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#include "rb_lapack.h"
extern VOID slatrd_(char* uplo, integer* n, integer* nb, real* a, integer* lda, real* e, real* tau, real* w, integer* ldw);
static VALUE
rblapack_slatrd(int argc, VALUE *argv, VALUE self){
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_nb;
integer nb;
VALUE rblapack_a;
real *a;
VALUE rblapack_e;
real *e;
VALUE rblapack_tau;
real *tau;
VALUE rblapack_w;
real *w;
VALUE rblapack_a_out__;
real *a_out__;
integer lda;
integer n;
integer ldw;
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 e, tau, w, a = NumRu::Lapack.slatrd( uplo, nb, a, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )\n\n* Purpose\n* =======\n*\n* SLATRD reduces NB rows and columns of a real symmetric matrix A to\n* symmetric tridiagonal form by an orthogonal similarity\n* transformation Q' * A * Q, and returns the matrices V and W which are\n* needed to apply the transformation to the unreduced part of A.\n*\n* If UPLO = 'U', SLATRD reduces the last NB rows and columns of a\n* matrix, of which the upper triangle is supplied;\n* if UPLO = 'L', SLATRD reduces the first NB rows and columns of a\n* matrix, of which the lower triangle is supplied.\n*\n* This is an auxiliary routine called by SSYTRD.\n*\n\n* Arguments\n* =========\n*\n* UPLO (input) CHARACTER*1\n* Specifies whether the upper or lower triangular part of the\n* symmetric matrix A is stored:\n* = 'U': Upper triangular\n* = 'L': Lower triangular\n*\n* N (input) INTEGER\n* The order of the matrix A.\n*\n* NB (input) INTEGER\n* The number of rows and columns to be reduced.\n*\n* A (input/output) REAL array, dimension (LDA,N)\n* On entry, the symmetric matrix A. If UPLO = 'U', the leading\n* n-by-n upper triangular part of A contains the upper\n* triangular part of the matrix A, and the strictly lower\n* triangular part of A is not referenced. If UPLO = 'L', the\n* leading n-by-n lower triangular part of A contains the lower\n* triangular part of the matrix A, and the strictly upper\n* triangular part of A is not referenced.\n* On exit:\n* if UPLO = 'U', the last NB columns have been reduced to\n* tridiagonal form, with the diagonal elements overwriting\n* the diagonal elements of A; the elements above the diagonal\n* with the array TAU, represent the orthogonal matrix Q as a\n* product of elementary reflectors;\n* if UPLO = 'L', the first NB columns have been reduced to\n* tridiagonal form, with the diagonal elements overwriting\n* the diagonal elements of A; the elements below the diagonal\n* with the array TAU, represent the orthogonal matrix Q as a\n* product of elementary reflectors.\n* See Further Details.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= (1,N).\n*\n* E (output) REAL array, dimension (N-1)\n* If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal\n* elements of the last NB columns of the reduced matrix;\n* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of\n* the first NB columns of the reduced matrix.\n*\n* TAU (output) REAL array, dimension (N-1)\n* The scalar factors of the elementary reflectors, stored in\n* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.\n* See Further Details.\n*\n* W (output) REAL array, dimension (LDW,NB)\n* The n-by-nb matrix W required to update the unreduced part\n* of A.\n*\n* LDW (input) INTEGER\n* The leading dimension of the array W. LDW >= max(1,N).\n*\n\n* Further Details\n* ===============\n*\n* If UPLO = 'U', the matrix Q is represented as a product of elementary\n* reflectors\n*\n* Q = H(n) H(n-1) . . . H(n-nb+1).\n*\n* Each H(i) has the form\n*\n* H(i) = I - tau * v * v'\n*\n* where tau is a real scalar, and v is a real vector with\n* v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),\n* and tau in TAU(i-1).\n*\n* If UPLO = 'L', the matrix Q is represented as a product of elementary\n* reflectors\n*\n* Q = H(1) H(2) . . . H(nb).\n*\n* Each H(i) has the form\n*\n* H(i) = I - tau * v * v'\n*\n* where tau is a real scalar, and v is a real vector with\n* v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),\n* and tau in TAU(i).\n*\n* The elements of the vectors v together form the n-by-nb matrix V\n* which is needed, with W, to apply the transformation to the unreduced\n* part of the matrix, using a symmetric rank-2k update of the form:\n* A := A - V*W' - W*V'.\n*\n* The contents of A on exit are illustrated by the following examples\n* with n = 5 and nb = 2:\n*\n* if UPLO = 'U': if UPLO = 'L':\n*\n* ( a a a v4 v5 ) ( d )\n* ( a a v4 v5 ) ( 1 d )\n* ( a 1 v5 ) ( v1 1 a )\n* ( d 1 ) ( v1 v2 a a )\n* ( d ) ( v1 v2 a a a )\n*\n* where d denotes a diagonal element of the reduced matrix, a denotes\n* an element of the original matrix that is unchanged, and vi denotes\n* an element of the vector defining H(i).\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n e, tau, w, a = NumRu::Lapack.slatrd( uplo, nb, a, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 3 && argc != 3)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 3)", argc);
rblapack_uplo = argv[0];
rblapack_nb = argv[1];
rblapack_a = argv[2];
if (argc == 3) {
} else if (rblapack_options != Qnil) {
} else {
}
uplo = StringValueCStr(rblapack_uplo)[0];
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*);
nb = NUM2INT(rblapack_nb);
ldw = MAX(1,n);
{
na_shape_t shape[1];
shape[0] = n-1;
rblapack_e = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
e = NA_PTR_TYPE(rblapack_e, real*);
{
na_shape_t shape[1];
shape[0] = n-1;
rblapack_tau = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
tau = NA_PTR_TYPE(rblapack_tau, real*);
{
na_shape_t shape[2];
shape[0] = ldw;
shape[1] = MAX(n,nb);
rblapack_w = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
w = NA_PTR_TYPE(rblapack_w, 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__;
slatrd_(&uplo, &n, &nb, a, &lda, e, tau, w, &ldw);
return rb_ary_new3(4, rblapack_e, rblapack_tau, rblapack_w, rblapack_a);
}
void
init_lapack_slatrd(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "slatrd", rblapack_slatrd, -1);
}
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