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#include "rb_lapack.h"
extern VOID zggsvd_(char* jobu, char* jobv, char* jobq, integer* m, integer* n, integer* p, integer* k, integer* l, doublecomplex* a, integer* lda, doublecomplex* b, integer* ldb, doublereal* alpha, doublereal* beta, doublecomplex* u, integer* ldu, doublecomplex* v, integer* ldv, doublecomplex* q, integer* ldq, doublecomplex* work, doublereal* rwork, integer* iwork, integer* info);
static VALUE
rblapack_zggsvd(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobu;
char jobu;
VALUE rblapack_jobv;
char jobv;
VALUE rblapack_jobq;
char jobq;
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_k;
integer k;
VALUE rblapack_l;
integer l;
VALUE rblapack_alpha;
doublereal *alpha;
VALUE rblapack_beta;
doublereal *beta;
VALUE rblapack_u;
doublecomplex *u;
VALUE rblapack_v;
doublecomplex *v;
VALUE rblapack_q;
doublecomplex *q;
VALUE rblapack_iwork;
integer *iwork;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublecomplex *a_out__;
VALUE rblapack_b_out__;
doublecomplex *b_out__;
doublecomplex *work;
doublereal *rwork;
integer lda;
integer n;
integer ldb;
integer ldu;
integer m;
integer ldv;
integer p;
integer ldq;
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 k, l, alpha, beta, u, v, q, iwork, info, a, b = NumRu::Lapack.zggsvd( jobu, jobv, jobq, a, b, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B, LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, RWORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZGGSVD computes the generalized singular value decomposition (GSVD)\n* of an M-by-N complex matrix A and P-by-N complex matrix B:\n*\n* U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R )\n*\n* where U, V and Q are unitary matrices, and Z' means the conjugate\n* transpose of Z. Let K+L = the effective numerical rank of the\n* matrix (A',B')', then R is a (K+L)-by-(K+L) nonsingular upper\n* triangular matrix, D1 and D2 are M-by-(K+L) and P-by-(K+L) \"diagonal\"\n* matrices and of the following structures, respectively:\n*\n* If M-K-L >= 0,\n*\n* K L\n* D1 = K ( I 0 )\n* L ( 0 C )\n* M-K-L ( 0 0 )\n*\n* K L\n* D2 = L ( 0 S )\n* P-L ( 0 0 )\n*\n* N-K-L K L\n* ( 0 R ) = K ( 0 R11 R12 )\n* L ( 0 0 R22 )\n* where\n*\n* C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),\n* S = diag( BETA(K+1), ... , BETA(K+L) ),\n* C**2 + S**2 = I.\n*\n* R is stored in A(1:K+L,N-K-L+1:N) on exit.\n*\n* If M-K-L < 0,\n*\n* K M-K K+L-M\n* D1 = K ( I 0 0 )\n* M-K ( 0 C 0 )\n*\n* K M-K K+L-M\n* D2 = M-K ( 0 S 0 )\n* K+L-M ( 0 0 I )\n* P-L ( 0 0 0 )\n*\n* N-K-L K M-K K+L-M\n* ( 0 R ) = K ( 0 R11 R12 R13 )\n* M-K ( 0 0 R22 R23 )\n* K+L-M ( 0 0 0 R33 )\n*\n* where\n*\n* C = diag( ALPHA(K+1), ... , ALPHA(M) ),\n* S = diag( BETA(K+1), ... , BETA(M) ),\n* C**2 + S**2 = I.\n*\n* (R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored\n* ( 0 R22 R23 )\n* in B(M-K+1:L,N+M-K-L+1:N) on exit.\n*\n* The routine computes C, S, R, and optionally the unitary\n* transformation matrices U, V and Q.\n*\n* In particular, if B is an N-by-N nonsingular matrix, then the GSVD of\n* A and B implicitly gives the SVD of A*inv(B):\n* A*inv(B) = U*(D1*inv(D2))*V'.\n* If ( A',B')' has orthnormal columns, then the GSVD of A and B is also\n* equal to the CS decomposition of A and B. Furthermore, the GSVD can\n* be used to derive the solution of the eigenvalue problem:\n* A'*A x = lambda* B'*B x.\n* In some literature, the GSVD of A and B is presented in the form\n* U'*A*X = ( 0 D1 ), V'*B*X = ( 0 D2 )\n* where U and V are orthogonal and X is nonsingular, and D1 and D2 are\n* ``diagonal''. The former GSVD form can be converted to the latter\n* form by taking the nonsingular matrix X as\n*\n* X = Q*( I 0 )\n* ( 0 inv(R) )\n*\n\n* Arguments\n* =========\n*\n* JOBU (input) CHARACTER*1\n* = 'U': Unitary matrix U is computed;\n* = 'N': U is not computed.\n*\n* JOBV (input) CHARACTER*1\n* = 'V': Unitary matrix V is computed;\n* = 'N': V is not computed.\n*\n* JOBQ (input) CHARACTER*1\n* = 'Q': Unitary matrix Q is computed;\n* = 'N': Q is not computed.\n*\n* M (input) INTEGER\n* The number of rows of the matrix A. M >= 0.\n*\n* N (input) INTEGER\n* The number of columns of the matrices A and B. N >= 0.\n*\n* P (input) INTEGER\n* The number of rows of the matrix B. P >= 0.\n*\n* K (output) INTEGER\n* L (output) INTEGER\n* On exit, K and L specify the dimension of the subblocks\n* described in Purpose.\n* K + L = effective numerical rank of (A',B')'.\n*\n* A (input/output) COMPLEX*16 array, dimension (LDA,N)\n* On entry, the M-by-N matrix A.\n* On exit, A contains the triangular matrix R, or part of R.\n* See Purpose for details.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,M).\n*\n* B (input/output) COMPLEX*16 array, dimension (LDB,N)\n* On entry, the P-by-N matrix B.\n* On exit, B contains part of the triangular matrix R if\n* M-K-L < 0. See Purpose for details.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,P).\n*\n* ALPHA (output) DOUBLE PRECISION array, dimension (N)\n* BETA (output) DOUBLE PRECISION array, dimension (N)\n* On exit, ALPHA and BETA contain the generalized singular\n* value pairs of A and B;\n* ALPHA(1:K) = 1,\n* BETA(1:K) = 0,\n* and if M-K-L >= 0,\n* ALPHA(K+1:K+L) = C,\n* BETA(K+1:K+L) = S,\n* or if M-K-L < 0,\n* ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0\n* BETA(K+1:M) = S, BETA(M+1:K+L) = 1\n* and\n* ALPHA(K+L+1:N) = 0\n* BETA(K+L+1:N) = 0\n*\n* U (output) COMPLEX*16 array, dimension (LDU,M)\n* If JOBU = 'U', U contains the M-by-M unitary matrix U.\n* If JOBU = 'N', U is not referenced.\n*\n* LDU (input) INTEGER\n* The leading dimension of the array U. LDU >= max(1,M) if\n* JOBU = 'U'; LDU >= 1 otherwise.\n*\n* V (output) COMPLEX*16 array, dimension (LDV,P)\n* If JOBV = 'V', V contains the P-by-P unitary matrix V.\n* If JOBV = 'N', V is not referenced.\n*\n* LDV (input) INTEGER\n* The leading dimension of the array V. LDV >= max(1,P) if\n* JOBV = 'V'; LDV >= 1 otherwise.\n*\n* Q (output) COMPLEX*16 array, dimension (LDQ,N)\n* If JOBQ = 'Q', Q contains the N-by-N unitary matrix Q.\n* If JOBQ = 'N', Q is not referenced.\n*\n* LDQ (input) INTEGER\n* The leading dimension of the array Q. LDQ >= max(1,N) if\n* JOBQ = 'Q'; LDQ >= 1 otherwise.\n*\n* WORK (workspace) COMPLEX*16 array, dimension (max(3*N,M,P)+N)\n*\n* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)\n*\n* IWORK (workspace/output) INTEGER array, dimension (N)\n* On exit, IWORK stores the sorting information. More\n* precisely, the following loop will sort ALPHA\n* for I = K+1, min(M,K+L)\n* swap ALPHA(I) and ALPHA(IWORK(I))\n* endfor\n* such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(N).\n*\n* INFO (output) INTEGER\n* = 0: successful exit.\n* < 0: if INFO = -i, the i-th argument had an illegal value.\n* > 0: if INFO = 1, the Jacobi-type procedure failed to\n* converge. For further details, see subroutine ZTGSJA.\n*\n* Internal Parameters\n* ===================\n*\n* TOLA DOUBLE PRECISION\n* TOLB DOUBLE PRECISION\n* TOLA and TOLB are the thresholds to determine the effective\n* rank of (A',B')'. Generally, they are set to\n* TOLA = MAX(M,N)*norm(A)*MAZHEPS,\n* TOLB = MAX(P,N)*norm(B)*MAZHEPS.\n* The size of TOLA and TOLB may affect the size of backward\n* errors of the decomposition.\n*\n\n* Further Details\n* ===============\n*\n* 2-96 Based on modifications by\n* Ming Gu and Huan Ren, Computer Science Division, University of\n* California at Berkeley, USA\n*\n* =====================================================================\n*\n* .. Local Scalars ..\n LOGICAL WANTQ, WANTU, WANTV\n INTEGER I, IBND, ISUB, J, NCYCLE\n DOUBLE PRECISION ANORM, BNORM, SMAX, TEMP, TOLA, TOLB, ULP, UNFL\n* ..\n* .. External Functions ..\n LOGICAL LSAME\n DOUBLE PRECISION DLAMCH, ZLANGE\n EXTERNAL LSAME, DLAMCH, ZLANGE\n* ..\n* .. External Subroutines ..\n EXTERNAL DCOPY, XERBLA, ZGGSVP, ZTGSJA\n* ..\n* .. Intrinsic Functions ..\n INTRINSIC MAX, MIN\n* ..\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n k, l, alpha, beta, u, v, q, iwork, info, a, b = NumRu::Lapack.zggsvd( jobu, jobv, jobq, a, b, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 5 && argc != 5)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 5)", argc);
rblapack_jobu = argv[0];
rblapack_jobv = argv[1];
rblapack_jobq = argv[2];
rblapack_a = argv[3];
rblapack_b = argv[4];
if (argc == 5) {
} else if (rblapack_options != Qnil) {
} else {
}
jobu = StringValueCStr(rblapack_jobu)[0];
jobq = StringValueCStr(rblapack_jobq)[0];
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (5th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (5th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
n = 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*);
p = ldb;
jobv = StringValueCStr(rblapack_jobv)[0];
ldv = lsame_(&jobv,"V") ? MAX(1,p) : 1;
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (4th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (4th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
if (NA_SHAPE1(rblapack_a) != n)
rb_raise(rb_eRuntimeError, "shape 1 of a must be the same as shape 1 of b");
if (NA_TYPE(rblapack_a) != NA_DCOMPLEX)
rblapack_a = na_change_type(rblapack_a, NA_DCOMPLEX);
a = NA_PTR_TYPE(rblapack_a, doublecomplex*);
ldq = lsame_(&jobq,"Q") ? MAX(1,n) : 1;
m = lda;
ldu = lsame_(&jobu,"U") ? MAX(1,m) : 1;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_alpha = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
alpha = NA_PTR_TYPE(rblapack_alpha, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_beta = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
beta = NA_PTR_TYPE(rblapack_beta, doublereal*);
{
na_shape_t shape[2];
shape[0] = ldu;
shape[1] = m;
rblapack_u = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
u = NA_PTR_TYPE(rblapack_u, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = ldv;
shape[1] = p;
rblapack_v = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
v = NA_PTR_TYPE(rblapack_v, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = ldq;
shape[1] = n;
rblapack_q = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
q = NA_PTR_TYPE(rblapack_q, doublecomplex*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_iwork = na_make_object(NA_LINT, 1, shape, cNArray);
}
iwork = NA_PTR_TYPE(rblapack_iwork, integer*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = n;
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] = n;
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__;
work = ALLOC_N(doublecomplex, (MAX(3*n,m)*(p)+n));
rwork = ALLOC_N(doublereal, (2*n));
zggsvd_(&jobu, &jobv, &jobq, &m, &n, &p, &k, &l, a, &lda, b, &ldb, alpha, beta, u, &ldu, v, &ldv, q, &ldq, work, rwork, iwork, &info);
free(work);
free(rwork);
rblapack_k = INT2NUM(k);
rblapack_l = INT2NUM(l);
rblapack_info = INT2NUM(info);
return rb_ary_new3(11, rblapack_k, rblapack_l, rblapack_alpha, rblapack_beta, rblapack_u, rblapack_v, rblapack_q, rblapack_iwork, rblapack_info, rblapack_a, rblapack_b);
}
void
init_lapack_zggsvd(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zggsvd", rblapack_zggsvd, -1);
}
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