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/* slahrd.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static real c_b4 = -1.f;
static real c_b5 = 1.f;
static integer c__1 = 1;
static real c_b38 = 0.f;
/* Subroutine */ int slahrd_(integer *n, integer *k, integer *nb, real *a,
integer *lda, real *tau, real *t, integer *ldt, real *y, integer *ldy)
{
/* System generated locals */
integer a_dim1, a_offset, t_dim1, t_offset, y_dim1, y_offset, i__1, i__2,
i__3;
real r__1;
/* Local variables */
integer i__;
real ei;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *),
sgemv_(char *, integer *, integer *, real *, real *, integer *,
real *, integer *, real *, real *, integer *), scopy_(
integer *, real *, integer *, real *, integer *), saxpy_(integer *
, real *, real *, integer *, real *, integer *), strmv_(char *,
char *, char *, integer *, real *, integer *, real *, integer *), slarfg_(integer *, real *, real *,
integer *, real *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAHRD reduces the first NB columns of a real general n-by-(n-k+1) */
/* matrix A so that elements below the k-th subdiagonal are zero. The */
/* reduction is performed by an orthogonal similarity transformation */
/* Q' * A * Q. The routine returns the matrices V and T which determine */
/* Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T. */
/* This is an OBSOLETE auxiliary routine. */
/* This routine will be 'deprecated' in a future release. */
/* Please use the new routine SLAHR2 instead. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. */
/* K (input) INTEGER */
/* The offset for the reduction. Elements below the k-th */
/* subdiagonal in the first NB columns are reduced to zero. */
/* NB (input) INTEGER */
/* The number of columns to be reduced. */
/* A (input/output) REAL array, dimension (LDA,N-K+1) */
/* On entry, the n-by-(n-k+1) general matrix A. */
/* On exit, the elements on and above the k-th subdiagonal in */
/* the first NB columns are overwritten with the corresponding */
/* elements of the reduced matrix; the elements below the k-th */
/* subdiagonal, with the array TAU, represent the matrix Q as a */
/* product of elementary reflectors. The other columns of A are */
/* unchanged. See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* TAU (output) REAL array, dimension (NB) */
/* The scalar factors of the elementary reflectors. See Further */
/* Details. */
/* T (output) REAL array, dimension (LDT,NB) */
/* The upper triangular matrix T. */
/* LDT (input) INTEGER */
/* The leading dimension of the array T. LDT >= NB. */
/* Y (output) REAL array, dimension (LDY,NB) */
/* The n-by-nb matrix Y. */
/* LDY (input) INTEGER */
/* The leading dimension of the array Y. LDY >= N. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of nb elementary reflectors */
/* Q = H(1) H(2) . . . H(nb). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a real scalar, and v is a real vector with */
/* v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in */
/* A(i+k+1:n,i), and tau in TAU(i). */
/* The elements of the vectors v together form the (n-k+1)-by-nb matrix */
/* V which is needed, with T and Y, to apply the transformation to the */
/* unreduced part of the matrix, using an update of the form: */
/* A := (I - V*T*V') * (A - Y*V'). */
/* The contents of A on exit are illustrated by the following example */
/* with n = 7, k = 3 and nb = 2: */
/* ( a h a a a ) */
/* ( a h a a a ) */
/* ( a h a a a ) */
/* ( h h a a a ) */
/* ( v1 h a a a ) */
/* ( v1 v2 a a a ) */
/* ( v1 v2 a a a ) */
/* where a denotes an element of the original matrix A, h denotes a */
/* modified element of the upper Hessenberg matrix H, and vi denotes an */
/* element of the vector defining H(i). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
--tau;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
/* Function Body */
if (*n <= 1) {
return 0;
}
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
if (i__ > 1) {
/* Update A(1:n,i) */
/* Compute i-th column of A - Y * V' */
i__2 = i__ - 1;
sgemv_("No transpose", n, &i__2, &c_b4, &y[y_offset], ldy, &a[*k
+ i__ - 1 + a_dim1], lda, &c_b5, &a[i__ * a_dim1 + 1], &
c__1);
/* Apply I - V * T' * V' to this column (call it b) from the */
/* left, using the last column of T as workspace */
/* Let V = ( V1 ) and b = ( b1 ) (first I-1 rows) */
/* ( V2 ) ( b2 ) */
/* where V1 is unit lower triangular */
/* w := V1' * b1 */
i__2 = i__ - 1;
scopy_(&i__2, &a[*k + 1 + i__ * a_dim1], &c__1, &t[*nb * t_dim1 +
1], &c__1);
i__2 = i__ - 1;
strmv_("Lower", "Transpose", "Unit", &i__2, &a[*k + 1 + a_dim1],
lda, &t[*nb * t_dim1 + 1], &c__1);
/* w := w + V2'*b2 */
i__2 = *n - *k - i__ + 1;
i__3 = i__ - 1;
sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[*k + i__ + a_dim1],
lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b5, &t[*nb *
t_dim1 + 1], &c__1);
/* w := T'*w */
i__2 = i__ - 1;
strmv_("Upper", "Transpose", "Non-unit", &i__2, &t[t_offset], ldt,
&t[*nb * t_dim1 + 1], &c__1);
/* b2 := b2 - V2*w */
i__2 = *n - *k - i__ + 1;
i__3 = i__ - 1;
sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[*k + i__ + a_dim1],
lda, &t[*nb * t_dim1 + 1], &c__1, &c_b5, &a[*k + i__ +
i__ * a_dim1], &c__1);
/* b1 := b1 - V1*w */
i__2 = i__ - 1;
strmv_("Lower", "No transpose", "Unit", &i__2, &a[*k + 1 + a_dim1]
, lda, &t[*nb * t_dim1 + 1], &c__1);
i__2 = i__ - 1;
saxpy_(&i__2, &c_b4, &t[*nb * t_dim1 + 1], &c__1, &a[*k + 1 + i__
* a_dim1], &c__1);
a[*k + i__ - 1 + (i__ - 1) * a_dim1] = ei;
}
/* Generate the elementary reflector H(i) to annihilate */
/* A(k+i+1:n,i) */
i__2 = *n - *k - i__ + 1;
/* Computing MIN */
i__3 = *k + i__ + 1;
slarfg_(&i__2, &a[*k + i__ + i__ * a_dim1], &a[min(i__3, *n)+ i__ *
a_dim1], &c__1, &tau[i__]);
ei = a[*k + i__ + i__ * a_dim1];
a[*k + i__ + i__ * a_dim1] = 1.f;
/* Compute Y(1:n,i) */
i__2 = *n - *k - i__ + 1;
sgemv_("No transpose", n, &i__2, &c_b5, &a[(i__ + 1) * a_dim1 + 1],
lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b38, &y[i__ *
y_dim1 + 1], &c__1);
i__2 = *n - *k - i__ + 1;
i__3 = i__ - 1;
sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[*k + i__ + a_dim1], lda, &
a[*k + i__ + i__ * a_dim1], &c__1, &c_b38, &t[i__ * t_dim1 +
1], &c__1);
i__2 = i__ - 1;
sgemv_("No transpose", n, &i__2, &c_b4, &y[y_offset], ldy, &t[i__ *
t_dim1 + 1], &c__1, &c_b5, &y[i__ * y_dim1 + 1], &c__1);
sscal_(n, &tau[i__], &y[i__ * y_dim1 + 1], &c__1);
/* Compute T(1:i,i) */
i__2 = i__ - 1;
r__1 = -tau[i__];
sscal_(&i__2, &r__1, &t[i__ * t_dim1 + 1], &c__1);
i__2 = i__ - 1;
strmv_("Upper", "No transpose", "Non-unit", &i__2, &t[t_offset], ldt,
&t[i__ * t_dim1 + 1], &c__1)
;
t[i__ + i__ * t_dim1] = tau[i__];
/* L10: */
}
a[*k + *nb + *nb * a_dim1] = ei;
return 0;
/* End of SLAHRD */
} /* slahrd_ */
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