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java.lang.Object | +----org.netlib.lapack.DGGRQF
DGGRQF is a simplified interface to the JLAPACK routine dggrqf. This interface converts Java-style 2D row-major arrays into the 1D column-major linearized arrays expected by the lower level JLAPACK routines. Using this interface also allows you to omit offset and leading dimension arguments. However, because of these conversions, these routines will be slower than the low level ones. Following is the description from the original Fortran source. Contact seymour@cs.utk.edu with any questions.* .. * * Purpose * ======= * * DGGRQF computes a generalized RQ factorization of an M-by-N matrix A * and a P-by-N matrix B: * * A = R*Q, B = Z*T*Q, * * where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal * matrix, and R and T assume one of the forms: * * if M <= N, R = ( 0 R12 ) M, or if M > N, R = ( R11 ) M-N, * N-M M ( R21 ) N * N * * where R12 or R21 is upper triangular, and * * if P >= N, T = ( T11 ) N , or if P < N, T = ( T11 T12 ) P, * ( 0 ) P-N P N-P * N * * where T11 is upper triangular. * * In particular, if B is square and nonsingular, the GRQ factorization * of A and B implicitly gives the RQ factorization of A*inv(B): * * A*inv(B) = (R*inv(T))*Z' * * where inv(B) denotes the inverse of the matrix B, and Z' denotes the * transpose of the matrix Z. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix A. M >= 0. * * P (input) INTEGER * The number of rows of the matrix B. P >= 0. * * N (input) INTEGER * The number of columns of the matrices A and B. N >= 0. * * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) * On entry, the M-by-N matrix A. * On exit, if M <= N, the upper triangle of the subarray * A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R; * if M > N, the elements on and above the (M-N)-th subdiagonal * contain the M-by-N upper trapezoidal matrix R; the remaining * elements, with the array TAUA, represent the orthogonal * matrix Q as a product of elementary reflectors (see Further * Details). * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M). * * TAUA (output) DOUBLE PRECISION array, dimension (min(M,N)) * The scalar factors of the elementary reflectors which * represent the orthogonal matrix Q (see Further Details). * * B (input/output) DOUBLE PRECISION array, dimension (LDB,N) * On entry, the P-by-N matrix B. * On exit, the elements on and above the diagonal of the array * contain the min(P,N)-by-N upper trapezoidal matrix T (T is * upper triangular if P >= N); the elements below the diagonal, * with the array TAUB, represent the orthogonal matrix Z as a * product of elementary reflectors (see Further Details). * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,P). * * TAUB (output) DOUBLE PRECISION array, dimension (min(P,N)) * The scalar factors of the elementary reflectors which * represent the orthogonal matrix Z (see Further Details). * * WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The dimension of the array WORK. LWORK >= max(1,N,M,P). * For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), * where NB1 is the optimal blocksize for the RQ factorization * of an M-by-N matrix, NB2 is the optimal blocksize for the * QR factorization of a P-by-N matrix, and NB3 is the optimal * blocksize for a call of DORMRQ. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INF0= -i, the i-th argument had an illegal value. * * Further Details * =============== * * The matrix Q is represented as a product of elementary reflectors * * Q = H(1) H(2) . . . H(k), where k = min(m,n). * * Each H(i) has the form * * H(i) = I - taua * v * v' * * where taua is a real scalar, and v is a real vector with * v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in * A(m-k+i,1:n-k+i-1), and taua in TAUA(i). * To form Q explicitly, use LAPACK subroutine DORGRQ. * To use Q to update another matrix, use LAPACK subroutine DORMRQ. * * The matrix Z is represented as a product of elementary reflectors * * Z = H(1) H(2) . . . H(k), where k = min(p,n). * * Each H(i) has the form * * H(i) = I - taub * v * v' * * where taub is a real scalar, and v is a real vector with * v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i), * and taub in TAUB(i). * To form Z explicitly, use LAPACK subroutine DORGQR. * To use Z to update another matrix, use LAPACK subroutine DORMQR. * * ===================================================================== * * .. Local Scalars ..
DGGRQF()
DGGRQF(int, int, int, double[][], double[], double[][], double[], double[], int, intW)
DGGRQF
public DGGRQF()
DGGRQF
public static void DGGRQF(int m,
int p,
int n,
double a[][],
double taua[],
double b[][],
double taub[],
double work[],
int lwork,
intW info)
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