#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sormlq_(char *side, char *trans, integer *m, integer *n, integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, real *work, integer *lwork, integer *info ) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SORMLQ overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by SGELQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. Arguments ========= SIDE (input) CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. TRANS (input) CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T. M (input) INTEGER The number of rows of the matrix C. M >= 0. N (input) INTEGER The number of columns of the matrix C. N >= 0. K (input) INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. A (input) REAL array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQF in the first k rows of its array argument A. A is modified by the routine but restored on exit. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,K). TAU (input) REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGELQF. C (input/output) REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== Test the input arguments Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static integer c__65 = 65; /* System generated locals */ address a__1[2]; integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, i__5; char ch__1[2]; /* Builtin functions Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ static integer i__; static real t[4160] /* was [65][64] */; static integer i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iws; static logical left; extern logical lsame_(char *, char *); static integer nbmin, iinfo; extern /* Subroutine */ int sorml2_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *), slarfb_(char *, char *, char *, char * , integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *, real *, integer *, real *, real *, integer *); static logical notran; static integer ldwork; static char transt[1]; static integer lwkopt; static logical lquery; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; --work; /* Function Body */ *info = 0; left = lsame_(side, "L"); notran = lsame_(trans, "N"); lquery = *lwork == -1; /* NQ is the order of Q and NW is the minimum dimension of WORK */ if (left) { nq = *m; nw = *n; } else { nq = *n; nw = *m; } if (! left && ! lsame_(side, "R")) { *info = -1; } else if (! notran && ! lsame_(trans, "T")) { *info = -2; } else if (*m < 0) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; } else if (*lda < max(1,*k)) { *info = -7; } else if (*ldc < max(1,*m)) { *info = -10; } else if (*lwork < max(1,nw) && ! lquery) { *info = -12; } if (*info == 0) { /* Determine the block size. NB may be at most NBMAX, where NBMAX is used to define the local array T. Computing MIN Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 64, i__2 = ilaenv_(&c__1, "SORMLQ", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nb = min(i__1,i__2); lwkopt = max(1,nw) * nb; work[1] = (real) lwkopt; } if (*info != 0) { i__1 = -(*info); xerbla_("SORMLQ", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { work[1] = 1.f; return 0; } nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { iws = nw * nb; if (*lwork < iws) { nb = *lwork / ldwork; /* Computing MAX Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 2, i__2 = ilaenv_(&c__2, "SORMLQ", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nbmin = max(i__1,i__2); } } else { iws = nw; } if (nb < nbmin || nb >= *k) { /* Use unblocked code */ sorml2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ c_offset], ldc, &work[1], &iinfo); } else { /* Use blocked code */ if (left && notran || ! left && ! notran) { i1 = 1; i2 = *k; i3 = nb; } else { i1 = (*k - 1) / nb * nb + 1; i2 = 1; i3 = -nb; } if (left) { ni = *n; jc = 1; } else { mi = *m; ic = 1; } if (notran) { *(unsigned char *)transt = 'T'; } else { *(unsigned char *)transt = 'N'; } i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__4 = nb, i__5 = *k - i__ + 1; ib = min(i__4,i__5); /* Form the triangular factor of the block reflector H = H(i) H(i+1) . . . H(i+ib-1) */ i__4 = nq - i__ + 1; slarft_("Forward", "Rowwise", &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], t, &c__65); if (left) { /* H or H' is applied to C(i:m,1:n) */ mi = *m - i__ + 1; ic = i__; } else { /* H or H' is applied to C(1:m,i:n) */ ni = *n - i__ + 1; jc = i__; } /* Apply H or H' */ slarfb_(side, transt, "Forward", "Rowwise", &mi, &ni, &ib, &a[i__ + i__ * a_dim1], lda, t, &c__65, &c__[ic + jc * c_dim1], ldc, &work[1], &ldwork); /* L10: */ } } work[1] = (real) lwkopt; return 0; /* End of SORMLQ */ } /* sormlq_ */