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#include "rb_lapack.h"
extern VOID sggrqf_(integer* m, integer* p, integer* n, real* a, integer* lda, real* taua, real* b, integer* ldb, real* taub, real* work, integer* lwork, integer* info);
static VALUE
rblapack_sggrqf(int argc, VALUE *argv, VALUE self){
VALUE rblapack_m;
integer m;
VALUE rblapack_p;
integer p;
VALUE rblapack_a;
real *a;
VALUE rblapack_b;
real *b;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_taua;
real *taua;
VALUE rblapack_taub;
real *taub;
VALUE rblapack_work;
real *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
real *a_out__;
VALUE rblapack_b_out__;
real *b_out__;
integer lda;
integer n;
integer ldb;
VALUE rblapack_options;
if (argc > 0 && TYPE(argv[argc-1]) == T_HASH) {
argc--;
rblapack_options = argv[argc];
if (rb_hash_aref(rblapack_options, sHelp) == Qtrue) {
printf("%s\n", "USAGE:\n taua, taub, work, info, a, b = NumRu::Lapack.sggrqf( m, p, a, b, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO )\n\n* Purpose\n* =======\n*\n* SGGRQF computes a generalized RQ factorization of an M-by-N matrix A\n* and a P-by-N matrix B:\n*\n* A = R*Q, B = Z*T*Q,\n*\n* where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal\n* matrix, and R and T assume one of the forms:\n*\n* if M <= N, R = ( 0 R12 ) M, or if M > N, R = ( R11 ) M-N,\n* N-M M ( R21 ) N\n* N\n*\n* where R12 or R21 is upper triangular, and\n*\n* if P >= N, T = ( T11 ) N , or if P < N, T = ( T11 T12 ) P,\n* ( 0 ) P-N P N-P\n* N\n*\n* where T11 is upper triangular.\n*\n* In particular, if B is square and nonsingular, the GRQ factorization\n* of A and B implicitly gives the RQ factorization of A*inv(B):\n*\n* A*inv(B) = (R*inv(T))*Z'\n*\n* where inv(B) denotes the inverse of the matrix B, and Z' denotes the\n* transpose of the matrix Z.\n*\n\n* Arguments\n* =========\n*\n* M (input) INTEGER\n* The number of rows of the matrix A. M >= 0.\n*\n* P (input) INTEGER\n* The number of rows of the matrix B. P >= 0.\n*\n* N (input) INTEGER\n* The number of columns of the matrices A and B. N >= 0.\n*\n* A (input/output) REAL array, dimension (LDA,N)\n* On entry, the M-by-N matrix A.\n* On exit, if M <= N, the upper triangle of the subarray\n* A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R;\n* if M > N, the elements on and above the (M-N)-th subdiagonal\n* contain the M-by-N upper trapezoidal matrix R; the remaining\n* elements, with the array TAUA, represent the orthogonal\n* matrix Q as a product of elementary reflectors (see Further\n* Details).\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,M).\n*\n* TAUA (output) REAL array, dimension (min(M,N))\n* The scalar factors of the elementary reflectors which\n* represent the orthogonal matrix Q (see Further Details).\n*\n* B (input/output) REAL array, dimension (LDB,N)\n* On entry, the P-by-N matrix B.\n* On exit, the elements on and above the diagonal of the array\n* contain the min(P,N)-by-N upper trapezoidal matrix T (T is\n* upper triangular if P >= N); the elements below the diagonal,\n* with the array TAUB, represent the orthogonal matrix Z as a\n* product of elementary reflectors (see Further Details).\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,P).\n*\n* TAUB (output) REAL array, dimension (min(P,N))\n* The scalar factors of the elementary reflectors which\n* represent the orthogonal matrix Z (see Further Details).\n*\n* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))\n* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n*\n* LWORK (input) INTEGER\n* The dimension of the array WORK. LWORK >= max(1,N,M,P).\n* For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),\n* where NB1 is the optimal blocksize for the RQ factorization\n* of an M-by-N matrix, NB2 is the optimal blocksize for the\n* QR factorization of a P-by-N matrix, and NB3 is the optimal\n* blocksize for a call of SORMRQ.\n*\n* If LWORK = -1, then a workspace query is assumed; the routine\n* only calculates the optimal size of the WORK array, returns\n* this value as the first entry of the WORK array, and no error\n* message related to LWORK is issued by XERBLA.\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INF0= -i, the i-th argument had an illegal value.\n*\n\n* Further Details\n* ===============\n*\n* The matrix Q is represented as a product of elementary reflectors\n*\n* Q = H(1) H(2) . . . H(k), where k = min(m,n).\n*\n* Each H(i) has the form\n*\n* H(i) = I - taua * v * v'\n*\n* where taua is a real scalar, and v is a real vector with\n* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in\n* A(m-k+i,1:n-k+i-1), and taua in TAUA(i).\n* To form Q explicitly, use LAPACK subroutine SORGRQ.\n* To use Q to update another matrix, use LAPACK subroutine SORMRQ.\n*\n* The matrix Z is represented as a product of elementary reflectors\n*\n* Z = H(1) H(2) . . . H(k), where k = min(p,n).\n*\n* Each H(i) has the form\n*\n* H(i) = I - taub * v * v'\n*\n* where taub is a real scalar, and v is a real vector with\n* v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),\n* and taub in TAUB(i).\n* To form Z explicitly, use LAPACK subroutine SORGQR.\n* To use Z to update another matrix, use LAPACK subroutine SORMQR.\n*\n* =====================================================================\n*\n* .. Local Scalars ..\n LOGICAL LQUERY\n INTEGER LOPT, LWKOPT, NB, NB1, NB2, NB3\n* ..\n* .. External Subroutines ..\n EXTERNAL SGEQRF, SGERQF, SORMRQ, XERBLA\n* ..\n* .. External Functions ..\n INTEGER ILAENV \n EXTERNAL ILAENV \n* ..\n* .. Intrinsic Functions ..\n INTRINSIC INT, MAX, MIN\n* ..\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n taua, taub, work, info, a, b = NumRu::Lapack.sggrqf( m, p, a, b, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 4 && argc != 5)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 4)", argc);
rblapack_m = argv[0];
rblapack_p = argv[1];
rblapack_a = argv[2];
rblapack_b = argv[3];
if (argc == 5) {
rblapack_lwork = argv[4];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
m = NUM2INT(rblapack_m);
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (3th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (3th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
n = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_SFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_SFLOAT);
a = NA_PTR_TYPE(rblapack_a, real*);
p = NUM2INT(rblapack_p);
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (4th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (4th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
if (NA_SHAPE1(rblapack_b) != n)
rb_raise(rb_eRuntimeError, "shape 1 of b must be the same as shape 1 of a");
if (NA_TYPE(rblapack_b) != NA_SFLOAT)
rblapack_b = na_change_type(rblapack_b, NA_SFLOAT);
b = NA_PTR_TYPE(rblapack_b, real*);
if (rblapack_lwork == Qnil)
lwork = MAX(MAX(n,m),p);
else {
lwork = NUM2INT(rblapack_lwork);
}
{
na_shape_t shape[1];
shape[0] = MIN(m,n);
rblapack_taua = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
taua = NA_PTR_TYPE(rblapack_taua, real*);
{
na_shape_t shape[1];
shape[0] = MIN(p,n);
rblapack_taub = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
taub = NA_PTR_TYPE(rblapack_taub, real*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, real*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = n;
rblapack_a_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, real*);
MEMCPY(a_out__, a, real, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = n;
rblapack_b_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, real*);
MEMCPY(b_out__, b, real, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
sggrqf_(&m, &p, &n, a, &lda, taua, b, &ldb, taub, work, &lwork, &info);
rblapack_info = INT2NUM(info);
return rb_ary_new3(6, rblapack_taua, rblapack_taub, rblapack_work, rblapack_info, rblapack_a, rblapack_b);
}
void
init_lapack_sggrqf(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sggrqf", rblapack_sggrqf, -1);
}
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