#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cggrqf_(integer *m, integer *p, integer *n, complex *a, integer *lda, complex *taua, complex *b, integer *ldb, complex *taub, complex *work, integer *lwork, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CGGRQF 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 unitary matrix, Z is a P-by-P unitary 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 conjugate 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) COMPLEX 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 unitary 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) COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the unitary matrix Q (see Further Details). B (input/output) COMPLEX 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 unitary 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) COMPLEX array, dimension (min(P,N)) The scalar factors of the elementary reflectors which represent the unitary matrix Z (see Further Details). WORK (workspace/output) COMPLEX 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 CUNMRQ. 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 (output) INTEGER = 0: successful exit < 0: if INFO=-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 complex scalar, and v is a complex 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 CUNGRQ. To use Q to update another matrix, use LAPACK subroutine CUNMRQ. 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 complex scalar, and v is a complex 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 CUNGQR. To use Z to update another matrix, use LAPACK subroutine CUNMQR. ===================================================================== Test the input parameters Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; /* Local variables */ static integer lopt, nb; extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), cgerqf_( integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); static integer nb1, nb2, nb3; extern /* Subroutine */ int cunmrq_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *); static integer lwkopt; static logical lquery; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --taua; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; --taub; --work; /* Function Body */ *info = 0; nb1 = ilaenv_(&c__1, "CGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); nb2 = ilaenv_(&c__1, "CGEQRF", " ", p, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); nb3 = ilaenv_(&c__1, "CUNMRQ", " ", m, n, p, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = max(nb1,nb2); nb = max(i__1,nb3); /* Computing MAX */ i__1 = max(*n,*m); lwkopt = max(i__1,*p) * nb; work[1].r = (real) lwkopt, work[1].i = 0.f; lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*p < 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*lda < max(1,*m)) { *info = -5; } else if (*ldb < max(1,*p)) { *info = -8; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = max(1,*m), i__1 = max(i__1,*p); if (*lwork < max(i__1,*n) && ! lquery) { *info = -11; } } if (*info != 0) { i__1 = -(*info); xerbla_("CGGRQF", &i__1); return 0; } else if (lquery) { return 0; } /* RQ factorization of M-by-N matrix A: A = R*Q */ cgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info); lopt = work[1].r; /* Update B := B*Q' Computing MAX */ i__1 = 1, i__2 = *m - *n + 1; i__3 = min(*m,*n); cunmrq_("Right", "Conjugate Transpose", p, n, &i__3, &a_ref(max(i__1,i__2) , 1), lda, &taua[1], &b[b_offset], ldb, &work[1], lwork, info); /* Computing MAX */ i__1 = lopt, i__2 = (integer) work[1].r; lopt = max(i__1,i__2); /* QR factorization of P-by-N matrix B: B = Z*T */ cgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info); /* Computing MAX */ i__2 = lopt, i__3 = (integer) work[1].r; i__1 = max(i__2,i__3); work[1].r = (real) i__1, work[1].i = 0.f; return 0; /* End of CGGRQF */ } /* cggrqf_ */ #undef a_ref #undef a_subscr