zgelss.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

		if (*nrhs > 1) {
/* 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, "ZUNMLQ", 
			"LC", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2);
		maxwrk = max(i__1,i__2);
	    } else {

/*              Path 2 - underdetermined   

                Space needed for ZBDSQR is BDSPAC = 5*M */

		maxwrk = (*m << 1) + (*n + *m) * ilaenv_(&c__1, "ZGEBRD", 
			" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
		i__1 = maxwrk, i__2 = (*m << 1) + *nrhs * ilaenv_(&c__1, 
			"ZUNMBR", "QLC", m, nrhs, m, &c_n1, (ftnlen)6, (
			ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR"
			, "P", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n * *nrhs;
		maxwrk = max(i__1,i__2);
	    }
	}
	minwrk = max(minwrk,1);
	maxwrk = max(minwrk,maxwrk);
	work[1].r = (doublereal) maxwrk, work[1].i = 0.;
    }

    if (*lwork < minwrk && ! lquery) {
	*info = -12;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGELSS", &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 = dlamch_("P");
    sfmin = dlamch_("S");
    lstime_1.opcnt[gelss - 1] += 2.;
    smlnum = sfmin / eps;
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);

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

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

/*        Scale matrix norm up to SMLNUM */

	lstime_1.opcnt[gelss - 1] += (doublereal) (*m * 6 * *n);
	zlascl_("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] += (doublereal) (*m * 6 * *n);
	zlascl_("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);
	zlaset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
	dlaset_("F", &minmn, &c__1, &c_b78, &c_b78, &s[1], &minmn);
	*rank = 0;
	goto L70;
    }

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

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

/*        Scale matrix norm up to SMLNUM */

	lstime_1.opcnt[gelss - 1] += (doublereal) (*m * 6 * *nrhs);
	zlascl_("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] += (doublereal) (*m * 6 * *nrhs);
	zlascl_("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   
             (CWorkspace: need 2*N, prefer N+N*NB)   
             (RWorkspace: none) */

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

/*           Multiply B by transpose(Q)   
             (CWorkspace: need N+NRHS, prefer N+NRHS*NB)   
             (RWorkspace: none) */

	    nb = ilaenv_(&c__1, "ZUNMQR", "LC", m, nrhs, n, &c_n1, (ftnlen)6, 
		    (ftnlen)2);
	    lstime_1.opcnt[unmqr - 1] += dopla_("ZUNMQR", m, nrhs, n, &c__0, &
		    nb);
	    t1 = dsecnd_();
	    i__1 = *lwork - iwork + 1;
	    zunmqr_("L", "C", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
		    b_offset], ldb, &work[iwork], &i__1, info);
	    t2 = dsecnd_();
	    lstime_1.timng[unmqr - 1] += t2 - t1;

/*           Zero out below R */

	    if (*n > 1) {
		i__1 = *n - 1;
		i__2 = *n - 1;
		zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &a_ref(2, 1), lda);
	    }
	}

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

/*        Bidiagonalize R in A   
          (CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB)   
          (RWorkspace: need N) */

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

/*        Multiply B by transpose of left bidiagonalizing vectors of R   
          (CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB)   
          (RWorkspace: none) */

	nb = ilaenv_(&c__1, "ZUNMBR", "QLC", &mm, nrhs, n, &c_n1, (ftnlen)6, (
		ftnlen)3);
	lstime_1.opcnt[unmbr - 1] += dopla2_("ZUNMBR", "QLC", &mm, nrhs, n, &
		c__0, &nb);
	t1 = dsecnd_();
	i__1 = *lwork - iwork + 1;
	zunmbr_("Q", "L", "C", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], 
		&b[b_offset], ldb, &work[iwork], &i__1, info);
	t2 = dsecnd_();
	lstime_1.timng[unmbr - 1] += t2 - t1;

/*        Generate right bidiagonalizing vectors of R in A   
          (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)   
          (RWorkspace: none) */

	nb = ilaenv_(&c__1, "ZUNGBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)
		1);
	lstime_1.opcnt[ungbr - 1] += dopla2_("ZUNGBR", "P", n, n, n, &c__0, &
		nb);
	t1 = dsecnd_();
	i__1 = *lwork - iwork + 1;
	zungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &
		i__1, info);
	t2 = dsecnd_();
	lstime_1.timng[ungbr - 1] += t2 - t1;
	irwork = ie + *n;

/*        Perform bidiagonal QR iteration   
            multiply B by transpose of left singular vectors   
            compute right singular vectors in A   
          (CWorkspace: none)   
          (RWorkspace: need BDSPAC) */

	latime_1.ops = 0.;
	t1 = dsecnd_();
	zbdsqr_("U", n, n, &c__0, nrhs, &s[1], &rwork[ie], &a[a_offset], lda, 
		vdum, &c__1, &b[b_offset], ldb, &rwork[irwork], info);
	t2 = dsecnd_();
	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.;
/* Computing MAX */
	d__1 = *rcond * s[1];
	thr = max(d__1,sfmin);
	if (*rcond < 0.) {
	    lstime_1.opcnt[gelss - 1] += 1.;
/* Computing MAX */
	    d__1 = eps * s[1];
	    thr = max(d__1,sfmin);
	}
	*rank = 0;
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (s[i__] > thr) {
		lstime_1.opcnt[gelss - 1] += (doublereal) (*nrhs * 6 + 3);
		zdrscl_(nrhs, &s[i__], &b_ref(i__, 1), ldb);
		++(*rank);
	    } else {
		zlaset_("F", &c__1, nrhs, &c_b1, &c_b1, &b_ref(i__, 1), ldb);
	    }
/* L10: */
	}

/*        Multiply B by right singular vectors   
          (CWorkspace: need N, prefer N*NRHS)   
          (RWorkspace: none) */

	if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
	    lstime_1.opcnt[gemm - 1] += dopbl3_("ZGEMM ", n, nrhs, n);
	    t1 = dsecnd_();
	    zgemm_("C", "N", n, nrhs, n, &c_b2, &a[a_offset], lda, &b[
		    b_offset], ldb, &c_b1, &work[1], ldb);
	    t2 = dsecnd_();
	    lstime_1.timng[gemm - 1] += t2 - t1;
	    zlacpy_("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] += dopbl3_("ZGEMM ", n, &bl, n);
		t1 = dsecnd_();
		zgemm_("C", "N", n, &bl, n, &c_b2, &a[a_offset], lda, &b_ref(
			1, i__), ldb, &c_b1, &work[1], n);
		t2 = dsecnd_();
		lstime_1.timng[gemm - 1] += t2 - t1;
		zlacpy_("G", n, &bl, &work[1], n, &b_ref(1, i__), ldb);
/* L20: */
	    }
	} else {
	    lstime_1.opcnt[gemv - 1] += dopbl2_("ZGEMV ", n, n, &c__0, &c__0);
	    t1 = dsecnd_();
	    zgemv_("C", n, n, &c_b2, &a[a_offset], lda, &b[b_offset], &c__1, &
		    c_b1, &work[1], &c__1);
	    t2 = dsecnd_();
	    lstime_1.timng[gemv - 1] += t2 - t1;
	    zcopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
	}

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

/*        Underdetermined case, M much less than N   

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

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

/*        Compute A=L*Q   
          (CWorkspace: need 2*M, prefer M+M*NB)   
          (RWorkspace: none) */

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