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252 lines
7.0 KiB
252 lines
7.0 KiB
/* sgeqrf.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 integer c_n1 = -1; |
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static integer c__3 = 3; |
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static integer c__2 = 2; |
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/* Subroutine */ int sgeqrf_(integer *m, integer *n, real *a, integer *lda, |
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real *tau, real *work, integer *lwork, integer *info) |
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{ |
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/* System generated locals */ |
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4; |
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/* Local variables */ |
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integer i__, k, ib, nb, nx, iws, nbmin, iinfo; |
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extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer |
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*, real *, real *, integer *), slarfb_(char *, char *, char *, |
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char *, integer *, integer *, integer *, real *, integer *, real * |
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, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *); |
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *, |
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integer *, integer *); |
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extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *, |
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real *, integer *, real *, real *, integer *); |
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integer ldwork, lwkopt; |
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logical lquery; |
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/* -- LAPACK 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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/* SGEQRF computes a QR factorization of a real M-by-N matrix A: */ |
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/* A = Q * R. */ |
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/* Arguments */ |
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/* ========= */ |
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/* M (input) INTEGER */ |
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/* The number of rows of the matrix A. M >= 0. */ |
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/* N (input) INTEGER */ |
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/* The number of columns of the matrix A. N >= 0. */ |
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/* A (input/output) REAL array, dimension (LDA,N) */ |
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/* On entry, the M-by-N matrix A. */ |
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/* On exit, the elements on and above the diagonal of the array */ |
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/* contain the min(M,N)-by-N upper trapezoidal matrix R (R is */ |
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/* upper triangular if m >= n); the elements below the diagonal, */ |
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/* with the array TAU, represent the orthogonal matrix Q as a */ |
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/* product of min(m,n) elementary reflectors (see Further */ |
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/* Details). */ |
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/* LDA (input) INTEGER */ |
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/* The leading dimension of the array A. LDA >= max(1,M). */ |
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/* TAU (output) REAL array, dimension (min(M,N)) */ |
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/* The scalar factors of the elementary reflectors (see Further */ |
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/* Details). */ |
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/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */ |
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/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ |
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/* LWORK (input) INTEGER */ |
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/* The dimension of the array WORK. LWORK >= max(1,N). */ |
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/* For optimum performance LWORK >= N*NB, where NB is */ |
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/* the optimal blocksize. */ |
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/* If LWORK = -1, then a workspace query is assumed; the routine */ |
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/* only calculates the optimal size of the WORK array, returns */ |
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/* this value as the first entry of the WORK array, and no error */ |
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/* message related to LWORK is issued by XERBLA. */ |
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/* INFO (output) INTEGER */ |
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/* = 0: successful exit */ |
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/* < 0: if INFO = -i, the i-th argument had an illegal value */ |
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/* Further Details */ |
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/* =============== */ |
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/* The matrix Q is represented as a product of elementary reflectors */ |
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/* Q = H(1) H(2) . . . H(k), where k = min(m,n). */ |
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/* Each H(i) has the form */ |
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/* H(i) = I - tau * v * v' */ |
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/* where tau is a real scalar, and v is a real vector with */ |
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/* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */ |
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/* and tau in TAU(i). */ |
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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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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. External Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input arguments */ |
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/* Parameter adjustments */ |
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a_dim1 = *lda; |
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a_offset = 1 + a_dim1; |
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a -= a_offset; |
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--tau; |
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--work; |
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/* Function Body */ |
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*info = 0; |
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nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1); |
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lwkopt = *n * nb; |
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work[1] = (real) lwkopt; |
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lquery = *lwork == -1; |
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if (*m < 0) { |
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*info = -1; |
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} else if (*n < 0) { |
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*info = -2; |
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} else if (*lda < max(1,*m)) { |
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*info = -4; |
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} else if (*lwork < max(1,*n) && ! lquery) { |
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*info = -7; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SGEQRF", &i__1); |
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return 0; |
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} else if (lquery) { |
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return 0; |
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} |
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/* Quick return if possible */ |
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k = min(*m,*n); |
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if (k == 0) { |
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work[1] = 1.f; |
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return 0; |
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} |
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nbmin = 2; |
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nx = 0; |
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iws = *n; |
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if (nb > 1 && nb < k) { |
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/* Determine when to cross over from blocked to unblocked code. */ |
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/* Computing MAX */ |
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i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQRF", " ", m, n, &c_n1, &c_n1); |
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nx = max(i__1,i__2); |
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if (nx < k) { |
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/* Determine if workspace is large enough for blocked code. */ |
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ldwork = *n; |
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iws = ldwork * nb; |
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if (*lwork < iws) { |
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/* Not enough workspace to use optimal NB: reduce NB and */ |
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/* determine the minimum value of NB. */ |
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nb = *lwork / ldwork; |
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/* Computing MAX */ |
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i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQRF", " ", m, n, &c_n1, & |
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c_n1); |
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nbmin = max(i__1,i__2); |
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} |
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} |
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} |
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if (nb >= nbmin && nb < k && nx < k) { |
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/* Use blocked code initially */ |
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i__1 = k - nx; |
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i__2 = nb; |
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for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { |
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/* Computing MIN */ |
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i__3 = k - i__ + 1; |
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ib = min(i__3,nb); |
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/* Compute the QR factorization of the current block */ |
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/* A(i:m,i:i+ib-1) */ |
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i__3 = *m - i__ + 1; |
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sgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ |
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1], &iinfo); |
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if (i__ + ib <= *n) { |
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/* Form the triangular factor of the block reflector */ |
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/* H = H(i) H(i+1) . . . H(i+ib-1) */ |
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i__3 = *m - i__ + 1; |
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slarft_("Forward", "Columnwise", &i__3, &ib, &a[i__ + i__ * |
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a_dim1], lda, &tau[i__], &work[1], &ldwork); |
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/* Apply H' to A(i:m,i+ib:n) from the left */ |
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i__3 = *m - i__ + 1; |
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i__4 = *n - i__ - ib + 1; |
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slarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, & |
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i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & |
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ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib |
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+ 1], &ldwork); |
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} |
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/* L10: */ |
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} |
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} else { |
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i__ = 1; |
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} |
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/* Use unblocked code to factor the last or only block. */ |
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if (i__ <= k) { |
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i__2 = *m - i__ + 1; |
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i__1 = *n - i__ + 1; |
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sgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] |
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, &iinfo); |
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} |
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work[1] = (real) iws; |
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return 0; |
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/* End of SGEQRF */ |
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} /* sgeqrf_ */
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