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authorshmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
committershmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
commit90d450f74722da7859d6f510a869f6c6908fd12f (patch)
tree538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/clahrd.c
parent01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff)
downloadydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz
[] add metering mode to CLI
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+/* clahrd.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 complex c_b1 = {0.f,0.f};
+static complex c_b2 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* Subroutine */ int clahrd_(integer *n, integer *k, integer *nb, complex *a,
+ integer *lda, complex *tau, complex *t, integer *ldt, complex *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;
+ complex q__1;
+
+ /* Local variables */
+ integer i__;
+ complex ei;
+ extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
+ integer *), cgemv_(char *, integer *, integer *, complex *,
+ complex *, integer *, complex *, integer *, complex *, complex *,
+ integer *), ccopy_(integer *, complex *, integer *,
+ complex *, integer *), caxpy_(integer *, complex *, complex *,
+ integer *, complex *, integer *), ctrmv_(char *, char *, char *,
+ integer *, complex *, integer *, complex *, integer *), clarfg_(integer *, complex *, complex *, integer
+ *, complex *), clacgv_(integer *, complex *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CLAHRD reduces the first NB columns of a complex general n-by-(n-k+1) */
+/* matrix A so that elements below the k-th subdiagonal are zero. The */
+/* reduction is performed by a unitary 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 CLAHR2 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) COMPLEX 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) COMPLEX array, dimension (NB) */
+/* The scalar factors of the elementary reflectors. See Further */
+/* Details. */
+
+/* T (output) COMPLEX array, dimension (LDT,NB) */
+/* The upper triangular matrix T. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= NB. */
+
+/* Y (output) COMPLEX array, dimension (LDY,NB) */
+/* The n-by-nb matrix Y. */
+
+/* LDY (input) INTEGER */
+/* The leading dimension of the array Y. LDY >= max(1,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 complex scalar, and v is a complex 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;
+ clacgv_(&i__2, &a[*k + i__ - 1 + a_dim1], lda);
+ i__2 = i__ - 1;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemv_("No transpose", n, &i__2, &q__1, &y[y_offset], ldy, &a[*k
+ + i__ - 1 + a_dim1], lda, &c_b2, &a[i__ * a_dim1 + 1], &
+ c__1);
+ i__2 = i__ - 1;
+ clacgv_(&i__2, &a[*k + i__ - 1 + a_dim1], lda);
+
+/* 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;
+ ccopy_(&i__2, &a[*k + 1 + i__ * a_dim1], &c__1, &t[*nb * t_dim1 +
+ 1], &c__1);
+ i__2 = i__ - 1;
+ ctrmv_("Lower", "Conjugate 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;
+ cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i__ +
+ a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b2, &
+ t[*nb * t_dim1 + 1], &c__1);
+
+/* w := T'*w */
+
+ i__2 = i__ - 1;
+ ctrmv_("Upper", "Conjugate 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;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemv_("No transpose", &i__2, &i__3, &q__1, &a[*k + i__ + a_dim1],
+ lda, &t[*nb * t_dim1 + 1], &c__1, &c_b2, &a[*k + i__ +
+ i__ * a_dim1], &c__1);
+
+/* b1 := b1 - V1*w */
+
+ i__2 = i__ - 1;
+ ctrmv_("Lower", "No transpose", "Unit", &i__2, &a[*k + 1 + a_dim1]
+, lda, &t[*nb * t_dim1 + 1], &c__1);
+ i__2 = i__ - 1;
+ q__1.r = -1.f, q__1.i = -0.f;
+ caxpy_(&i__2, &q__1, &t[*nb * t_dim1 + 1], &c__1, &a[*k + 1 + i__
+ * a_dim1], &c__1);
+
+ i__2 = *k + i__ - 1 + (i__ - 1) * a_dim1;
+ a[i__2].r = ei.r, a[i__2].i = ei.i;
+ }
+
+/* Generate the elementary reflector H(i) to annihilate */
+/* A(k+i+1:n,i) */
+
+ i__2 = *k + i__ + i__ * a_dim1;
+ ei.r = a[i__2].r, ei.i = a[i__2].i;
+ i__2 = *n - *k - i__ + 1;
+/* Computing MIN */
+ i__3 = *k + i__ + 1;
+ clarfg_(&i__2, &ei, &a[min(i__3, *n)+ i__ * a_dim1], &c__1, &tau[i__])
+ ;
+ i__2 = *k + i__ + i__ * a_dim1;
+ a[i__2].r = 1.f, a[i__2].i = 0.f;
+
+/* Compute Y(1:n,i) */
+
+ i__2 = *n - *k - i__ + 1;
+ cgemv_("No transpose", n, &i__2, &c_b2, &a[(i__ + 1) * a_dim1 + 1],
+ lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b1, &y[i__ *
+ y_dim1 + 1], &c__1);
+ i__2 = *n - *k - i__ + 1;
+ i__3 = i__ - 1;
+ cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i__ +
+ a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b1, &t[
+ i__ * t_dim1 + 1], &c__1);
+ i__2 = i__ - 1;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemv_("No transpose", n, &i__2, &q__1, &y[y_offset], ldy, &t[i__ *
+ t_dim1 + 1], &c__1, &c_b2, &y[i__ * y_dim1 + 1], &c__1);
+ cscal_(n, &tau[i__], &y[i__ * y_dim1 + 1], &c__1);
+
+/* Compute T(1:i,i) */
+
+ i__2 = i__ - 1;
+ i__3 = i__;
+ q__1.r = -tau[i__3].r, q__1.i = -tau[i__3].i;
+ cscal_(&i__2, &q__1, &t[i__ * t_dim1 + 1], &c__1);
+ i__2 = i__ - 1;
+ ctrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[t_offset], ldt,
+ &t[i__ * t_dim1 + 1], &c__1)
+ ;
+ i__2 = i__ + i__ * t_dim1;
+ i__3 = i__;
+ t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i;
+
+/* L10: */
+ }
+ i__1 = *k + *nb + *nb * a_dim1;
+ a[i__1].r = ei.r, a[i__1].i = ei.i;
+
+ return 0;
+
+/* End of CLAHRD */
+
+} /* clahrd_ */