X-Git-Url: http://vcs.maemo.org/git/?a=blobdiff_plain;f=3rdparty%2Flapack%2Fdgels.c;fp=3rdparty%2Flapack%2Fdgels.c;h=2018399f5eb0480d72ec3dfb98caf877fe0cd284;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hp=0000000000000000000000000000000000000000;hpb=454138ff8a20f6edb9b65a910101403d8b520643;p=opencv

diff --git a/3rdparty/lapack/dgels.c b/3rdparty/lapack/dgels.c
new file mode 100644
index 0000000..2018399
--- /dev/null
+++ b/3rdparty/lapack/dgels.c
@@ -0,0 +1,502 @@
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static doublereal c_b33 = 0.;
+static integer c__0 = 0;
+
+/* Subroutine */ int dgels_(char *trans, integer *m, integer *n, integer *
+	nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
+	doublereal *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
+
+    /* Local variables */
+    integer i__, j, nb, mn;
+    doublereal anrm, bnrm;
+    integer brow;
+    logical tpsd;
+    integer iascl, ibscl;
+    extern logical lsame_(char *, char *);
+    integer wsize;
+    doublereal rwork[1];
+    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
+    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
+	    integer *, doublereal *, integer *, doublereal *);
+    extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, 
+	    integer *, doublereal *, doublereal *, integer *, integer *), 
+	    dlascl_(char *, integer *, integer *, doublereal *, doublereal *, 
+	    integer *, integer *, doublereal *, integer *, integer *),
+	     dgeqrf_(integer *, integer *, doublereal *, integer *, 
+	    doublereal *, doublereal *, integer *, integer *), dlaset_(char *, 
+	     integer *, integer *, doublereal *, doublereal *, doublereal *, 
+	    integer *), xerbla_(char *, integer *);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *);
+    integer scllen;
+    doublereal bignum;
+    extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, 
+	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
+	    integer *, doublereal *, integer *, integer *), 
+	    dormqr_(char *, char *, integer *, integer *, integer *, 
+	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
+	    doublereal *, integer *, integer *);
+    doublereal smlnum;
+    logical lquery;
+    extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *, 
+	    integer *, doublereal *, integer *, doublereal *, integer *, 
+	    integer *);
+
+
+/*  -- LAPACK driver routine (version 3.1) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  DGELS solves overdetermined or underdetermined real linear systems */
+/*  involving an M-by-N matrix A, or its transpose, using a QR or LQ */
+/*  factorization of A.  It is assumed that A has full rank. */
+
+/*  The following options are provided: */
+
+/*  1. If TRANS = 'N' and m >= n:  find the least squares solution of */
+/*     an overdetermined system, i.e., solve the least squares problem */
+/*                  minimize || B - A*X ||. */
+
+/*  2. If TRANS = 'N' and m < n:  find the minimum norm solution of */
+/*     an underdetermined system A * X = B. */
+
+/*  3. If TRANS = 'T' and m >= n:  find the minimum norm solution of */
+/*     an undetermined system A**T * X = B. */
+
+/*  4. If TRANS = 'T' and m < n:  find the least squares solution of */
+/*     an overdetermined system, i.e., solve the least squares problem */
+/*                  minimize || B - A**T * X ||. */
+
+/*  Several right hand side vectors b and solution vectors x can be */
+/*  handled in a single call; they are stored as the columns of the */
+/*  M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
+/*  matrix X. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  TRANS   (input) CHARACTER*1 */
+/*          = 'N': the linear system involves A; */
+/*          = 'T': the linear system involves A**T. */
+
+/*  M       (input) INTEGER */
+/*          The number of rows of the matrix A.  M >= 0. */
+
+/*  N       (input) INTEGER */
+/*          The number of columns of the matrix A.  N >= 0. */
+
+/*  NRHS    (input) INTEGER */
+/*          The number of right hand sides, i.e., the number of */
+/*          columns of the matrices B and X. NRHS >=0. */
+
+/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
+/*          On entry, the M-by-N matrix A. */
+/*          On exit, */
+/*            if M >= N, A is overwritten by details of its QR */
+/*                       factorization as returned by DGEQRF; */
+/*            if M <  N, A is overwritten by details of its LQ */
+/*                       factorization as returned by DGELQF. */
+
+/*  LDA     (input) INTEGER */
+/*          The leading dimension of the array A.  LDA >= max(1,M). */
+
+/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
+/*          On entry, the matrix B of right hand side vectors, stored */
+/*          columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
+/*          if TRANS = 'T'. */
+/*          On exit, if INFO = 0, B is overwritten by the solution */
+/*          vectors, stored columnwise: */
+/*          if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
+/*          squares solution vectors; the residual sum of squares for the */
+/*          solution in each column is given by the sum of squares of */
+/*          elements N+1 to M in that column; */
+/*          if TRANS = 'N' and m < n, rows 1 to N of B contain the */
+/*          minimum norm solution vectors; */
+/*          if TRANS = 'T' and m >= n, rows 1 to M of B contain the */
+/*          minimum norm solution vectors; */
+/*          if TRANS = 'T' and m < n, rows 1 to M of B contain the */
+/*          least squares solution vectors; the residual sum of squares */
+/*          for the solution in each column is given by the sum of */
+/*          squares of elements M+1 to N in that column. */
+
+/*  LDB     (input) INTEGER */
+/*          The leading dimension of the array B. LDB >= MAX(1,M,N). */
+
+/*  WORK    (workspace/output) DOUBLE PRECISION 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. */
+/*          LWORK >= max( 1, MN + max( MN, NRHS ) ). */
+/*          For optimal performance, */
+/*          LWORK >= max( 1, MN + max( MN, NRHS )*NB ). */
+/*          where MN = min(M,N) and NB is the optimum block size. */
+
+/*          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 */
+/*          > 0:  if INFO =  i, the i-th diagonal element of the */
+/*                triangular factor of A is zero, so that A does not have */
+/*                full rank; the least squares solution could not be */
+/*                computed. */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Test the input arguments. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    mn = min(*m,*n);
+    lquery = *lwork == -1;
+    if (! (lsame_(trans, "N") || lsame_(trans, "T"))) {
+	*info = -1;
+    } else if (*m < 0) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -3;
+    } else if (*nrhs < 0) {
+	*info = -4;
+    } else if (*lda < max(1,*m)) {
+	*info = -6;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = max(1,*m);
+	if (*ldb < max(i__1,*n)) {
+	    *info = -8;
+	} else /* if(complicated condition) */ {
+/* Computing MAX */
+	    i__1 = 1, i__2 = mn + max(mn,*nrhs);
+	    if (*lwork < max(i__1,i__2) && ! lquery) {
+		*info = -10;
+	    }
+	}
+    }
+
+/*     Figure out optimal block size */
+
+    if (*info == 0 || *info == -10) {
+
+	tpsd = TRUE_;
+	if (lsame_(trans, "N")) {
+	    tpsd = FALSE_;
+	}
+
+	if (*m >= *n) {
+	    nb = ilaenv_(&c__1, "DGEQRF", " ", m, n, &c_n1, &c_n1);
+	    if (tpsd) {
+/* Computing MAX */
+		i__1 = nb, i__2 = ilaenv_(&c__1, "DORMQR", "LN", m, nrhs, n, &
+			c_n1);
+		nb = max(i__1,i__2);
+	    } else {
+/* Computing MAX */
+		i__1 = nb, i__2 = ilaenv_(&c__1, "DORMQR", "LT", m, nrhs, n, &
+			c_n1);
+		nb = max(i__1,i__2);
+	    }
+	} else {
+	    nb = ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1, &c_n1);
+	    if (tpsd) {
+/* Computing MAX */
+		i__1 = nb, i__2 = ilaenv_(&c__1, "DORMLQ", "LT", n, nrhs, m, &
+			c_n1);
+		nb = max(i__1,i__2);
+	    } else {
+/* Computing MAX */
+		i__1 = nb, i__2 = ilaenv_(&c__1, "DORMLQ", "LN", n, nrhs, m, &
+			c_n1);
+		nb = max(i__1,i__2);
+	    }
+	}
+
+/* Computing MAX */
+	i__1 = 1, i__2 = mn + max(mn,*nrhs) * nb;
+	wsize = max(i__1,i__2);
+	work[1] = (doublereal) wsize;
+
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DGELS ", &i__1);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+/* Computing MIN */
+    i__1 = min(*m,*n);
+    if (min(i__1,*nrhs) == 0) {
+	i__1 = max(*m,*n);
+	dlaset_("Full", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb);
+	return 0;
+    }
+
+/*     Get machine parameters */
+
+    smlnum = dlamch_("S") / dlamch_("P");
+    bignum = 1. / smlnum;
+    dlabad_(&smlnum, &bignum);
+
+/*     Scale A, B if max element outside range [SMLNUM,BIGNUM] */
+
+    anrm = dlange_("M", m, n, &a[a_offset], lda, rwork);
+    iascl = 0;
+    if (anrm > 0. && anrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 1;
+    } else if (anrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 2;
+    } else if (anrm == 0.) {
+
+/*        Matrix all zero. Return zero solution. */
+
+	i__1 = max(*m,*n);
+	dlaset_("F", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb);
+	goto L50;
+    }
+
+    brow = *m;
+    if (tpsd) {
+	brow = *n;
+    }
+    bnrm = dlange_("M", &brow, nrhs, &b[b_offset], ldb, rwork);
+    ibscl = 0;
+    if (bnrm > 0. && bnrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset], 
+		ldb, info);
+	ibscl = 1;
+    } else if (bnrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	dlascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset], 
+		ldb, info);
+	ibscl = 2;
+    }
+
+    if (*m >= *n) {
+
+/*        compute QR factorization of A */
+
+	i__1 = *lwork - mn;
+	dgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
+		;
+
+/*        workspace at least N, optimally N*NB */
+
+	if (! tpsd) {
+
+/*           Least-Squares Problem min || A * X - B || */
+
+/*           B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
+
+	    i__1 = *lwork - mn;
+	    dormqr_("Left", "Transpose", m, nrhs, n, &a[a_offset], lda, &work[
+		    1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+/*           B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */
+
+	    dtrtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset]
+, lda, &b[b_offset], ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+	    scllen = *n;
+
+	} else {
+
+/*           Overdetermined system of equations A' * X = B */
+
+/*           B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS) */
+
+	    dtrtrs_("Upper", "Transpose", "Non-unit", n, nrhs, &a[a_offset], 
+		    lda, &b[b_offset], ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+/*           B(N+1:M,1:NRHS) = ZERO */
+
+	    i__1 = *nrhs;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = *n + 1; i__ <= i__2; ++i__) {
+		    b[i__ + j * b_dim1] = 0.;
+/* L10: */
+		}
+/* L20: */
+	    }
+
+/*           B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */
+
+	    i__1 = *lwork - mn;
+	    dormqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, &
+		    work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+	    scllen = *m;
+
+	}
+
+    } else {
+
+/*        Compute LQ factorization of A */
+
+	i__1 = *lwork - mn;
+	dgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
+		;
+
+/*        workspace at least M, optimally M*NB. */
+
+	if (! tpsd) {
+
+/*           underdetermined system of equations A * X = B */
+
+/*           B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */
+
+	    dtrtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset]
+, lda, &b[b_offset], ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+/*           B(M+1:N,1:NRHS) = 0 */
+
+	    i__1 = *nrhs;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *n;
+		for (i__ = *m + 1; i__ <= i__2; ++i__) {
+		    b[i__ + j * b_dim1] = 0.;
+/* L30: */
+		}
+/* L40: */
+	    }
+
+/*           B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS) */
+
+	    i__1 = *lwork - mn;
+	    dormlq_("Left", "Transpose", n, nrhs, m, &a[a_offset], lda, &work[
+		    1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+	    scllen = *n;
+
+	} else {
+
+/*           overdetermined system min || A' * X - B || */
+
+/*           B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */
+
+	    i__1 = *lwork - mn;
+	    dormlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, &
+		    work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+/*           B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS) */
+
+	    dtrtrs_("Lower", "Transpose", "Non-unit", m, nrhs, &a[a_offset], 
+		    lda, &b[b_offset], ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+	    scllen = *m;
+
+	}
+
+    }
+
+/*     Undo scaling */
+
+    if (iascl == 1) {
+	dlascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
+, ldb, info);
+    } else if (iascl == 2) {
+	dlascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
+, ldb, info);
+    }
+    if (ibscl == 1) {
+	dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
+, ldb, info);
+    } else if (ibscl == 2) {
+	dlascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
+, ldb, info);
+    }
+
+L50:
+    work[1] = (doublereal) wsize;
+
+    return 0;
+
+/*     End of DGELS */
+
+} /* dgels_ */