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325 lines
9.5 KiB
325 lines
9.5 KiB
/* dlarft.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#include "clapack.h" |
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/* Table of constant values */ |
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static integer c__1 = 1; |
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static doublereal c_b8 = 0.; |
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/* Subroutine */ int dlarft_(char *direct, char *storev, integer *n, integer * |
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k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, |
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integer *ldt) |
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{ |
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/* System generated locals */ |
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integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3; |
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doublereal d__1; |
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/* Local variables */ |
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integer i__, j, prevlastv; |
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doublereal vii; |
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extern logical lsame_(char *, char *); |
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extern /* Subroutine */ int dgemv_(char *, integer *, integer *, |
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doublereal *, doublereal *, integer *, doublereal *, integer *, |
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doublereal *, doublereal *, integer *); |
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integer lastv; |
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extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, |
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doublereal *, integer *, doublereal *, integer *); |
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/* -- LAPACK auxiliary routine (version 3.2) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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/* Purpose */ |
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/* ======= */ |
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/* DLARFT forms the triangular factor T of a real block reflector H */ |
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/* of order n, which is defined as a product of k elementary reflectors. */ |
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/* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */ |
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/* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */ |
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/* If STOREV = 'C', the vector which defines the elementary reflector */ |
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/* H(i) is stored in the i-th column of the array V, and */ |
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/* H = I - V * T * V' */ |
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/* If STOREV = 'R', the vector which defines the elementary reflector */ |
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/* H(i) is stored in the i-th row of the array V, and */ |
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/* H = I - V' * T * V */ |
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/* Arguments */ |
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/* ========= */ |
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/* DIRECT (input) CHARACTER*1 */ |
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/* Specifies the order in which the elementary reflectors are */ |
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/* multiplied to form the block reflector: */ |
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/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */ |
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/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */ |
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/* STOREV (input) CHARACTER*1 */ |
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/* Specifies how the vectors which define the elementary */ |
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/* reflectors are stored (see also Further Details): */ |
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/* = 'C': columnwise */ |
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/* = 'R': rowwise */ |
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/* N (input) INTEGER */ |
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/* The order of the block reflector H. N >= 0. */ |
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/* K (input) INTEGER */ |
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/* The order of the triangular factor T (= the number of */ |
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/* elementary reflectors). K >= 1. */ |
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/* V (input/output) DOUBLE PRECISION array, dimension */ |
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/* (LDV,K) if STOREV = 'C' */ |
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/* (LDV,N) if STOREV = 'R' */ |
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/* The matrix V. See further details. */ |
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/* LDV (input) INTEGER */ |
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/* The leading dimension of the array V. */ |
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/* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */ |
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/* TAU (input) DOUBLE PRECISION array, dimension (K) */ |
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/* TAU(i) must contain the scalar factor of the elementary */ |
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/* reflector H(i). */ |
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/* T (output) DOUBLE PRECISION array, dimension (LDT,K) */ |
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/* The k by k triangular factor T of the block reflector. */ |
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/* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */ |
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/* lower triangular. The rest of the array is not used. */ |
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/* LDT (input) INTEGER */ |
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/* The leading dimension of the array T. LDT >= K. */ |
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/* Further Details */ |
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/* =============== */ |
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/* The shape of the matrix V and the storage of the vectors which define */ |
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/* the H(i) is best illustrated by the following example with n = 5 and */ |
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/* k = 3. The elements equal to 1 are not stored; the corresponding */ |
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/* array elements are modified but restored on exit. The rest of the */ |
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/* array is not used. */ |
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/* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ |
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/* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ |
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/* ( v1 1 ) ( 1 v2 v2 v2 ) */ |
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/* ( v1 v2 1 ) ( 1 v3 v3 ) */ |
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/* ( v1 v2 v3 ) */ |
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/* ( v1 v2 v3 ) */ |
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/* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ |
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/* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ |
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/* ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ |
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/* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ |
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/* ( 1 v3 ) */ |
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/* ( 1 ) */ |
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/* ===================================================================== */ |
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/* .. Parameters .. */ |
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/* .. */ |
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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. External Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Quick return if possible */ |
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/* Parameter adjustments */ |
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v_dim1 = *ldv; |
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v_offset = 1 + v_dim1; |
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v -= v_offset; |
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--tau; |
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t_dim1 = *ldt; |
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t_offset = 1 + t_dim1; |
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t -= t_offset; |
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/* Function Body */ |
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if (*n == 0) { |
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return 0; |
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} |
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if (lsame_(direct, "F")) { |
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prevlastv = *n; |
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i__1 = *k; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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prevlastv = max(i__,prevlastv); |
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if (tau[i__] == 0.) { |
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/* H(i) = I */ |
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i__2 = i__; |
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for (j = 1; j <= i__2; ++j) { |
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t[j + i__ * t_dim1] = 0.; |
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/* L10: */ |
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} |
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} else { |
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/* general case */ |
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vii = v[i__ + i__ * v_dim1]; |
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v[i__ + i__ * v_dim1] = 1.; |
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if (lsame_(storev, "C")) { |
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/* Skip any trailing zeros. */ |
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i__2 = i__ + 1; |
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for (lastv = *n; lastv >= i__2; --lastv) { |
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if (v[lastv + i__ * v_dim1] != 0.) { |
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break; |
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} |
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} |
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j = min(lastv,prevlastv); |
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/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i) */ |
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i__2 = j - i__ + 1; |
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i__3 = i__ - 1; |
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d__1 = -tau[i__]; |
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dgemv_("Transpose", &i__2, &i__3, &d__1, &v[i__ + v_dim1], |
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ldv, &v[i__ + i__ * v_dim1], &c__1, &c_b8, &t[ |
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i__ * t_dim1 + 1], &c__1); |
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} else { |
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/* Skip any trailing zeros. */ |
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i__2 = i__ + 1; |
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for (lastv = *n; lastv >= i__2; --lastv) { |
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if (v[i__ + lastv * v_dim1] != 0.) { |
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break; |
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} |
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} |
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j = min(lastv,prevlastv); |
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/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)' */ |
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i__2 = i__ - 1; |
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i__3 = j - i__ + 1; |
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d__1 = -tau[i__]; |
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dgemv_("No transpose", &i__2, &i__3, &d__1, &v[i__ * |
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v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, & |
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c_b8, &t[i__ * t_dim1 + 1], &c__1); |
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} |
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v[i__ + i__ * v_dim1] = vii; |
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/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */ |
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i__2 = i__ - 1; |
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dtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[ |
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t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1); |
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t[i__ + i__ * t_dim1] = tau[i__]; |
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if (i__ > 1) { |
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prevlastv = max(prevlastv,lastv); |
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} else { |
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prevlastv = lastv; |
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} |
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} |
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/* L20: */ |
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} |
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} else { |
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prevlastv = 1; |
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for (i__ = *k; i__ >= 1; --i__) { |
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if (tau[i__] == 0.) { |
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/* H(i) = I */ |
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i__1 = *k; |
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for (j = i__; j <= i__1; ++j) { |
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t[j + i__ * t_dim1] = 0.; |
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/* L30: */ |
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} |
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} else { |
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/* general case */ |
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if (i__ < *k) { |
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if (lsame_(storev, "C")) { |
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vii = v[*n - *k + i__ + i__ * v_dim1]; |
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v[*n - *k + i__ + i__ * v_dim1] = 1.; |
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/* Skip any leading zeros. */ |
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i__1 = i__ - 1; |
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for (lastv = 1; lastv <= i__1; ++lastv) { |
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if (v[lastv + i__ * v_dim1] != 0.) { |
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break; |
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} |
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} |
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j = max(lastv,prevlastv); |
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/* T(i+1:k,i) := */ |
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/* - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i) */ |
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i__1 = *n - *k + i__ - j + 1; |
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i__2 = *k - i__; |
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d__1 = -tau[i__]; |
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dgemv_("Transpose", &i__1, &i__2, &d__1, &v[j + (i__ |
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+ 1) * v_dim1], ldv, &v[j + i__ * v_dim1], & |
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c__1, &c_b8, &t[i__ + 1 + i__ * t_dim1], & |
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c__1); |
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v[*n - *k + i__ + i__ * v_dim1] = vii; |
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} else { |
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vii = v[i__ + (*n - *k + i__) * v_dim1]; |
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v[i__ + (*n - *k + i__) * v_dim1] = 1.; |
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/* Skip any leading zeros. */ |
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i__1 = i__ - 1; |
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for (lastv = 1; lastv <= i__1; ++lastv) { |
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if (v[i__ + lastv * v_dim1] != 0.) { |
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break; |
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} |
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} |
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j = max(lastv,prevlastv); |
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/* T(i+1:k,i) := */ |
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/* - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)' */ |
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i__1 = *k - i__; |
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i__2 = *n - *k + i__ - j + 1; |
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d__1 = -tau[i__]; |
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dgemv_("No transpose", &i__1, &i__2, &d__1, &v[i__ + |
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1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], |
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ldv, &c_b8, &t[i__ + 1 + i__ * t_dim1], &c__1); |
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v[i__ + (*n - *k + i__) * v_dim1] = vii; |
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} |
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/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */ |
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i__1 = *k - i__; |
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dtrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__ |
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+ 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * |
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t_dim1], &c__1) |
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; |
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if (i__ > 1) { |
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prevlastv = min(prevlastv,lastv); |
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} else { |
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prevlastv = lastv; |
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} |
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} |
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t[i__ + i__ * t_dim1] = tau[i__]; |
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} |
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/* L40: */ |
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} |
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} |
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return 0; |
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/* End of DLARFT */ |
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} /* dlarft_ */
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