clalsd.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

/*        Since B is complex, the following call to SGEMM is performed   
          in two steps (real and imaginary parts). That is for V * B   
          (in the real version of the code V' is stored in WORK).   

          CALL SGEMM( 'T', 'N', N, NRHS, N, ONE, WORK, N, B, LDB, ZERO,   
      $               WORK( NWORK ), N ) */

	j = irwb - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++j;
		i__3 = b_subscr(jrow, jcol);
		rwork[j] = b[i__3].r;
/* L110: */
	    }
/* L120: */
	}
	latime_1.ops += sopbl3_("SGEMM ", n, nrhs, n);
	sgemm_("T", "N", n, nrhs, n, &c_b10, &rwork[irwvt], n, &rwork[irwb], 
		n, &c_b35, &rwork[irwrb], n);
	j = irwb - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++j;
		rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L130: */
	    }
/* L140: */
	}
	latime_1.ops += sopbl3_("SGEMM ", n, nrhs, n);
	sgemm_("T", "N", n, nrhs, n, &c_b10, &rwork[irwvt], n, &rwork[irwb], 
		n, &c_b35, &rwork[irwib], n);
	jreal = irwrb - 1;
	jimag = irwib - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++jreal;
		++jimag;
		i__3 = b_subscr(jrow, jcol);
		i__4 = jreal;
		i__5 = jimag;
		q__1.r = rwork[i__4], q__1.i = rwork[i__5];
		b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L150: */
	    }
/* L160: */
	}

/*        Unscale. */

	latime_1.ops += (real) (*n + *n * 6 * *nrhs);
	slascl_("G", &c__0, &c__0, &c_b10, &orgnrm, n, &c__1, &d__[1], n, 
		info);
	slasrt_("D", n, &d__[1], info);
	clascl_("G", &c__0, &c__0, &orgnrm, &c_b10, n, nrhs, &b[b_offset], 
		ldb, info);

	return 0;
    }

/*     Book-keeping and setting up some constants. */

    nlvl = (integer) (log((real) (*n) / (real) (*smlsiz + 1)) / log(2.f)) + 1;

    smlszp = *smlsiz + 1;

    u = 1;
    vt = *smlsiz * *n + 1;
    difl = vt + smlszp * *n;
    difr = difl + nlvl * *n;
    z__ = difr + (nlvl * *n << 1);
    c__ = z__ + nlvl * *n;
    s = c__ + *n;
    poles = s + *n;
    givnum = poles + (nlvl << 1) * *n;
    nrwork = givnum + (nlvl << 1) * *n;
    bx = 1;

    irwrb = nrwork;
    irwib = irwrb + *smlsiz * *nrhs;
    irwb = irwib + *smlsiz * *nrhs;

    sizei = *n + 1;
    k = sizei + *n;
    givptr = k + *n;
    perm = givptr + *n;
    givcol = perm + nlvl * *n;
    iwk = givcol + (nlvl * *n << 1);

    st = 1;
    sqre = 0;
    icmpq1 = 1;
    icmpq2 = 0;
    nsub = 0;

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if ((r__1 = d__[i__], dabs(r__1)) < eps) {
	    d__[i__] = r_sign(&eps, &d__[i__]);
	}
/* L170: */
    }

    i__1 = nm1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if ((r__1 = e[i__], dabs(r__1)) < eps || i__ == nm1) {
	    ++nsub;
	    iwork[nsub] = st;

/*           Subproblem found. First determine its size and then   
             apply divide and conquer on it. */

	    if (i__ < nm1) {

/*              A subproblem with E(I) small for I < NM1. */

		nsize = i__ - st + 1;
		iwork[sizei + nsub - 1] = nsize;
	    } else if ((r__1 = e[i__], dabs(r__1)) >= eps) {

/*              A subproblem with E(NM1) not too small but I = NM1. */

		nsize = *n - st + 1;
		iwork[sizei + nsub - 1] = nsize;
	    } else {

/*              A subproblem with E(NM1) small. This implies an   
                1-by-1 subproblem at D(N), which is not solved   
                explicitly. */

		nsize = i__ - st + 1;
		iwork[sizei + nsub - 1] = nsize;
		++nsub;
		iwork[nsub] = *n;
		iwork[sizei + nsub - 1] = 1;
		ccopy_(nrhs, &b_ref(*n, 1), ldb, &work[bx + nm1], n);
	    }
	    st1 = st - 1;
	    if (nsize == 1) {

/*              This is a 1-by-1 subproblem and is not solved   
                explicitly. */

		ccopy_(nrhs, &b_ref(st, 1), ldb, &work[bx + st1], n);
	    } else if (nsize <= *smlsiz) {

/*              This is a small subproblem and is solved by SLASDQ. */

		slaset_("A", &nsize, &nsize, &c_b35, &c_b10, &rwork[vt + st1],
			 n);
		slaset_("A", &nsize, &nsize, &c_b35, &c_b10, &rwork[u + st1], 
			n);
		slasdq_("U", &c__0, &nsize, &nsize, &nsize, &c__0, &d__[st], &
			e[st], &rwork[vt + st1], n, &rwork[u + st1], n, &
			rwork[nrwork], &c__1, &rwork[nrwork], info)
			;
		if (*info != 0) {
		    return 0;
		}

/*              In the real version, B is passed to SLASDQ and multiplied   
                internally by Q'. Here B is complex and that product is   
                computed below in two steps (real and imaginary parts). */

		j = irwb - 1;
		i__2 = *nrhs;
		for (jcol = 1; jcol <= i__2; ++jcol) {
		    i__3 = st + nsize - 1;
		    for (jrow = st; jrow <= i__3; ++jrow) {
			++j;
			i__4 = b_subscr(jrow, jcol);
			rwork[j] = b[i__4].r;
/* L180: */
		    }
/* L190: */
		}
		latime_1.ops += sopbl3_("SGEMM ", &nsize, nrhs, &nsize);
		sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b10, &rwork[u + st1]
			, n, &rwork[irwb], &nsize, &c_b35, &rwork[irwrb], &
			nsize);
		j = irwb - 1;
		i__2 = *nrhs;
		for (jcol = 1; jcol <= i__2; ++jcol) {
		    i__3 = st + nsize - 1;
		    for (jrow = st; jrow <= i__3; ++jrow) {
			++j;
			rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L200: */
		    }
/* L210: */
		}
		latime_1.ops += sopbl3_("SGEMM ", &nsize, nrhs, &nsize);
		sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b10, &rwork[u + st1]
			, n, &rwork[irwb], &nsize, &c_b35, &rwork[irwib], &
			nsize);
		jreal = irwrb - 1;
		jimag = irwib - 1;
		i__2 = *nrhs;
		for (jcol = 1; jcol <= i__2; ++jcol) {
		    i__3 = st + nsize - 1;
		    for (jrow = st; jrow <= i__3; ++jrow) {
			++jreal;
			++jimag;
			i__4 = b_subscr(jrow, jcol);
			i__5 = jreal;
			i__6 = jimag;
			q__1.r = rwork[i__5], q__1.i = rwork[i__6];
			b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L220: */
		    }
/* L230: */
		}

		clacpy_("A", &nsize, nrhs, &b_ref(st, 1), ldb, &work[bx + st1]
			, n);
	    } else {

/*              A large problem. Solve it using divide and conquer. */

		slasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], &
			rwork[u + st1], n, &rwork[vt + st1], &iwork[k + st1], 
			&rwork[difl + st1], &rwork[difr + st1], &rwork[z__ + 
			st1], &rwork[poles + st1], &iwork[givptr + st1], &
			iwork[givcol + st1], n, &iwork[perm + st1], &rwork[
			givnum + st1], &rwork[c__ + st1], &rwork[s + st1], &
			rwork[nrwork], &iwork[iwk], info);
		if (*info != 0) {
		    return 0;
		}
		bxst = bx + st1;
		clalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b_ref(st, 1), ldb, &
			work[bxst], n, &rwork[u + st1], n, &rwork[vt + st1], &
			iwork[k + st1], &rwork[difl + st1], &rwork[difr + st1]
			, &rwork[z__ + st1], &rwork[poles + st1], &iwork[
			givptr + st1], &iwork[givcol + st1], n, &iwork[perm + 
			st1], &rwork[givnum + st1], &rwork[c__ + st1], &rwork[
			s + st1], &rwork[nrwork], &iwork[iwk], info);
		if (*info != 0) {
		    return 0;
		}
	    }
	    st = i__ + 1;
	}
/* L240: */
    }

/*     Apply the singular values and treat the tiny ones as zero. */

    latime_1.ops += 1.f;
    tol = *rcond * (r__1 = d__[isamax_(n, &d__[1], &c__1)], dabs(r__1));

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {

/*        Some of the elements in D can be negative because 1-by-1   
          subproblems were not solved explicitly. */

	if ((r__1 = d__[i__], dabs(r__1)) <= tol) {
	    claset_("A", &c__1, nrhs, &c_b1, &c_b1, &work[bx + i__ - 1], n);
	} else {
	    ++(*rank);
	    latime_1.ops += (real) (*nrhs * 6);
	    clascl_("G", &c__0, &c__0, &d__[i__], &c_b10, &c__1, nrhs, &work[
		    bx + i__ - 1], n, info);
	}
	d__[i__] = (r__1 = d__[i__], dabs(r__1));
/* L250: */
    }

/*     Now apply back the right singular vectors. */

    icmpq2 = 1;
    i__1 = nsub;
    for (i__ = 1; i__ <= i__1; ++i__) {
	st = iwork[i__];
	st1 = st - 1;
	nsize = iwork[sizei + i__ - 1];
	bxst = bx + st1;
	if (nsize == 1) {
	    ccopy_(nrhs, &work[bxst], n, &b_ref(st, 1), ldb);
	} else if (nsize <= *smlsiz) {

/*           Since B and BX are complex, the following call to SGEMM   
             is performed in two steps (real and imaginary parts).   

             CALL SGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE,   
      $                  RWORK( VT+ST1 ), N, RWORK( BXST ), N, ZERO,   
      $                  B( ST, 1 ), LDB ) */

	    j = bxst - *n - 1;
	    jreal = irwb - 1;
	    i__2 = *nrhs;
	    for (jcol = 1; jcol <= i__2; ++jcol) {
		j += *n;
		i__3 = nsize;
		for (jrow = 1; jrow <= i__3; ++jrow) {
		    ++jreal;
		    i__4 = j + jrow;
		    rwork[jreal] = work[i__4].r;
/* L260: */
		}
/* L270: */
	    }
	    latime_1.ops += sopbl3_("SGEMM ", &nsize, nrhs, &nsize)
		    ;
	    sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b10, &rwork[vt + st1], 
		    n, &rwork[irwb], &nsize, &c_b35, &rwork[irwrb], &nsize);
	    j = bxst - *n - 1;
	    jimag = irwb - 1;
	    i__2 = *nrhs;
	    for (jcol = 1; jcol <= i__2; ++jcol) {
		j += *n;
		i__3 = nsize;
		for (jrow = 1; jrow <= i__3; ++jrow) {
		    ++jimag;
		    rwork[jimag] = r_imag(&work[j + jrow]);
/* L280: */
		}
/* L290: */
	    }
	    latime_1.ops += sopbl3_("SGEMM ", &nsize, nrhs, &nsize)
		    ;
	    sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b10, &rwork[vt + st1], 
		    n, &rwork[irwb], &nsize, &c_b35, &rwork[irwib], &nsize);
	    jreal = irwrb - 1;
	    jimag = irwib - 1;
	    i__2 = *nrhs;
	    for (jcol = 1; jcol <= i__2; ++jcol) {
		i__3 = st + nsize - 1;
		for (jrow = st; jrow <= i__3; ++jrow) {
		    ++jreal;
		    ++jimag;
		    i__4 = b_subscr(jrow, jcol);
		    i__5 = jreal;
		    i__6 = jimag;
		    q__1.r = rwork[i__5], q__1.i = rwork[i__6];
		    b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L300: */
		}
/* L310: */
	    }
	} else {
	    clalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b_ref(st, 
		    1), ldb, &rwork[u + st1], n, &rwork[vt + st1], &iwork[k + 
		    st1], &rwork[difl + st1], &rwork[difr + st1], &rwork[z__ 
		    + st1], &rwork[poles + st1], &iwork[givptr + st1], &iwork[
		    givcol + st1], n, &iwork[perm + st1], &rwork[givnum + st1]
		    , &rwork[c__ + st1], &rwork[s + st1], &rwork[nrwork], &
		    iwork[iwk], info);
	    if (*info != 0) {
		return 0;
	    }
	}
/* L320: */
    }

/*     Unscale and sort the singular values. */

    latime_1.ops += (real) (*n + *n * 6 * *nrhs);
    slascl_("G", &c__0, &c__0, &c_b10, &orgnrm, n, &c__1, &d__[1], n, info);
    slasrt_("D", n, &d__[1], info);
    clascl_("G", &c__0, &c__0, &orgnrm, &c_b10, n, nrhs, &b[b_offset], ldb, 
	    info);

    return 0;

/*     End of CLALSD */

} /* clalsd_ */

#undef b_ref
#undef b_subscr