cggqrf-f(3)

cggqrf.f –

Synopsis

Functions/Subroutines

subroutine cggqrf (N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO)
CGGQRF

Function/Subroutine Documentation

subroutine cggqrf (integerN, integerM, integerP, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAUA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( * )TAUB, complex, dimension( * )WORK, integerLWORK, integerINFO)

CGGQRF

Purpose:

 CGGQRF computes a generalized QR factorization of an N-by-M matrix A
 and an N-by-P matrix B:
 A = Q*R, B = Q*T*Z,
 where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix,
 and R and T assume one of the forms:
 if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,
 ( 0 ) N-M N M-N
 M
 where R11 is upper triangular, and
 if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P,
 P-N N ( T21 ) P
 P
 where T12 or T21 is upper triangular.
 In particular, if B is square and nonsingular, the GQR factorization
 of A and B implicitly gives the QR factorization of inv(B)*A:
 inv(B)*A = Z**H * (inv(T)*R)
 where inv(B) denotes the inverse of the matrix B, and Z' denotes the
 conjugate transpose of matrix Z.

Parameters:

 N is INTEGER
 The number of rows of the matrices A and B. N >= 0.

 M is INTEGER
 The number of columns of the matrix A. M >= 0.

 P is INTEGER
 The number of columns of the matrix B. P >= 0.

 A is COMPLEX array, dimension (LDA,M)
 On entry, the N-by-M matrix A.
 On exit, the elements on and above the diagonal of the array
 contain the min(N,M)-by-M upper trapezoidal matrix R (R is
 upper triangular if N >= M); the elements below the diagonal,
 with the array TAUA, represent the unitary matrix Q as a
 product of min(N,M) elementary reflectors (see Further
 Details).

LDA

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(1,N).

TAUA

 TAUA is COMPLEX array, dimension (min(N,M))
 The scalar factors of the elementary reflectors which
 represent the unitary matrix Q (see Further Details).

 B is COMPLEX array, dimension (LDB,P)
 On entry, the N-by-P matrix B.
 On exit, if N <= P, the upper triangle of the subarray
 B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
 if N > P, the elements on and above the (N-P)-th subdiagonal
 contain the N-by-P upper trapezoidal matrix T; the remaining
 elements, with the array TAUB, represent the unitary
 matrix Z as a product of elementary reflectors (see Further
 Details).

LDB

 LDB is INTEGER
 The leading dimension of the array B. LDB >= max(1,N).

TAUB

 TAUB is COMPLEX array, dimension (min(N,P))
 The scalar factors of the elementary reflectors which
 represent the unitary matrix Z (see Further Details).

WORK

 WORK is COMPLEX array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is 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 QR factorization
 of an N-by-M matrix, NB2 is the optimal blocksize for the
 RQ factorization of an N-by-P matrix, and NB3 is the optimal
 blocksize for a call of CUNMQR.
 If LWORK = -1, then a workspace query is assumed; the routine
 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 LWORK is issued by XERBLA.

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details:

 The matrix Q is represented as a product of elementary reflectors
 Q = H(1) H(2) . . . H(k), where k = min(n,m).
 Each H(i) has the form
 H(i) = I - taua * v * v**H
 where taua is a complex scalar, and v is a complex vector with
 v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
 and taua in TAUA(i).
 To form Q explicitly, use LAPACK subroutine CUNGQR.
 To use Q to update another matrix, use LAPACK subroutine CUNMQR.
 The matrix Z is represented as a product of elementary reflectors
 Z = H(1) H(2) . . . H(k), where k = min(n,p).
 Each H(i) has the form
 H(i) = I - taub * v * v**H
 where taub is a complex scalar, and v is a complex vector with
 v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
 B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
 To form Z explicitly, use LAPACK subroutine CUNGRQ.
 To use Z to update another matrix, use LAPACK subroutine CUNMRQ.

Definition at line 215 of file cggqrf.f.

Author

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