sgelss.c

著名的LAPACK矩阵计算软件包, 是比较新的版本, 一般用到矩阵分解的朋友也许会用到

/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
		    maxwrk = max(i__1,i__2);
		} else {
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
		    maxwrk = max(i__1,i__2);
		}
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "SORMLQ", 
			"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2);
		maxwrk = max(i__1,i__2);
	    } else {

/*              Path 2 - underdetermined */

		maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "SGEBRD", " ", m,
			 n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "SORMBR"
			, "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORGBR", 
			"P", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1);
		maxwrk = max(i__1,i__2);
		maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n * *nrhs;
		maxwrk = max(i__1,i__2);
	    }
	}
	maxwrk = max(minwrk,maxwrk);
	work[1] = (real) maxwrk;
    }

    minwrk = max(minwrk,1);
    if (*lwork < minwrk && ! lquery) {
	*info = -12;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGELSS", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {
	*rank = 0;
	return 0;
    }

/*     Get machine parameters */

    eps = slamch_("P");
    sfmin = slamch_("S");
    lstime_1.opcnt[gelss - 1] += 2.f;
    smlnum = sfmin / eps;
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);

/*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    anrm = slange_("M", m, n, &a[a_offset], lda, &work[1]);
    iascl = 0;
    if (anrm > 0.f && anrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	lstime_1.opcnt[gelss - 1] += (real) (*m * *n);
	slascl_("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 */

	lstime_1.opcnt[gelss - 1] += (real) (*m * *n);
	slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
		info);
	iascl = 2;
    } else if (anrm == 0.f) {

/*        Matrix all zero. Return zero solution. */

	i__1 = max(*m,*n);
	slaset_("F", &i__1, nrhs, &c_b74, &c_b74, &b[b_offset], ldb);
	slaset_("F", &minmn, &c__1, &c_b74, &c_b74, &s[1], &c__1);
	*rank = 0;
	goto L70;
    }

/*     Scale B if max element outside range [SMLNUM,BIGNUM] */

    bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
    ibscl = 0;
    if (bnrm > 0.f && bnrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	lstime_1.opcnt[gelss - 1] += (real) (*m * *nrhs);
	slascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
		 info);
	ibscl = 1;
    } else if (bnrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	lstime_1.opcnt[gelss - 1] += (real) (*m * *nrhs);
	slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
		 info);
	ibscl = 2;
    }

/*     Overdetermined case */

    if (*m >= *n) {

/*        Path 1 - overdetermined or exactly determined */

	mm = *m;
	if (*m >= mnthr) {

/*           Path 1a - overdetermined, with many more rows than columns */

	    mm = *n;
	    itau = 1;
	    iwork = itau + *n;

/*           Compute A=Q*R   
             (Workspace: need 2*N, prefer N+N*NB) */

	    nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
		    (ftnlen)1);
	    lstime_1.opcnt[geqrf - 1] += sopla_("SGEQRF", m, n, &c__0, &c__0, 
		    &nb);
	    t1 = second_();
	    i__1 = *lwork - iwork + 1;
	    sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1,
		     info);
	    t2 = second_();
	    lstime_1.timng[geqrf - 1] += t2 - t1;

/*           Multiply B by transpose(Q)   
             (Workspace: need N+NRHS, prefer N+NRHS*NB) */

	    nb = ilaenv_(&c__1, "SORMQR", "LT", m, nrhs, n, &c_n1, (ftnlen)6, 
		    (ftnlen)2);
	    lstime_1.opcnt[ormqr - 1] += sopla_("SORMQR", m, nrhs, n, &c__0, &
		    nb);
	    t1 = second_();
	    i__1 = *lwork - iwork + 1;
	    sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
		    b_offset], ldb, &work[iwork], &i__1, info);
	    t2 = second_();
	    lstime_1.timng[ormqr - 1] += t2 - t1;

/*           Zero out below R */

	    if (*n > 1) {
		i__1 = *n - 1;
		i__2 = *n - 1;
		slaset_("L", &i__1, &i__2, &c_b74, &c_b74, &a_ref(2, 1), lda);
	    }
	}

	ie = 1;
	itauq = ie + *n;
	itaup = itauq + *n;
	iwork = itaup + *n;

/*        Bidiagonalize R in A   
          (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */

	nb = ilaenv_(&c__1, "SGEBRD", " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (
		ftnlen)1);
	lstime_1.opcnt[gebrd - 1] += sopla_("SGEBRD", &mm, n, &c__0, &c__0, &
		nb);
	t1 = second_();
	i__1 = *lwork - iwork + 1;
	sgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		work[itaup], &work[iwork], &i__1, info);
	t2 = second_();
	lstime_1.timng[gebrd - 1] += t2 - t1;

/*        Multiply B by transpose of left bidiagonalizing vectors of R   
          (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */

	nb = ilaenv_(&c__1, "SORMBR", "QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (
		ftnlen)3);
	lstime_1.opcnt[ormbr - 1] += sopla2_("SORMBR", "QLT", &mm, nrhs, n, &
		c__0, &nb);
	t1 = second_();
	i__1 = *lwork - iwork + 1;
	sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], 
		&b[b_offset], ldb, &work[iwork], &i__1, info);
	t2 = second_();
	lstime_1.timng[ormbr - 1] += t2 - t1;

/*        Generate right bidiagonalizing vectors of R in A   
          (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */

	nb = ilaenv_(&c__1, "SORGBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)
		1);
	lstime_1.opcnt[orgbr - 1] += sopla2_("SORGBR", "P", n, n, n, &c__0, &
		nb);
	t1 = second_();
	i__1 = *lwork - iwork + 1;
	sorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &
		i__1, info);
	t2 = second_();
	lstime_1.timng[orgbr - 1] += t2 - t1;
	iwork = ie + *n;

/*        Perform bidiagonal QR iteration   
            multiply B by transpose of left singular vectors   
            compute right singular vectors in A   
          (Workspace: need BDSPAC) */

	latime_1.ops = 0.f;
	t1 = second_();
	sbdsqr_("U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, 
		vdum, &c__1, &b[b_offset], ldb, &work[iwork], info)
		;
	t2 = second_();
	lstime_1.timng[bdsqr - 1] += t2 - t1;
	lstime_1.opcnt[bdsqr - 1] += latime_1.ops;
	if (*info != 0) {
	    goto L70;
	}

/*        Multiply B by reciprocals of singular values */

	lstime_1.opcnt[gelss - 1] += 1.f;
/* Computing MAX */
	r__1 = *rcond * s[1];
	thr = dmax(r__1,sfmin);
	if (*rcond < 0.f) {
	    lstime_1.opcnt[gelss - 1] += 1.f;
/* Computing MAX */
	    r__1 = eps * s[1];
	    thr = dmax(r__1,sfmin);
	}
	*rank = 0;
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (s[i__] > thr) {
		lstime_1.opcnt[gelss - 1] += (real) (*nrhs + 3);
		srscl_(nrhs, &s[i__], &b_ref(i__, 1), ldb);
		++(*rank);
	    } else {
		slaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b_ref(i__, 1), ldb);
	    }
/* L10: */
	}

/*        Multiply B by right singular vectors   
          (Workspace: need N, prefer N*NRHS) */

	if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
	    lstime_1.opcnt[gemm - 1] += sopbl3_("SGEMM ", n, nrhs, n);
	    t1 = second_();
	    sgemm_("T", "N", n, nrhs, n, &c_b145, &a[a_offset], lda, &b[
		    b_offset], ldb, &c_b74, &work[1], ldb);
	    t2 = second_();
	    lstime_1.timng[gemm - 1] += t2 - t1;
	    slacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb)
		    ;
	} else if (*nrhs > 1) {
	    chunk = *lwork / *n;
	    i__1 = *nrhs;
	    i__2 = chunk;
	    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
		i__3 = *nrhs - i__ + 1;
		bl = min(i__3,chunk);
		lstime_1.opcnt[gemm - 1] += sopbl3_("SGEMM ", n, &bl, n);
		t1 = second_();
		sgemm_("T", "N", n, &bl, n, &c_b145, &a[a_offset], lda, &
			b_ref(1, i__), ldb, &c_b74, &work[1], n);
		t2 = second_();
		lstime_1.timng[gemm - 1] += t2 - t1;
		slacpy_("G", n, &bl, &work[1], n, &b_ref(1, i__), ldb);
/* L20: */
	    }
	} else {
	    lstime_1.opcnt[gemv - 1] += sopbl2_("SGEMV ", n, n, &c__0, &c__0);
	    t1 = second_();
	    sgemv_("T", n, n, &c_b145, &a[a_offset], lda, &b[b_offset], &c__1,
		     &c_b74, &work[1], &c__1);
	    t2 = second_();
	    lstime_1.timng[gemv - 1] += t2 - t1;
	    scopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
	}

    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max(
		i__2,*nrhs), i__1 = *n - *m * 3;
	if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) {

/*        Path 2a - underdetermined, with many more columns than rows   
          and sufficient workspace for an efficient algorithm */

	    ldwork = *m;
/* Computing MAX   
   Computing MAX */
	    i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = 
		    max(i__3,*nrhs), i__4 = *n - *m * 3;
	    i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda + 
		    *m + *m * *nrhs;
	    if (*lwork >= max(i__2,i__1)) {
		ldwork = *lda;
	    }
	    itau = 1;
	    iwork = *m + 1;

/*        Compute A=L*Q   
          (Workspace: need 2*M, prefer M+M*NB) */

	    nb = ilaenv_(&c__1, "SGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
		    (ftnlen)1);
	    lstime_1.opcnt[gelqf - 1] += sopla_("SGELQF", m, n, &c__0, &c__0, 
		    &nb);
	    t1 = second_();
	    i__2 = *lwork - iwork + 1;
	    sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2,
		     info);
	    t2 = second_();
	    lstime_1.timng[gelqf - 1] += t2 - t1;
	    il = iwork;