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#include "rb_lapack.h"
extern VOID zggqrf_(integer* n, integer* m, integer* p, doublecomplex* a, integer* lda, doublecomplex* taua, doublecomplex* b, integer* ldb, doublecomplex* taub, doublecomplex* work, integer* lwork, integer* info);
static VALUE
rblapack_zggqrf(int argc, VALUE *argv, VALUE self){
VALUE rblapack_n;
integer n;
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_taua;
doublecomplex *taua;
VALUE rblapack_taub;
doublecomplex *taub;
VALUE rblapack_work;
doublecomplex *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublecomplex *a_out__;
VALUE rblapack_b_out__;
doublecomplex *b_out__;
integer lda;
integer m;
integer ldb;
integer p;
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.zggqrf( n, a, b, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZGGQRF computes a generalized QR factorization of an N-by-M matrix A\n* and an N-by-P matrix B:\n*\n* A = Q*R, B = Q*T*Z,\n*\n* where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix,\n* and R and T assume one of the forms:\n*\n* if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,\n* ( 0 ) N-M N M-N\n* M\n*\n* where R11 is upper triangular, and\n*\n* if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P,\n* P-N N ( T21 ) P\n* P\n*\n* where T12 or T21 is upper triangular.\n*\n* In particular, if B is square and nonsingular, the GQR factorization\n* of A and B implicitly gives the QR factorization of inv(B)*A:\n*\n* inv(B)*A = Z'*(inv(T)*R)\n*\n* where inv(B) denotes the inverse of the matrix B, and Z' denotes the\n* conjugate transpose of matrix Z.\n*\n\n* Arguments\n* =========\n*\n* N (input) INTEGER\n* The number of rows of the matrices A and B. N >= 0.\n*\n* M (input) INTEGER\n* The number of columns of the matrix A. M >= 0.\n*\n* P (input) INTEGER\n* The number of columns of the matrix B. P >= 0.\n*\n* A (input/output) COMPLEX*16 array, dimension (LDA,M)\n* On entry, the N-by-M matrix A.\n* On exit, the elements on and above the diagonal of the array\n* contain the min(N,M)-by-M upper trapezoidal matrix R (R is\n* upper triangular if N >= M); the elements below the diagonal,\n* with the array TAUA, represent the unitary matrix Q as a\n* product of min(N,M) elementary reflectors (see Further\n* Details).\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,N).\n*\n* TAUA (output) COMPLEX*16 array, dimension (min(N,M))\n* The scalar factors of the elementary reflectors which\n* represent the unitary matrix Q (see Further Details).\n*\n* B (input/output) COMPLEX*16 array, dimension (LDB,P)\n* On entry, the N-by-P matrix B.\n* On exit, if N <= P, the upper triangle of the subarray\n* B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;\n* if N > P, the elements on and above the (N-P)-th subdiagonal\n* contain the N-by-P upper trapezoidal matrix T; the remaining\n* elements, with the array TAUB, represent the unitary\n* matrix Z as a product of elementary reflectors (see Further\n* Details).\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,N).\n*\n* TAUB (output) COMPLEX*16 array, dimension (min(N,P))\n* The scalar factors of the elementary reflectors which\n* represent the unitary matrix Z (see Further Details).\n*\n* WORK (workspace/output) COMPLEX*16 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 QR factorization\n* of an N-by-M matrix, NB2 is the optimal blocksize for the\n* RQ factorization of an N-by-P matrix, and NB3 is the optimal\n* blocksize for a call of ZUNMQR.\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 INFO = -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(n,m).\n*\n* Each H(i) has the form\n*\n* H(i) = I - taua * v * v'\n*\n* where taua is a complex scalar, and v is a complex vector with\n* v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),\n* and taua in TAUA(i).\n* To form Q explicitly, use LAPACK subroutine ZUNGQR.\n* To use Q to update another matrix, use LAPACK subroutine ZUNMQR.\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(n,p).\n*\n* Each H(i) has the form\n*\n* H(i) = I - taub * v * v'\n*\n* where taub is a complex scalar, and v is a complex vector with\n* v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in\n* B(n-k+i,1:p-k+i-1), and taub in TAUB(i).\n* To form Z explicitly, use LAPACK subroutine ZUNGRQ.\n* To use Z to update another matrix, use LAPACK subroutine ZUNMRQ.\n*\n* =====================================================================\n*\n* .. Local Scalars ..\n LOGICAL LQUERY\n INTEGER LOPT, LWKOPT, NB, NB1, NB2, NB3\n* ..\n* .. External Subroutines ..\n EXTERNAL XERBLA, ZGEQRF, ZGERQF, ZUNMQR\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.zggqrf( n, a, b, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 3 && argc != 4)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 3)", argc);
rblapack_n = argv[0];
rblapack_a = argv[1];
rblapack_b = argv[2];
if (argc == 4) {
rblapack_lwork = argv[3];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
n = NUM2INT(rblapack_n);
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (3th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (3th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
p = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_DCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_DCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, doublecomplex*);
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (2th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (2th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
m = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_DCOMPLEX)
rblapack_a = na_change_type(rblapack_a, NA_DCOMPLEX);
a = NA_PTR_TYPE(rblapack_a, doublecomplex*);
if (rblapack_lwork == Qnil)
lwork = MAX(MAX(n,m),p);
else {
lwork = NUM2INT(rblapack_lwork);
}
{
na_shape_t shape[1];
shape[0] = MIN(n,m);
rblapack_taua = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
taua = NA_PTR_TYPE(rblapack_taua, doublecomplex*);
{
na_shape_t shape[1];
shape[0] = MIN(n,p);
rblapack_taub = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
taub = NA_PTR_TYPE(rblapack_taub, doublecomplex*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = m;
rblapack_a_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, doublecomplex*);
MEMCPY(a_out__, a, doublecomplex, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = p;
rblapack_b_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, doublecomplex*);
MEMCPY(b_out__, b, doublecomplex, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
zggqrf_(&n, &m, &p, 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_zggqrf(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zggqrf", rblapack_zggqrf, -1);
}
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