ap_offset,
double afp[],
int _afp_offset,
StringW equed,
double s[],
int _s_offset,
double b[],
int _b_offset,
int ldb,
double x[],
int _x_offset,
int ldx,
doubleW rcond,
double ferr[],
int _ferr_offset,
double berr[],
int _berr_offset,
double work[],
int _work_offset,
int iwork[],
int _iwork_offset,
intW info)
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