#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sgehrd_(integer *n, integer *ilo, integer *ihi, real *a, integer *lda, real *tau, real *work, integer *lwork, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SGEHRD reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H . Arguments ========= N (input) INTEGER The order of the matrix A. N >= 0. ILO (input) INTEGER IHI (input) INTEGER It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a previous call to SGEBAL; otherwise they should be set to 1 and N respectively. See Further Details. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. A (input/output) REAL array, dimension (LDA,N) On entry, the N-by-N general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, and the elements below the first subdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). TAU (output) REAL array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to zero. WORK (workspace/output) REAL array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The length of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, 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. Further Details =============== The matrix Q is represented as a product of (ihi-ilo) elementary reflectors Q = H(ilo) H(ilo+1) . . . H(ihi-1). 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) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in TAU(i). The contents of A are illustrated by the following example, with n = 7, ilo = 2 and ihi = 6: on entry, on exit, ( a a a a a a a ) ( a a h h h h a ) ( a a a a a a ) ( a h h h h a ) ( a a a a a a ) ( h h h h h h ) ( a a a a a a ) ( v2 h h h h h ) ( a a a a a a ) ( v2 v3 h h h h ) ( a a a a a a ) ( v2 v3 v4 h h h ) ( 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). This file is a slight modification of LAPACK-3.0's SGEHRD subroutine incorporating improvements proposed by Quintana-Orti and Van de Geijn (2005). ===================================================================== Test the input parameters Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; static integer c__65 = 65; static real c_b25 = -1.f; static real c_b26 = 1.f; /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ static integer i__, j; static real t[4160] /* was [65][64] */; static integer ib; static real ei; static integer nb, nh, nx, iws, nbmin, iinfo; extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), strmm_(char *, char *, char *, char *, integer *, integer *, real *, real *, integer *, real *, integer *), saxpy_(integer *, real *, real *, integer *, real *, integer *), sgehd2_(integer *, integer *, integer *, real *, integer *, real *, real *, integer * ), slahr2_(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); static integer ldwork, lwkopt; static logical lquery; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; /* Function Body */ *info = 0; /* Computing MIN */ i__1 = 64, i__2 = ilaenv_(&c__1, "SGEHRD", " ", n, ilo, ihi, &c_n1, ( ftnlen)6, (ftnlen)1); nb = min(i__1,i__2); lwkopt = *n * nb; work[1] = (real) lwkopt; lquery = *lwork == -1; if (*n < 0) { *info = -1; } else if (*ilo < 1 || *ilo > max(1,*n)) { *info = -2; } else if (*ihi < min(*ilo,*n) || *ihi > *n) { *info = -3; } else if (*lda < max(1,*n)) { *info = -5; } else if (*lwork < max(1,*n) && ! lquery) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_("SGEHRD", &i__1); return 0; } else if (lquery) { return 0; } /* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */ i__1 = *ilo - 1; for (i__ = 1; i__ <= i__1; ++i__) { tau[i__] = 0.f; /* L10: */ } i__1 = *n - 1; for (i__ = max(1,*ihi); i__ <= i__1; ++i__) { tau[i__] = 0.f; /* L20: */ } /* Quick return if possible */ nh = *ihi - *ilo + 1; if (nh <= 1) { work[1] = 1.f; return 0; } /* Determine the block size Computing MIN */ i__1 = 64, i__2 = ilaenv_(&c__1, "SGEHRD", " ", n, ilo, ihi, &c_n1, ( ftnlen)6, (ftnlen)1); nb = min(i__1,i__2); nbmin = 2; iws = 1; if (nb > 1 && nb < nh) { /* Determine when to cross over from blocked to unblocked code (last block is always handled by unblocked code) Computing MAX */ i__1 = nb, i__2 = ilaenv_(&c__3, "SGEHRD", " ", n, ilo, ihi, &c_n1, ( ftnlen)6, (ftnlen)1); nx = max(i__1,i__2); if (nx < nh) { /* Determine if workspace is large enough for blocked code */ iws = *n * nb; if (*lwork < iws) { /* Not enough workspace to use optimal NB: determine the minimum value of NB, and reduce NB or force use of unblocked code Computing MAX */ i__1 = 2, i__2 = ilaenv_(&c__2, "SGEHRD", " ", n, ilo, ihi, & c_n1, (ftnlen)6, (ftnlen)1); nbmin = max(i__1,i__2); if (*lwork >= *n * nbmin) { nb = *lwork / *n; } else { nb = 1; } } } } ldwork = *n; if (nb < nbmin || nb >= nh) { /* Use unblocked code below */ i__ = *ilo; } else { /* Use blocked code */ i__1 = *ihi - 1 - nx; i__2 = nb; for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = nb, i__4 = *ihi - i__; ib = min(i__3,i__4); /* Reduce columns i:i+ib-1 to Hessenberg form, returning the matrices V and T of the block reflector H = I - V*T*V' which performs the reduction, and also the matrix Y = A*V*T */ slahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, & c__65, &work[1], &ldwork); /* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the right, computing A := A - Y * V'. V(i+ib,ib-1) must be set to 1 */ ei = a[i__ + ib + (i__ + ib - 1) * a_dim1]; a[i__ + ib + (i__ + ib - 1) * a_dim1] = 1.f; i__3 = *ihi - i__ - ib + 1; sgemm_("No transpose", "Transpose", ihi, &i__3, &ib, &c_b25, & work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda, & c_b26, &a[(i__ + ib) * a_dim1 + 1], lda); a[i__ + ib + (i__ + ib - 1) * a_dim1] = ei; /* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the right */ i__3 = ib - 1; strmm_("Right", "Lower", "Transpose", "Unit", &i__, &i__3, &c_b26, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], &ldwork); i__3 = ib - 2; for (j = 0; j <= i__3; ++j) { saxpy_(&i__, &c_b25, &work[ldwork * j + 1], &c__1, &a[(i__ + j + 1) * a_dim1 + 1], &c__1); /* L30: */ } /* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the left */ i__3 = *ihi - i__; i__4 = *n - i__ - ib + 1; slarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, & i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &c__65, &a[ i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &ldwork); /* L40: */ } } /* Use unblocked code to reduce the rest of the matrix */ sgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo); work[1] = (real) iws; return 0; /* End of SGEHRD */ } /* sgehrd_ */