/* Subroutine */ int stgex2_(logical *wantq, logical *wantz, integer *n, real
*a, integer *lda, real *b, integer *ldb, real *q, integer *ldq, real *
z__, integer *ldz, integer *j1, integer *n1, integer *n2, real *work,
integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
z_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real f, g;
integer i__, m;
real s[16] /* was [4][4] */, t[16] /* was [4][4] */, be[2], ai[2], ar[2],
sa, sb, li[16] /* was [4][4] */, ir[16] /* was [4][4]
*/, ss, ws, eps;
logical weak;
real ddum;
integer idum;
real taul[4], dsum, taur[4], scpy[16] /* was [4][4] */, tcpy[16]
/* was [4][4] */;
extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
integer *, real *, real *);
real scale, bqra21, brqa21;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
real licop[16] /* was [4][4] */;
integer linfo;
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
real ircop[16] /* was [4][4] */, dnorm;
integer iwork[4];
extern /* Subroutine */ int slagv2_(real *, integer *, real *, integer *,
real *, real *, real *, real *, real *, real *, real *), sgeqr2_(
integer *, integer *, real *, integer *, real *, real *, integer *
), sgerq2_(integer *, integer *, real *, integer *, real *, real *
, integer *), sorg2r_(integer *, integer *, integer *, real *,
integer *, real *, real *, integer *), sorgr2_(integer *, integer
*, integer *, real *, integer *, real *, real *, integer *),
sorm2r_(char *, char *, integer *, integer *, integer *, real *,
integer *, real *, real *, integer *, real *, integer *), sormr2_(char *, char *, integer *, integer *, integer *,
real *, integer *, real *, real *, integer *, real *, integer *);
real dscale;
extern /* Subroutine */ int stgsy2_(char *, integer *, integer *, integer
*, real *, integer *, real *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slartg_(real *, real *,
real *, real *, real *);
real thresh;
extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *,
real *, real *, integer *), slassq_(integer *, real *,
integer *, real *, real *);
real smlnum;
logical strong;
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) */
/* of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair */
/* (A, B) by an orthogonal equivalence transformation. */
/* (A, B) must be in generalized real Schur canonical form (as returned */
/* by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 */
/* diagonal blocks. B is upper triangular. */
/* Optionally, the matrices Q and Z of generalized Schur vectors are */
/* updated. */
/* Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' */
/* Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' */
/* Arguments */
/* ========= */
/* WANTQ (input) LOGICAL */
/* .TRUE. : update the left transformation matrix Q; */
/* .FALSE.: do not update Q. */
/* WANTZ (input) LOGICAL */
/* .TRUE. : update the right transformation matrix Z; */
/* .FALSE.: do not update Z. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* A (input/output) REAL arrays, dimensions (LDA,N) */
/* On entry, the matrix A in the pair (A, B). */
/* On exit, the updated matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input/output) REAL arrays, dimensions (LDB,N) */
/* On entry, the matrix B in the pair (A, B). */
/* On exit, the updated matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* Q (input/output) REAL array, dimension (LDZ,N) */
/* On entry, if WANTQ = .TRUE., the orthogonal matrix Q. */
/* On exit, the updated matrix Q. */
/* Not referenced if WANTQ = .FALSE.. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= 1. */
/* If WANTQ = .TRUE., LDQ >= N. */
/* Z (input/output) REAL array, dimension (LDZ,N) */
/* On entry, if WANTZ =.TRUE., the orthogonal matrix Z. */
/* On exit, the updated matrix Z. */
/* Not referenced if WANTZ = .FALSE.. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1. */
/* If WANTZ = .TRUE., LDZ >= N. */
/* J1 (input) INTEGER */
/* The index to the first block (A11, B11). 1 <= J1 <= N. */
/* N1 (input) INTEGER */
/* The order of the first block (A11, B11). N1 = 0, 1 or 2. */
/* N2 (input) INTEGER */
/* The order of the second block (A22, B22). N2 = 0, 1 or 2. */
/* WORK (workspace) REAL array, dimension (MAX(1,LWORK)). */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 ) */
/* INFO (output) INTEGER */
/* =0: Successful exit */
/* >0: If INFO = 1, the transformed matrix (A, B) would be */
/* too far from generalized Schur form; the blocks are */
/* not swapped and (A, B) and (Q, Z) are unchanged. */
/* The problem of swapping is too ill-conditioned. */
/* <0: If INFO = -16: LWORK is too small. Appropriate value */
/* for LWORK is returned in WORK(1). */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* In the current code both weak and strong stability tests are */
/* performed. The user can omit the strong stability test by changing */
/* the internal logical parameter WANDS to .FALSE.. See ref. [2] for */
/* details. */
/* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
/* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
/* M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
/* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
/* [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
/* Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
/* Estimation: Theory, Algorithms and Software, */
/* Report UMINF - 94.04, Department of Computing Science, Umea */
/* University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working */
/* Note 87. To appear in Numerical Algorithms, 1996. */
/* ===================================================================== */
/* Replaced various illegal calls to SCOPY by calls to SLASET, or by DO */
/* loops. Sven Hammarling, 1/5/02. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n <= 1 || *n1 <= 0 || *n2 <= 0) {
return 0;
}
if (*n1 > *n || *j1 + *n1 > *n) {
return 0;
}
m = *n1 + *n2;
/* Computing MAX */
i__1 = *n * m, i__2 = m * m << 1;
if (*lwork < max(i__1,i__2)) {
*info = -16;
/* Computing MAX */
i__1 = *n * m, i__2 = m * m << 1;
work[1] = (real) max(i__1,i__2);
return 0;
}
weak = FALSE_;
strong = FALSE_;
/* Make a local copy of selected block */
slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, li, &c__4);
slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, ir, &c__4);
slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, s, &c__4);
slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, t, &c__4);
/* Compute threshold for testing acceptance of swapping. */
eps = slamch_("P");
smlnum = slamch_("S") / eps;
dscale = 0.f;
dsum = 1.f;
slacpy_("Full", &m, &m, s, &c__4, &work[1], &m);
i__1 = m * m;
slassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
slacpy_("Full", &m, &m, t, &c__4, &work[1], &m);
i__1 = m * m;
slassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
dnorm = dscale * sqrt(dsum);
/* Computing MAX */
r__1 = eps * 10.f * dnorm;
thresh = dmax(r__1,smlnum);
if (m == 2) {
/* CASE 1: Swap 1-by-1 and 1-by-1 blocks. */
/* Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks */
/* using Givens rotations and perform the swap tentatively. */
f = s[5] * t[0] - t[5] * s[0];
g = s[5] * t[4] - t[5] * s[4];
sb = dabs(t[5]);
sa = dabs(s[5]);
slartg_(&f, &g, &ir[4], ir, &ddum);
ir[1] = -ir[4];
ir[5] = ir[0];
srot_(&c__2, s, &c__1, &s[4], &c__1, ir, &ir[1]);
srot_(&c__2, t, &c__1, &t[4], &c__1, ir, &ir[1]);
if (sa >= sb) {
slartg_(s, &s[1], li, &li[1], &ddum);
} else {
slartg_(t, &t[1], li, &li[1], &ddum);
}
srot_(&c__2, s, &c__4, &s[1], &c__4, li, &li[1]);
srot_(&c__2, t, &c__4, &t[1], &c__4, li, &li[1]);
li[5] = li[0];
li[4] = -li[1];
/* Weak stability test: */
/* |S21| + |T21| <= O(EPS * F-norm((S, T))) */
ws = dabs(s[1]) + dabs(t[1]);
weak = ws <= thresh;
if (! weak) {
goto L70;
}
if (TRUE_) {
/* Strong stability test: */
/* F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B))) */
slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m
+ 1], &m);
sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
work[1], &m);
sgemm_("N", "T", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
c_b42, &work[m * m + 1], &m);
dscale = 0.f;
dsum = 1.f;
i__1 = m * m;
slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m
+ 1], &m);
sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
work[1], &m);
sgemm_("N", "T", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
c_b42, &work[m * m + 1], &m);
i__1 = m * m;
slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
ss = dscale * sqrt(dsum);
strong = ss <= thresh;
if (! strong) {
goto L70;
}
}
/* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and */
/* (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
i__1 = *j1 + 1;
srot_(&i__1, &a[*j1 * a_dim1 + 1], &c__1, &a[(*j1 + 1) * a_dim1 + 1],
&c__1, ir, &ir[1]);
i__1 = *j1 + 1;
srot_(&i__1, &b[*j1 * b_dim1 + 1], &c__1, &b[(*j1 + 1) * b_dim1 + 1],
&c__1, ir, &ir[1]);
i__1 = *n - *j1 + 1;
srot_(&i__1, &a[*j1 + *j1 * a_dim1], lda, &a[*j1 + 1 + *j1 * a_dim1],
lda, li, &li[1]);
i__1 = *n - *j1 + 1;
srot_(&i__1, &b[*j1 + *j1 * b_dim1], ldb, &b[*j1 + 1 + *j1 * b_dim1],
ldb, li, &li[1]);
/* Set N1-by-N2 (2,1) - blocks to ZERO. */
a[*j1 + 1 + *j1 * a_dim1] = 0.f;
b[*j1 + 1 + *j1 * b_dim1] = 0.f;
/* Accumulate transformations into Q and Z if requested. */
if (*wantz) {
srot_(n, &z__[*j1 * z_dim1 + 1], &c__1, &z__[(*j1 + 1) * z_dim1 +
1], &c__1, ir, &ir[1]);
}
if (*wantq) {
srot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[(*j1 + 1) * q_dim1 + 1],
&c__1, li, &li[1]);
}
/* Exit with INFO = 0 if swap was successfully performed. */
return 0;
} else {
/* CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2 */
/* and 2-by-2 blocks. */
/* Solve the generalized Sylvester equation */
/* S11 * R - L * S22 = SCALE * S12 */
/* T11 * R - L * T22 = SCALE * T12 */
/* for R and L. Solutions in LI and IR. */
slacpy_("Full", n1, n2, &t[(*n1 + 1 << 2) - 4], &c__4, li, &c__4);
slacpy_("Full", n1, n2, &s[(*n1 + 1 << 2) - 4], &c__4, &ir[*n2 + 1 + (
*n1 + 1 << 2) - 5], &c__4);
stgsy2_("N", &c__0, n1, n2, s, &c__4, &s[*n1 + 1 + (*n1 + 1 << 2) - 5]
, &c__4, &ir[*n2 + 1 + (*n1 + 1 << 2) - 5], &c__4, t, &c__4, &
t[*n1 + 1 + (*n1 + 1 << 2) - 5], &c__4, li, &c__4, &scale, &
dsum, &dscale, iwork, &idum, &linfo);
/* Compute orthogonal matrix QL: */
/* QL' * LI = [ TL ] */
/* [ 0 ] */
/* where */
/* LI = [ -L ] */
/* [ SCALE * identity(N2) ] */
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
sscal_(n1, &c_b48, &li[(i__ << 2) - 4], &c__1);
li[*n1 + i__ + (i__ << 2) - 5] = scale;
/* L10: */
}
sgeqr2_(&m, n2, li, &c__4, taul, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
sorg2r_(&m, &m, n2, li, &c__4, taul, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
/* Compute orthogonal matrix RQ: */
/* IR * RQ' = [ 0 TR], */
/* where IR = [ SCALE * identity(N1), R ] */
i__1 = *n1;
for (i__ = 1; i__ <= i__1; ++i__) {
ir[*n2 + i__ + (i__ << 2) - 5] = scale;
/* L20: */
}
sgerq2_(n1, &m, &ir[*n2], &c__4, taur, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
sorgr2_(&m, &m, n1, ir, &c__4, taur, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
/* Perform the swapping tentatively: */
sgemm_("T", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
work[1], &m);
sgemm_("N", "T", &m, &m, &m, &c_b42, &work[1], &m, ir, &c__4, &c_b5,
s, &c__4);
sgemm_("T", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
work[1], &m);
sgemm_("N", "T", &m, &m, &m, &c_b42, &work[1], &m, ir, &c__4, &c_b5,
t, &c__4);
slacpy_("F", &m, &m, s, &c__4, scpy, &c__4);
slacpy_("F", &m, &m, t, &c__4, tcpy, &c__4);
slacpy_("F", &m, &m, ir, &c__4, ircop, &c__4);
slacpy_("F", &m, &m, li, &c__4, licop, &c__4);
/* Triangularize the B-part by an RQ factorization. */
/* Apply transformation (from left) to A-part, giving S. */
sgerq2_(&m, &m, t, &c__4, taur, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
sormr2_("R", "T", &m, &m, &m, t, &c__4, taur, s, &c__4, &work[1], &
linfo);
if (linfo != 0) {
goto L70;
}
sormr2_("L", "N", &m, &m, &m, t, &c__4, taur, ir, &c__4, &work[1], &
linfo);
if (linfo != 0) {
goto L70;
}
/* Compute F-norm(S21) in BRQA21. (T21 is 0.) */
dscale = 0.f;
dsum = 1.f;
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
slassq_(n1, &s[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &dsum);
/* L30: */
}
brqa21 = dscale * sqrt(dsum);
/* Triangularize the B-part by a QR factorization. */
/* Apply transformation (from right) to A-part, giving S. */
sgeqr2_(&m, &m, tcpy, &c__4, taul, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
sorm2r_("L", "T", &m, &m, &m, tcpy, &c__4, taul, scpy, &c__4, &work[1]
, info);
sorm2r_("R", "N", &m, &m, &m, tcpy, &c__4, taul, licop, &c__4, &work[
1], info);
if (linfo != 0) {
goto L70;
}
/* Compute F-norm(S21) in BQRA21. (T21 is 0.) */
dscale = 0.f;
dsum = 1.f;
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
slassq_(n1, &scpy[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &
dsum);
/* L40: */
}
bqra21 = dscale * sqrt(dsum);
/* Decide which method to use. */
/* Weak stability test: */
/* F-norm(S21) <= O(EPS * F-norm((S, T))) */
if (bqra21 <= brqa21 && bqra21 <= thresh) {
slacpy_("F", &m, &m, scpy, &c__4, s, &c__4);
slacpy_("F", &m, &m, tcpy, &c__4, t, &c__4);
slacpy_("F", &m, &m, ircop, &c__4, ir, &c__4);
slacpy_("F", &m, &m, licop, &c__4, li, &c__4);
} else if (brqa21 >= thresh) {
goto L70;
}
/* Set lower triangle of B-part to zero */
i__1 = m - 1;
i__2 = m - 1;
slaset_("Lower", &i__1, &i__2, &c_b5, &c_b5, &t[1], &c__4);
if (TRUE_) {
/* Strong stability test: */
/* F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B))) */
slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m
+ 1], &m);
sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
work[1], &m);
sgemm_("N", "N", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
c_b42, &work[m * m + 1], &m);
dscale = 0.f;
dsum = 1.f;
i__1 = m * m;
slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m
+ 1], &m);
sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
work[1], &m);
sgemm_("N", "N", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
c_b42, &work[m * m + 1], &m);
i__1 = m * m;
slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
ss = dscale * sqrt(dsum);
strong = ss <= thresh;
if (! strong) {
goto L70;
}
}
/* If the swap is accepted ("weakly" and "strongly"), apply the */
/* transformations and set N1-by-N2 (2,1)-block to zero. */
slaset_("Full", n1, n2, &c_b5, &c_b5, &s[*n2], &c__4);
/* copy back M-by-M diagonal block starting at index J1 of (A, B) */
slacpy_("F", &m, &m, s, &c__4, &a[*j1 + *j1 * a_dim1], lda)
;
slacpy_("F", &m, &m, t, &c__4, &b[*j1 + *j1 * b_dim1], ldb)
;
slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, t, &c__4);
/* Standardize existing 2-by-2 blocks. */
i__1 = m * m;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.f;
/* L50: */
}
work[1] = 1.f;
t[0] = 1.f;
idum = *lwork - m * m - 2;
if (*n2 > 1) {
slagv2_(&a[*j1 + *j1 * a_dim1], lda, &b[*j1 + *j1 * b_dim1], ldb,
ar, ai, be, &work[1], &work[2], t, &t[1]);
work[m + 1] = -work[2];
work[m + 2] = work[1];
t[*n2 + (*n2 << 2) - 5] = t[0];
t[4] = -t[1];
}
work[m * m] = 1.f;
t[m + (m << 2) - 5] = 1.f;
if (*n1 > 1) {
slagv2_(&a[*j1 + *n2 + (*j1 + *n2) * a_dim1], lda, &b[*j1 + *n2 +
(*j1 + *n2) * b_dim1], ldb, taur, taul, &work[m * m + 1],
&work[*n2 * m + *n2 + 1], &work[*n2 * m + *n2 + 2], &t[*
n2 + 1 + (*n2 + 1 << 2) - 5], &t[m + (m - 1 << 2) - 5]);
work[m * m] = work[*n2 * m + *n2 + 1];
work[m * m - 1] = -work[*n2 * m + *n2 + 2];
t[m + (m << 2) - 5] = t[*n2 + 1 + (*n2 + 1 << 2) - 5];
t[m - 1 + (m << 2) - 5] = -t[m + (m - 1 << 2) - 5];
}
sgemm_("T", "N", n2, n1, n2, &c_b42, &work[1], &m, &a[*j1 + (*j1 + *
n2) * a_dim1], lda, &c_b5, &work[m * m + 1], n2);
slacpy_("Full", n2, n1, &work[m * m + 1], n2, &a[*j1 + (*j1 + *n2) *
a_dim1], lda);
sgemm_("T", "N", n2, n1, n2, &c_b42, &work[1], &m, &b[*j1 + (*j1 + *
n2) * b_dim1], ldb, &c_b5, &work[m * m + 1], n2);
slacpy_("Full", n2, n1, &work[m * m + 1], n2, &b[*j1 + (*j1 + *n2) *
b_dim1], ldb);
sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, &work[1], &m, &c_b5, &
work[m * m + 1], &m);
slacpy_("Full", &m, &m, &work[m * m + 1], &m, li, &c__4);
sgemm_("N", "N", n2, n1, n1, &c_b42, &a[*j1 + (*j1 + *n2) * a_dim1],
lda, &t[*n2 + 1 + (*n2 + 1 << 2) - 5], &c__4, &c_b5, &work[1],
n2);
slacpy_("Full", n2, n1, &work[1], n2, &a[*j1 + (*j1 + *n2) * a_dim1],
lda);
sgemm_("N", "N", n2, n1, n1, &c_b42, &b[*j1 + (*j1 + *n2) * b_dim1],
ldb, &t[*n2 + 1 + (*n2 + 1 << 2) - 5], &c__4, &c_b5, &work[1],
n2);
slacpy_("Full", n2, n1, &work[1], n2, &b[*j1 + (*j1 + *n2) * b_dim1],
ldb);
sgemm_("T", "N", &m, &m, &m, &c_b42, ir, &c__4, t, &c__4, &c_b5, &
work[1], &m);
slacpy_("Full", &m, &m, &work[1], &m, ir, &c__4);
/* Accumulate transformations into Q and Z if requested. */
if (*wantq) {
sgemm_("N", "N", n, &m, &m, &c_b42, &q[*j1 * q_dim1 + 1], ldq, li,
&c__4, &c_b5, &work[1], n);
slacpy_("Full", n, &m, &work[1], n, &q[*j1 * q_dim1 + 1], ldq);
}
if (*wantz) {
sgemm_("N", "N", n, &m, &m, &c_b42, &z__[*j1 * z_dim1 + 1], ldz,
ir, &c__4, &c_b5, &work[1], n);
slacpy_("Full", n, &m, &work[1], n, &z__[*j1 * z_dim1 + 1], ldz);
}
/* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and */
/* (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
i__ = *j1 + m;
if (i__ <= *n) {
i__1 = *n - i__ + 1;
sgemm_("T", "N", &m, &i__1, &m, &c_b42, li, &c__4, &a[*j1 + i__ *
a_dim1], lda, &c_b5, &work[1], &m);
i__1 = *n - i__ + 1;
slacpy_("Full", &m, &i__1, &work[1], &m, &a[*j1 + i__ * a_dim1],
lda);
i__1 = *n - i__ + 1;
sgemm_("T", "N", &m, &i__1, &m, &c_b42, li, &c__4, &b[*j1 + i__ *
b_dim1], ldb, &c_b5, &work[1], &m);
i__1 = *n - i__ + 1;
slacpy_("Full", &m, &i__1, &work[1], &m, &b[*j1 + i__ * b_dim1],
ldb);
}
i__ = *j1 - 1;
if (i__ > 0) {
sgemm_("N", "N", &i__, &m, &m, &c_b42, &a[*j1 * a_dim1 + 1], lda,
ir, &c__4, &c_b5, &work[1], &i__);
slacpy_("Full", &i__, &m, &work[1], &i__, &a[*j1 * a_dim1 + 1],
lda);
sgemm_("N", "N", &i__, &m, &m, &c_b42, &b[*j1 * b_dim1 + 1], ldb,
ir, &c__4, &c_b5, &work[1], &i__);
slacpy_("Full", &i__, &m, &work[1], &i__, &b[*j1 * b_dim1 + 1],
ldb);
}
/* Exit with INFO = 0 if swap was successfully performed. */
return 0;
}
/* Exit with INFO = 1 if swap was rejected. */
L70:
*info = 1;
return 0;
/* End of STGEX2 */
} /* stgex2_ */
/* Subroutine */ int sgeqrf_(integer *m, integer *n, real *a, integer *lda,
real *tau, real *work, integer *lwork, integer *info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
SGEQRF computes a QR factorization of a real M-by-N matrix A:
A = Q * R.
Arguments
=========
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.
A (input/output) REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i, k, nbmin, iinfo;
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *);
static integer ib, nb, nx;
extern /* Subroutine */ int slarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
static integer ldwork, iws;
#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if (*lwork < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEQRF", &i__1);
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
WORK(1) = 1.f;
return 0;
}
/* Determine the block size. */
nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1, 6L, 1L);
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQRF", " ", m, n, &c_n1, &c_n1, 6L,
1L);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked co
de. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduc
e NB and
determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQRF", " ", m, n, &c_n1, &
c_n1, 6L, 1L);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i = 1; nb < 0 ? i >= k-nx : i <= k-nx; i += nb) {
/* Computing MIN */
i__3 = k - i + 1;
ib = min(i__3,nb);
/* Compute the QR factorization of the current block
A(i:m,i:i+ib-1) */
i__3 = *m - i + 1;
sgeqr2_(&i__3, &ib, &A(i,i), lda, &TAU(i), &WORK(1), &
iinfo);
if (i + ib <= *n) {
/* Form the triangular factor of the block reflec
tor
H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *m - i + 1;
slarft_("Forward", "Columnwise", &i__3, &ib, &A(i,i), lda, &TAU(i), &WORK(1), &ldwork);
/* Apply H' to A(i:m,i+ib:n) from the left */
i__3 = *m - i + 1;
i__4 = *n - i - ib + 1;
slarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, &
i__4, &ib, &A(i,i), lda, &WORK(1), &ldwork,
&A(i,i+ib), lda, &WORK(ib + 1), &
ldwork);
}
/* L10: */
}
} else {
i = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i <= k) {
i__2 = *m - i + 1;
i__1 = *n - i + 1;
sgeqr2_(&i__2, &i__1, &A(i,i), lda, &TAU(i), &WORK(1), &
iinfo);
}
WORK(1) = (real) iws;
return 0;
/* End of SGEQRF */
} /* sgeqrf_ */
/* Subroutine */ int schktz_(logical *dotype, integer *nm, integer *mval,
integer *nn, integer *nval, real *thresh, logical *tsterr, real *a,
real *copya, real *s, real *copys, real *tau, real *work, integer *
nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
/* Format strings */
static char fmt_9999[] = "(\002 M =\002,i5,\002, N =\002,i5,\002, type"
" \002,i2,\002, test \002,i2,\002, ratio =\002,g12.5)";
/* System generated locals */
integer i__1, i__2, i__3, i__4;
real r__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, k, m, n, im, in, lda;
real eps;
integer mode, info;
char path[3];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer nfail, iseed[4], imode, mnmin, nerrs;
extern doublereal sqrt12_(integer *, integer *, real *, integer *, real *,
real *, integer *);
integer lwork;
extern doublereal srzt01_(integer *, integer *, real *, real *, integer *,
real *, real *, integer *), srzt02_(integer *, integer *, real *,
integer *, real *, real *, integer *), stzt01_(integer *,
integer *, real *, real *, integer *, real *, real *, integer *),
stzt02_(integer *, integer *, real *, integer *, real *, real *,
integer *);
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *), slaord_(char *, integer *, real *, integer
*), slacpy_(char *, integer *, integer *, real *, integer
*, real *, integer *), slaset_(char *, integer *, integer
*, real *, real *, real *, integer *), slatms_(integer *,
integer *, char *, integer *, char *, real *, integer *, real *,
real *, integer *, integer *, char *, real *, integer *, real *,
integer *);
real result[6];
extern /* Subroutine */ int serrtz_(char *, integer *), stzrqf_(
integer *, integer *, real *, integer *, real *, integer *),
stzrzf_(integer *, integer *, real *, integer *, real *, real *,
integer *, integer *);
/* Fortran I/O blocks */
static cilist io___21 = { 0, 0, 0, fmt_9999, 0 };
/* -- LAPACK test routine (version 3.1.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* January 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SCHKTZ tests STZRQF and STZRZF. */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NM (input) INTEGER */
/* The number of values of M contained in the vector MVAL. */
/* MVAL (input) INTEGER array, dimension (NM) */
/* The values of the matrix row dimension M. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension N. */
/* THRESH (input) REAL */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* A (workspace) REAL array, dimension (MMAX*NMAX) */
/* where MMAX is the maximum value of M in MVAL and NMAX is the */
/* maximum value of N in NVAL. */
/* COPYA (workspace) REAL array, dimension (MMAX*NMAX) */
/* S (workspace) REAL array, dimension */
/* (min(MMAX,NMAX)) */
/* COPYS (workspace) REAL array, dimension */
/* (min(MMAX,NMAX)) */
/* TAU (workspace) REAL array, dimension (MMAX) */
/* WORK (workspace) REAL array, dimension */
/* (MMAX*NMAX + 4*NMAX + MMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--work;
--tau;
--copys;
--s;
--copya;
--a;
--nval;
--mval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "TZ", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
eps = slamch_("Epsilon");
/* Test the error exits */
if (*tsterr) {
serrtz_(path, nout);
}
infoc_1.infot = 0;
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
/* Do for each value of M in MVAL. */
m = mval[im];
lda = max(1,m);
i__2 = *nn;
for (in = 1; in <= i__2; ++in) {
/* Do for each value of N in NVAL for which M .LE. N. */
n = nval[in];
mnmin = min(m,n);
/* Computing MAX */
i__3 = 1, i__4 = n * n + (m << 2) + n, i__3 = max(i__3,i__4),
i__4 = m * n + (mnmin << 1) + (n << 2);
lwork = max(i__3,i__4);
if (m <= n) {
for (imode = 1; imode <= 3; ++imode) {
if (! dotype[imode]) {
goto L50;
}
/* Do for each type of singular value distribution. */
/* 0: zero matrix */
/* 1: one small singular value */
/* 2: exponential distribution */
mode = imode - 1;
/* Test STZRQF */
/* Generate test matrix of size m by n using */
/* singular value distribution indicated by `mode'. */
if (mode == 0) {
slaset_("Full", &m, &n, &c_b10, &c_b10, &a[1], &lda);
i__3 = mnmin;
for (i__ = 1; i__ <= i__3; ++i__) {
copys[i__] = 0.f;
/* L20: */
}
} else {
r__1 = 1.f / eps;
slatms_(&m, &n, "Uniform", iseed, "Nonsymmetric", &
copys[1], &imode, &r__1, &c_b15, &m, &n,
"No packing", &a[1], &lda, &work[1], &info);
sgeqr2_(&m, &n, &a[1], &lda, &work[1], &work[mnmin +
1], &info);
i__3 = m - 1;
slaset_("Lower", &i__3, &n, &c_b10, &c_b10, &a[2], &
lda);
slaord_("Decreasing", &mnmin, ©s[1], &c__1);
}
/* Save A and its singular values */
slacpy_("All", &m, &n, &a[1], &lda, ©a[1], &lda);
/* Call STZRQF to reduce the upper trapezoidal matrix to */
/* upper triangular form. */
s_copy(srnamc_1.srnamt, "STZRQF", (ftnlen)32, (ftnlen)6);
stzrqf_(&m, &n, &a[1], &lda, &tau[1], &info);
/* Compute norm(svd(a) - svd(r)) */
result[0] = sqrt12_(&m, &m, &a[1], &lda, ©s[1], &work[
1], &lwork);
/* Compute norm( A - R*Q ) */
result[1] = stzt01_(&m, &n, ©a[1], &a[1], &lda, &tau[
1], &work[1], &lwork);
/* Compute norm(Q'*Q - I). */
result[2] = stzt02_(&m, &n, &a[1], &lda, &tau[1], &work[1]
, &lwork);
/* Test STZRZF */
/* Generate test matrix of size m by n using */
/* singular value distribution indicated by `mode'. */
if (mode == 0) {
slaset_("Full", &m, &n, &c_b10, &c_b10, &a[1], &lda);
i__3 = mnmin;
for (i__ = 1; i__ <= i__3; ++i__) {
copys[i__] = 0.f;
/* L30: */
}
} else {
r__1 = 1.f / eps;
slatms_(&m, &n, "Uniform", iseed, "Nonsymmetric", &
copys[1], &imode, &r__1, &c_b15, &m, &n,
"No packing", &a[1], &lda, &work[1], &info);
sgeqr2_(&m, &n, &a[1], &lda, &work[1], &work[mnmin +
1], &info);
i__3 = m - 1;
slaset_("Lower", &i__3, &n, &c_b10, &c_b10, &a[2], &
lda);
slaord_("Decreasing", &mnmin, ©s[1], &c__1);
}
/* Save A and its singular values */
slacpy_("All", &m, &n, &a[1], &lda, ©a[1], &lda);
/* Call STZRZF to reduce the upper trapezoidal matrix to */
/* upper triangular form. */
s_copy(srnamc_1.srnamt, "STZRZF", (ftnlen)32, (ftnlen)6);
stzrzf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lwork, &
info);
/* Compute norm(svd(a) - svd(r)) */
result[3] = sqrt12_(&m, &m, &a[1], &lda, ©s[1], &work[
1], &lwork);
/* Compute norm( A - R*Q ) */
result[4] = srzt01_(&m, &n, ©a[1], &a[1], &lda, &tau[
1], &work[1], &lwork);
/* Compute norm(Q'*Q - I). */
result[5] = srzt02_(&m, &n, &a[1], &lda, &tau[1], &work[1]
, &lwork);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = 1; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___21.ciunit = *nout;
s_wsfe(&io___21);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&imode, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(real));
e_wsfe();
++nfail;
}
/* L40: */
}
nrun += 6;
L50:
;
}
}
/* L60: */
}
/* L70: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
/* End if SCHKTZ */
return 0;
} /* schktz_ */
/* ----------------------------------------------------------------------- */
/* Subroutine */ int sneupd_(logical *rvec, char *howmny, logical *select,
real *dr, real *di, real *z__, integer *ldz, real *sigmar, real *
sigmai, real *workev, char *bmat, integer *n, char *which, integer *
nev, real *tol, real *resid, integer *ncv, real *v, integer *ldv,
integer *iparam, integer *ipntr, real *workd, real *workl, integer *
lworkl, integer *info, ftnlen howmny_len, ftnlen bmat_len, ftnlen
which_len)
{
/* System generated locals */
integer v_dim1, v_offset, z_dim1, z_offset, i__1;
real r__1, r__2;
doublereal d__1;
/* Local variables */
static integer j, k, ih, jj, np;
static real vl[1] /* was [1][1] */;
static integer ibd, ldh, ldq, iri;
static real sep;
static integer irr, wri, wrr, mode;
static real eps23;
extern /* Subroutine */ int sger_(integer *, integer *, real *, real *,
integer *, real *, integer *, real *, integer *);
static integer ierr;
static real temp;
static integer iwev;
static char type__[6];
static real temp1;
extern doublereal snrm2_(integer *, real *, integer *);
static integer ihbds, iconj;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
static real conds;
static logical reord;
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *,
ftnlen);
static integer nconv, iwork[1];
static real rnorm;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
static integer ritzi;
extern /* Subroutine */ int strmm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
, ftnlen, ftnlen, ftnlen, ftnlen), ivout_(integer *, integer *,
integer *, integer *, char *, ftnlen), smout_(integer *, integer *
, integer *, real *, integer *, integer *, char *, ftnlen);
static integer ritzr;
extern /* Subroutine */ int svout_(integer *, integer *, real *, integer *
, char *, ftnlen), sgeqr2_(integer *, integer *, real *, integer *
, real *, real *, integer *);
static integer nconv2;
extern doublereal slapy2_(real *, real *);
extern /* Subroutine */ int sorm2r_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, ftnlen, ftnlen);
static integer iheigi, iheigr, bounds, invsub, iuptri, msglvl, outncv,
ishift, numcnv;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *, ftnlen), slahqr_(logical *, logical
*, integer *, integer *, integer *, real *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *),
slaset_(char *, integer *, integer *, real *, real *, real *,
integer *, ftnlen), strevc_(char *, char *, logical *, integer *,
real *, integer *, real *, integer *, real *, integer *, integer *
, integer *, real *, integer *, ftnlen, ftnlen), strsen_(char *,
char *, logical *, integer *, real *, integer *, real *, integer *
, real *, real *, integer *, real *, real *, real *, integer *,
integer *, integer *, integer *, ftnlen, ftnlen);
extern doublereal slamch_(char *, ftnlen);
extern /* Subroutine */ int sngets_(integer *, char *, integer *, integer
*, real *, real *, real *, real *, real *, ftnlen);
/* %----------------------------------------------------% */
/* | Include files for debugging and timing information | */
/* %----------------------------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %---------------------------------% */
/* | See debug.doc for documentation | */
/* %---------------------------------% */
/* %------------------% */
/* | Scalar Arguments | */
/* %------------------% */
/* %--------------------------------% */
/* | See stat.doc for documentation | */
/* %--------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: stat.h SID: 2.2 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %-----------------% */
/* | Array Arguments | */
/* %-----------------% */
/* %------------% */
/* | Parameters | */
/* %------------% */
/* %---------------% */
/* | Local Scalars | */
/* %---------------% */
/* %----------------------% */
/* | External Subroutines | */
/* %----------------------% */
/* %--------------------% */
/* | External Functions | */
/* %--------------------% */
/* %---------------------% */
/* | Intrinsic Functions | */
/* %---------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* %------------------------% */
/* | Set default parameters | */
/* %------------------------% */
/* Parameter adjustments */
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--workd;
--resid;
--di;
--dr;
--workev;
--select;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--iparam;
--ipntr;
--workl;
/* Function Body */
msglvl = debug_1.mneupd;
mode = iparam[7];
nconv = iparam[5];
*info = 0;
/* %---------------------------------% */
/* | Get machine dependent constant. | */
/* %---------------------------------% */
eps23 = slamch_("Epsilon-Machine", (ftnlen)15);
d__1 = (doublereal) eps23;
eps23 = pow_dd(&d__1, &c_b3);
/* %--------------% */
/* | Quick return | */
/* %--------------% */
ierr = 0;
if (nconv <= 0) {
ierr = -14;
} else if (*n <= 0) {
ierr = -1;
} else if (*nev <= 0) {
ierr = -2;
} else if (*ncv <= *nev + 1 || *ncv > *n) {
ierr = -3;
} else if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which,
"SM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which, "LR", (ftnlen)2,
(ftnlen)2) != 0 && s_cmp(which, "SR", (ftnlen)2, (ftnlen)2) != 0
&& s_cmp(which, "LI", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which,
"SI", (ftnlen)2, (ftnlen)2) != 0) {
ierr = -5;
} else if (*(unsigned char *)bmat != 'I' && *(unsigned char *)bmat != 'G')
{
ierr = -6;
} else /* if(complicated condition) */ {
/* Computing 2nd power */
i__1 = *ncv;
if (*lworkl < i__1 * i__1 * 3 + *ncv * 6) {
ierr = -7;
} else if (*(unsigned char *)howmny != 'A' && *(unsigned char *)
howmny != 'P' && *(unsigned char *)howmny != 'S' && *rvec) {
ierr = -13;
} else if (*(unsigned char *)howmny == 'S') {
ierr = -12;
}
}
if (mode == 1 || mode == 2) {
s_copy(type__, "REGULR", (ftnlen)6, (ftnlen)6);
} else if (mode == 3 && *sigmai == 0.f) {
s_copy(type__, "SHIFTI", (ftnlen)6, (ftnlen)6);
} else if (mode == 3) {
s_copy(type__, "REALPT", (ftnlen)6, (ftnlen)6);
} else if (mode == 4) {
s_copy(type__, "IMAGPT", (ftnlen)6, (ftnlen)6);
} else {
ierr = -10;
}
if (mode == 1 && *(unsigned char *)bmat == 'G') {
ierr = -11;
}
/* %------------% */
/* | Error Exit | */
/* %------------% */
if (ierr != 0) {
*info = ierr;
goto L9000;
}
/* %--------------------------------------------------------% */
/* | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | */
/* | etc... and the remaining workspace. | */
/* | Also update pointer to be used on output. | */
/* | Memory is laid out as follows: | */
/* | workl(1:ncv*ncv) := generated Hessenberg matrix | */
/* | workl(ncv*ncv+1:ncv*ncv+2*ncv) := real and imaginary | */
/* | parts of ritz values | */
/* | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := error bounds | */
/* %--------------------------------------------------------% */
/* %-----------------------------------------------------------% */
/* | The following is used and set by SNEUPD. | */
/* | workl(ncv*ncv+3*ncv+1:ncv*ncv+4*ncv) := The untransformed | */
/* | real part of the Ritz values. | */
/* | workl(ncv*ncv+4*ncv+1:ncv*ncv+5*ncv) := The untransformed | */
/* | imaginary part of the Ritz values. | */
/* | workl(ncv*ncv+5*ncv+1:ncv*ncv+6*ncv) := The untransformed | */
/* | error bounds of the Ritz values | */
/* | workl(ncv*ncv+6*ncv+1:2*ncv*ncv+6*ncv) := Holds the upper | */
/* | quasi-triangular matrix for H | */
/* | workl(2*ncv*ncv+6*ncv+1: 3*ncv*ncv+6*ncv) := Holds the | */
/* | associated matrix representation of the invariant | */
/* | subspace for H. | */
/* | GRAND total of NCV * ( 3 * NCV + 6 ) locations. | */
/* %-----------------------------------------------------------% */
ih = ipntr[5];
ritzr = ipntr[6];
ritzi = ipntr[7];
bounds = ipntr[8];
ldh = *ncv;
ldq = *ncv;
iheigr = bounds + ldh;
iheigi = iheigr + ldh;
ihbds = iheigi + ldh;
iuptri = ihbds + ldh;
invsub = iuptri + ldh * *ncv;
ipntr[9] = iheigr;
ipntr[10] = iheigi;
ipntr[11] = ihbds;
ipntr[12] = iuptri;
ipntr[13] = invsub;
wrr = 1;
wri = *ncv + 1;
iwev = wri + *ncv;
/* %-----------------------------------------% */
/* | irr points to the REAL part of the Ritz | */
/* | values computed by _neigh before | */
/* | exiting _naup2. | */
/* | iri points to the IMAGINARY part of the | */
/* | Ritz values computed by _neigh | */
/* | before exiting _naup2. | */
/* | ibd points to the Ritz estimates | */
/* | computed by _neigh before exiting | */
/* | _naup2. | */
/* %-----------------------------------------% */
irr = ipntr[14] + *ncv * *ncv;
iri = irr + *ncv;
ibd = iri + *ncv;
/* %------------------------------------% */
/* | RNORM is B-norm of the RESID(1:N). | */
/* %------------------------------------% */
rnorm = workl[ih + 2];
workl[ih + 2] = 0.f;
if (msglvl > 2) {
svout_(&debug_1.logfil, ncv, &workl[irr], &debug_1.ndigit, "_neupd: "
"Real part of Ritz values passed in from _NAUPD.", (ftnlen)55);
svout_(&debug_1.logfil, ncv, &workl[iri], &debug_1.ndigit, "_neupd: "
"Imag part of Ritz values passed in from _NAUPD.", (ftnlen)55);
svout_(&debug_1.logfil, ncv, &workl[ibd], &debug_1.ndigit, "_neupd: "
"Ritz estimates passed in from _NAUPD.", (ftnlen)45);
}
if (*rvec) {
reord = FALSE_;
/* %---------------------------------------------------% */
/* | Use the temporary bounds array to store indices | */
/* | These will be used to mark the select array later | */
/* %---------------------------------------------------% */
i__1 = *ncv;
for (j = 1; j <= i__1; ++j) {
workl[bounds + j - 1] = (real) j;
select[j] = FALSE_;
/* L10: */
}
/* %-------------------------------------% */
/* | Select the wanted Ritz values. | */
/* | Sort the Ritz values so that the | */
/* | wanted ones appear at the tailing | */
/* | NEV positions of workl(irr) and | */
/* | workl(iri). Move the corresponding | */
/* | error estimates in workl(bound) | */
/* | accordingly. | */
/* %-------------------------------------% */
np = *ncv - *nev;
ishift = 0;
sngets_(&ishift, which, nev, &np, &workl[irr], &workl[iri], &workl[
bounds], &workl[1], &workl[np + 1], (ftnlen)2);
if (msglvl > 2) {
svout_(&debug_1.logfil, ncv, &workl[irr], &debug_1.ndigit, "_neu"
"pd: Real part of Ritz values after calling _NGETS.", (
ftnlen)54);
svout_(&debug_1.logfil, ncv, &workl[iri], &debug_1.ndigit, "_neu"
"pd: Imag part of Ritz values after calling _NGETS.", (
ftnlen)54);
svout_(&debug_1.logfil, ncv, &workl[bounds], &debug_1.ndigit,
"_neupd: Ritz value indices after calling _NGETS.", (
ftnlen)48);
}
/* %-----------------------------------------------------% */
/* | Record indices of the converged wanted Ritz values | */
/* | Mark the select array for possible reordering | */
/* %-----------------------------------------------------% */
numcnv = 0;
i__1 = *ncv;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
r__1 = eps23, r__2 = slapy2_(&workl[irr + *ncv - j], &workl[iri +
*ncv - j]);
temp1 = dmax(r__1,r__2);
jj = workl[bounds + *ncv - j];
if (numcnv < nconv && workl[ibd + jj - 1] <= *tol * temp1) {
select[jj] = TRUE_;
++numcnv;
if (jj > nconv) {
reord = TRUE_;
}
}
/* L11: */
}
/* %-----------------------------------------------------------% */
/* | Check the count (numcnv) of converged Ritz values with | */
/* | the number (nconv) reported by dnaupd. If these two | */
/* | are different then there has probably been an error | */
/* | caused by incorrect passing of the dnaupd data. | */
/* %-----------------------------------------------------------% */
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, &numcnv, &debug_1.ndigit, "_neupd"
": Number of specified eigenvalues", (ftnlen)39);
ivout_(&debug_1.logfil, &c__1, &nconv, &debug_1.ndigit, "_neupd:"
" Number of \"converged\" eigenvalues", (ftnlen)41);
}
if (numcnv != nconv) {
*info = -15;
goto L9000;
}
/* %-----------------------------------------------------------% */
/* | Call LAPACK routine slahqr to compute the real Schur form | */
/* | of the upper Hessenberg matrix returned by SNAUPD. | */
/* | Make a copy of the upper Hessenberg matrix. | */
/* | Initialize the Schur vector matrix Q to the identity. | */
/* %-----------------------------------------------------------% */
i__1 = ldh * *ncv;
scopy_(&i__1, &workl[ih], &c__1, &workl[iuptri], &c__1);
slaset_("All", ncv, ncv, &c_b37, &c_b38, &workl[invsub], &ldq, (
ftnlen)3);
slahqr_(&c_true, &c_true, ncv, &c__1, ncv, &workl[iuptri], &ldh, &
workl[iheigr], &workl[iheigi], &c__1, ncv, &workl[invsub], &
ldq, &ierr);
scopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &c__1);
if (ierr != 0) {
*info = -8;
goto L9000;
}
if (msglvl > 1) {
svout_(&debug_1.logfil, ncv, &workl[iheigr], &debug_1.ndigit,
"_neupd: Real part of the eigenvalues of H", (ftnlen)41);
svout_(&debug_1.logfil, ncv, &workl[iheigi], &debug_1.ndigit,
"_neupd: Imaginary part of the Eigenvalues of H", (ftnlen)
46);
svout_(&debug_1.logfil, ncv, &workl[ihbds], &debug_1.ndigit,
"_neupd: Last row of the Schur vector matrix", (ftnlen)43)
;
if (msglvl > 3) {
smout_(&debug_1.logfil, ncv, ncv, &workl[iuptri], &ldh, &
debug_1.ndigit, "_neupd: The upper quasi-triangular "
"matrix ", (ftnlen)42);
}
}
if (reord) {
/* %-----------------------------------------------------% */
/* | Reorder the computed upper quasi-triangular matrix. | */
/* %-----------------------------------------------------% */
strsen_("None", "V", &select[1], ncv, &workl[iuptri], &ldh, &
workl[invsub], &ldq, &workl[iheigr], &workl[iheigi], &
nconv2, &conds, &sep, &workl[ihbds], ncv, iwork, &c__1, &
ierr, (ftnlen)4, (ftnlen)1);
if (nconv2 < nconv) {
nconv = nconv2;
}
if (ierr == 1) {
*info = 1;
goto L9000;
}
if (msglvl > 2) {
svout_(&debug_1.logfil, ncv, &workl[iheigr], &debug_1.ndigit,
"_neupd: Real part of the eigenvalues of H--reordered"
, (ftnlen)52);
svout_(&debug_1.logfil, ncv, &workl[iheigi], &debug_1.ndigit,
"_neupd: Imag part of the eigenvalues of H--reordered"
, (ftnlen)52);
if (msglvl > 3) {
smout_(&debug_1.logfil, ncv, ncv, &workl[iuptri], &ldq, &
debug_1.ndigit, "_neupd: Quasi-triangular matrix"
" after re-ordering", (ftnlen)49);
}
}
}
/* %---------------------------------------% */
/* | Copy the last row of the Schur vector | */
/* | into workl(ihbds). This will be used | */
/* | to compute the Ritz estimates of | */
/* | converged Ritz values. | */
/* %---------------------------------------% */
scopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &c__1);
/* %----------------------------------------------------% */
/* | Place the computed eigenvalues of H into DR and DI | */
/* | if a spectral transformation was not used. | */
/* %----------------------------------------------------% */
if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
scopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
scopy_(&nconv, &workl[iheigi], &c__1, &di[1], &c__1);
}
/* %----------------------------------------------------------% */
/* | Compute the QR factorization of the matrix representing | */
/* | the wanted invariant subspace located in the first NCONV | */
/* | columns of workl(invsub,ldq). | */
/* %----------------------------------------------------------% */
sgeqr2_(ncv, &nconv, &workl[invsub], &ldq, &workev[1], &workev[*ncv +
1], &ierr);
/* %---------------------------------------------------------% */
/* | * Postmultiply V by Q using sorm2r. | */
/* | * Copy the first NCONV columns of VQ into Z. | */
/* | * Postmultiply Z by R. | */
/* | The N by NCONV matrix Z is now a matrix representation | */
/* | of the approximate invariant subspace associated with | */
/* | the Ritz values in workl(iheigr) and workl(iheigi) | */
/* | The first NCONV columns of V are now approximate Schur | */
/* | vectors associated with the real upper quasi-triangular | */
/* | matrix of order NCONV in workl(iuptri) | */
/* %---------------------------------------------------------% */
sorm2r_("Right", "Notranspose", n, ncv, &nconv, &workl[invsub], &ldq,
&workev[1], &v[v_offset], ldv, &workd[*n + 1], &ierr, (ftnlen)
5, (ftnlen)11);
slacpy_("All", n, &nconv, &v[v_offset], ldv, &z__[z_offset], ldz, (
ftnlen)3);
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
/* %---------------------------------------------------% */
/* | Perform both a column and row scaling if the | */
/* | diagonal element of workl(invsub,ldq) is negative | */
/* | I'm lazy and don't take advantage of the upper | */
/* | quasi-triangular form of workl(iuptri,ldq) | */
/* | Note that since Q is orthogonal, R is a diagonal | */
/* | matrix consisting of plus or minus ones | */
/* %---------------------------------------------------% */
if (workl[invsub + (j - 1) * ldq + j - 1] < 0.f) {
sscal_(&nconv, &c_b64, &workl[iuptri + j - 1], &ldq);
sscal_(&nconv, &c_b64, &workl[iuptri + (j - 1) * ldq], &c__1);
}
/* L20: */
}
if (*(unsigned char *)howmny == 'A') {
/* %--------------------------------------------% */
/* | Compute the NCONV wanted eigenvectors of T | */
/* | located in workl(iuptri,ldq). | */
/* %--------------------------------------------% */
i__1 = *ncv;
for (j = 1; j <= i__1; ++j) {
if (j <= nconv) {
select[j] = TRUE_;
} else {
select[j] = FALSE_;
}
/* L30: */
}
strevc_("Right", "Select", &select[1], ncv, &workl[iuptri], &ldq,
vl, &c__1, &workl[invsub], &ldq, ncv, &outncv, &workev[1],
&ierr, (ftnlen)5, (ftnlen)6);
if (ierr != 0) {
*info = -9;
goto L9000;
}
/* %------------------------------------------------% */
/* | Scale the returning eigenvectors so that their | */
/* | Euclidean norms are all one. LAPACK subroutine | */
/* | strevc returns each eigenvector normalized so | */
/* | that the element of largest magnitude has | */
/* | magnitude 1; | */
/* %------------------------------------------------% */
iconj = 0;
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
if (workl[iheigi + j - 1] == 0.f) {
/* %----------------------% */
/* | real eigenvalue case | */
/* %----------------------% */
temp = snrm2_(ncv, &workl[invsub + (j - 1) * ldq], &c__1);
r__1 = 1.f / temp;
sscal_(ncv, &r__1, &workl[invsub + (j - 1) * ldq], &c__1);
} else {
/* %-------------------------------------------% */
/* | Complex conjugate pair case. Note that | */
/* | since the real and imaginary part of | */
/* | the eigenvector are stored in consecutive | */
/* | columns, we further normalize by the | */
/* | square root of two. | */
/* %-------------------------------------------% */
if (iconj == 0) {
r__1 = snrm2_(ncv, &workl[invsub + (j - 1) * ldq], &
c__1);
r__2 = snrm2_(ncv, &workl[invsub + j * ldq], &c__1);
temp = slapy2_(&r__1, &r__2);
r__1 = 1.f / temp;
sscal_(ncv, &r__1, &workl[invsub + (j - 1) * ldq], &
c__1);
r__1 = 1.f / temp;
sscal_(ncv, &r__1, &workl[invsub + j * ldq], &c__1);
iconj = 1;
} else {
iconj = 0;
}
}
/* L40: */
}
sgemv_("T", ncv, &nconv, &c_b38, &workl[invsub], &ldq, &workl[
ihbds], &c__1, &c_b37, &workev[1], &c__1, (ftnlen)1);
iconj = 0;
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
if (workl[iheigi + j - 1] != 0.f) {
/* %-------------------------------------------% */
/* | Complex conjugate pair case. Note that | */
/* | since the real and imaginary part of | */
/* | the eigenvector are stored in consecutive | */
/* %-------------------------------------------% */
if (iconj == 0) {
workev[j] = slapy2_(&workev[j], &workev[j + 1]);
workev[j + 1] = workev[j];
iconj = 1;
} else {
iconj = 0;
}
}
/* L45: */
}
if (msglvl > 2) {
scopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &
c__1);
svout_(&debug_1.logfil, ncv, &workl[ihbds], &debug_1.ndigit,
"_neupd: Last row of the eigenvector matrix for T", (
ftnlen)48);
if (msglvl > 3) {
smout_(&debug_1.logfil, ncv, ncv, &workl[invsub], &ldq, &
debug_1.ndigit, "_neupd: The eigenvector matrix "
"for T", (ftnlen)36);
}
}
/* %---------------------------------------% */
/* | Copy Ritz estimates into workl(ihbds) | */
/* %---------------------------------------% */
scopy_(&nconv, &workev[1], &c__1, &workl[ihbds], &c__1);
/* %---------------------------------------------------------% */
/* | Compute the QR factorization of the eigenvector matrix | */
/* | associated with leading portion of T in the first NCONV | */
/* | columns of workl(invsub,ldq). | */
/* %---------------------------------------------------------% */
sgeqr2_(ncv, &nconv, &workl[invsub], &ldq, &workev[1], &workev[*
ncv + 1], &ierr);
/* %----------------------------------------------% */
/* | * Postmultiply Z by Q. | */
/* | * Postmultiply Z by R. | */
/* | The N by NCONV matrix Z is now contains the | */
/* | Ritz vectors associated with the Ritz values | */
/* | in workl(iheigr) and workl(iheigi). | */
/* %----------------------------------------------% */
sorm2r_("Right", "Notranspose", n, ncv, &nconv, &workl[invsub], &
ldq, &workev[1], &z__[z_offset], ldz, &workd[*n + 1], &
ierr, (ftnlen)5, (ftnlen)11);
strmm_("Right", "Upper", "No transpose", "Non-unit", n, &nconv, &
c_b38, &workl[invsub], &ldq, &z__[z_offset], ldz, (ftnlen)
5, (ftnlen)5, (ftnlen)12, (ftnlen)8);
}
} else {
/* %------------------------------------------------------% */
/* | An approximate invariant subspace is not needed. | */
/* | Place the Ritz values computed SNAUPD into DR and DI | */
/* %------------------------------------------------------% */
scopy_(&nconv, &workl[ritzr], &c__1, &dr[1], &c__1);
scopy_(&nconv, &workl[ritzi], &c__1, &di[1], &c__1);
scopy_(&nconv, &workl[ritzr], &c__1, &workl[iheigr], &c__1);
scopy_(&nconv, &workl[ritzi], &c__1, &workl[iheigi], &c__1);
scopy_(&nconv, &workl[bounds], &c__1, &workl[ihbds], &c__1);
}
/* %------------------------------------------------% */
/* | Transform the Ritz values and possibly vectors | */
/* | and corresponding error bounds of OP to those | */
/* | of A*x = lambda*B*x. | */
/* %------------------------------------------------% */
if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
if (*rvec) {
sscal_(ncv, &rnorm, &workl[ihbds], &c__1);
}
} else {
/* %---------------------------------------% */
/* | A spectral transformation was used. | */
/* | * Determine the Ritz estimates of the | */
/* | Ritz values in the original system. | */
/* %---------------------------------------% */
if (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
if (*rvec) {
sscal_(ncv, &rnorm, &workl[ihbds], &c__1);
}
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
temp = slapy2_(&workl[iheigr + k - 1], &workl[iheigi + k - 1])
;
workl[ihbds + k - 1] = (r__1 = workl[ihbds + k - 1], dabs(
r__1)) / temp / temp;
/* L50: */
}
} else if (s_cmp(type__, "REALPT", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
/* L60: */
}
} else if (s_cmp(type__, "IMAGPT", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
/* L70: */
}
}
/* %-----------------------------------------------------------% */
/* | * Transform the Ritz values back to the original system. | */
/* | For TYPE = 'SHIFTI' the transformation is | */
/* | lambda = 1/theta + sigma | */
/* | For TYPE = 'REALPT' or 'IMAGPT' the user must from | */
/* | Rayleigh quotients or a projection. See remark 3 above.| */
/* | NOTES: | */
/* | *The Ritz vectors are not affected by the transformation. | */
/* %-----------------------------------------------------------% */
if (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
temp = slapy2_(&workl[iheigr + k - 1], &workl[iheigi + k - 1])
;
workl[iheigr + k - 1] = workl[iheigr + k - 1] / temp / temp +
*sigmar;
workl[iheigi + k - 1] = -workl[iheigi + k - 1] / temp / temp
+ *sigmai;
/* L80: */
}
scopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
scopy_(&nconv, &workl[iheigi], &c__1, &di[1], &c__1);
} else if (s_cmp(type__, "REALPT", (ftnlen)6, (ftnlen)6) == 0 ||
s_cmp(type__, "IMAGPT", (ftnlen)6, (ftnlen)6) == 0) {
scopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
scopy_(&nconv, &workl[iheigi], &c__1, &di[1], &c__1);
}
}
if (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0 && msglvl > 1) {
svout_(&debug_1.logfil, &nconv, &dr[1], &debug_1.ndigit, "_neupd: Un"
"transformed real part of the Ritz valuess.", (ftnlen)52);
svout_(&debug_1.logfil, &nconv, &di[1], &debug_1.ndigit, "_neupd: Un"
"transformed imag part of the Ritz valuess.", (ftnlen)52);
svout_(&debug_1.logfil, &nconv, &workl[ihbds], &debug_1.ndigit, "_ne"
"upd: Ritz estimates of untransformed Ritz values.", (ftnlen)
52);
} else if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0 && msglvl >
1) {
svout_(&debug_1.logfil, &nconv, &dr[1], &debug_1.ndigit, "_neupd: Re"
"al parts of converged Ritz values.", (ftnlen)44);
svout_(&debug_1.logfil, &nconv, &di[1], &debug_1.ndigit, "_neupd: Im"
"ag parts of converged Ritz values.", (ftnlen)44);
svout_(&debug_1.logfil, &nconv, &workl[ihbds], &debug_1.ndigit, "_ne"
"upd: Associated Ritz estimates.", (ftnlen)34);
}
/* %-------------------------------------------------% */
/* | Eigenvector Purification step. Formally perform | */
/* | one of inverse subspace iteration. Only used | */
/* | for MODE = 2. | */
/* %-------------------------------------------------% */
if (*rvec && *(unsigned char *)howmny == 'A' && s_cmp(type__, "SHIFTI", (
ftnlen)6, (ftnlen)6) == 0) {
/* %------------------------------------------------% */
/* | Purify the computed Ritz vectors by adding a | */
/* | little bit of the residual vector: | */
/* | T | */
/* | resid(:)*( e s ) / theta | */
/* | NCV | */
/* | where H s = s theta. Remember that when theta | */
/* | has nonzero imaginary part, the corresponding | */
/* | Ritz vector is stored across two columns of Z. | */
/* %------------------------------------------------% */
iconj = 0;
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
if (workl[iheigi + j - 1] == 0.f) {
workev[j] = workl[invsub + (j - 1) * ldq + *ncv - 1] / workl[
iheigr + j - 1];
} else if (iconj == 0) {
temp = slapy2_(&workl[iheigr + j - 1], &workl[iheigi + j - 1])
;
workev[j] = (workl[invsub + (j - 1) * ldq + *ncv - 1] * workl[
iheigr + j - 1] + workl[invsub + j * ldq + *ncv - 1] *
workl[iheigi + j - 1]) / temp / temp;
workev[j + 1] = (workl[invsub + j * ldq + *ncv - 1] * workl[
iheigr + j - 1] - workl[invsub + (j - 1) * ldq + *ncv
- 1] * workl[iheigi + j - 1]) / temp / temp;
iconj = 1;
} else {
iconj = 0;
}
/* L110: */
}
/* %---------------------------------------% */
/* | Perform a rank one update to Z and | */
/* | purify all the Ritz vectors together. | */
/* %---------------------------------------% */
sger_(n, &nconv, &c_b38, &resid[1], &c__1, &workev[1], &c__1, &z__[
z_offset], ldz);
}
L9000:
return 0;
/* %---------------% */
/* | End of SNEUPD | */
/* %---------------% */
} /* sneupd_ */
/* Subroutine */ int sggsvp_(char *jobu, char *jobv, char *jobq, integer *m,
integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb,
real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu,
real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real *
tau, real *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
u_offset, v_dim1, v_offset, i__1, i__2, i__3;
real r__1;
/* Local variables */
integer i__, j;
extern logical lsame_(char *, char *);
logical wantq, wantu, wantv;
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *), sgerq2_(integer *, integer *, real
*, integer *, real *, real *, integer *), sorg2r_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
), sorm2r_(char *, char *, integer *, integer *, integer *, real *
, integer *, real *, real *, integer *, real *, integer *), sormr2_(char *, char *, integer *, integer *, integer *,
real *, integer *, real *, real *, integer *, real *, integer *), xerbla_(char *, integer *), sgeqpf_(
integer *, integer *, real *, integer *, integer *, real *, real *
, integer *), slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *), slapmt_(
logical *, integer *, integer *, real *, integer *, integer *);
logical forwrd;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGGSVP computes orthogonal matrices U, V and Q such that */
/* N-K-L K L */
/* U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; */
/* L ( 0 0 A23 ) */
/* M-K-L ( 0 0 0 ) */
/* N-K-L K L */
/* = K ( 0 A12 A13 ) if M-K-L < 0; */
/* M-K ( 0 0 A23 ) */
/* N-K-L K L */
/* V'*B*Q = L ( 0 0 B13 ) */
/* P-L ( 0 0 0 ) */
/* where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
/* upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
/* otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective */
/* numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the */
/* transpose of Z. */
/* This decomposition is the preprocessing step for computing the */
/* Generalized Singular Value Decomposition (GSVD), see subroutine */
/* SGGSVD. */
/* Arguments */
/* ========= */
/* JOBU (input) CHARACTER*1 */
/* = 'U': Orthogonal matrix U is computed; */
/* = 'N': U is not computed. */
/* JOBV (input) CHARACTER*1 */
/* = 'V': Orthogonal matrix V is computed; */
/* = 'N': V is not computed. */
/* JOBQ (input) CHARACTER*1 */
/* = 'Q': Orthogonal matrix Q is computed; */
/* = 'N': Q is not computed. */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* P (input) INTEGER */
/* The number of rows of the matrix B. P >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrices A and B. N >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, A contains the triangular (or trapezoidal) matrix */
/* described in the Purpose section. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* B (input/output) REAL array, dimension (LDB,N) */
/* On entry, the P-by-N matrix B. */
/* On exit, B contains the triangular matrix described in */
/* the Purpose section. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,P). */
/* TOLA (input) REAL */
/* TOLB (input) REAL */
/* TOLA and TOLB are the thresholds to determine the effective */
/* numerical rank of matrix B and a subblock of A. Generally, */
/* they are set to */
/* TOLA = MAX(M,N)*norm(A)*MACHEPS, */
/* TOLB = MAX(P,N)*norm(B)*MACHEPS. */
/* The size of TOLA and TOLB may affect the size of backward */
/* errors of the decomposition. */
/* K (output) INTEGER */
/* L (output) INTEGER */
/* On exit, K and L specify the dimension of the subblocks */
/* described in Purpose. */
/* K + L = effective numerical rank of (A',B')'. */
/* U (output) REAL array, dimension (LDU,M) */
/* If JOBU = 'U', U contains the orthogonal matrix U. */
/* If JOBU = 'N', U is not referenced. */
/* LDU (input) INTEGER */
/* The leading dimension of the array U. LDU >= max(1,M) if */
/* JOBU = 'U'; LDU >= 1 otherwise. */
/* V (output) REAL array, dimension (LDV,M) */
/* If JOBV = 'V', V contains the orthogonal matrix V. */
/* If JOBV = 'N', V is not referenced. */
/* LDV (input) INTEGER */
/* The leading dimension of the array V. LDV >= max(1,P) if */
/* JOBV = 'V'; LDV >= 1 otherwise. */
/* Q (output) REAL array, dimension (LDQ,N) */
/* If JOBQ = 'Q', Q contains the orthogonal matrix Q. */
/* If JOBQ = 'N', Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,N) if */
/* JOBQ = 'Q'; LDQ >= 1 otherwise. */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* TAU (workspace) REAL array, dimension (N) */
/* WORK (workspace) REAL array, dimension (max(3*N,M,P)) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The subroutine uses LAPACK subroutine SGEQPF for the QR factorization */
/* with column pivoting to detect the effective numerical rank of the */
/* a matrix. It may be replaced by a better rank determination strategy. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--iwork;
--tau;
--work;
/* Function Body */
wantu = lsame_(jobu, "U");
wantv = lsame_(jobv, "V");
wantq = lsame_(jobq, "Q");
forwrd = TRUE_;
*info = 0;
if (! (wantu || lsame_(jobu, "N"))) {
*info = -1;
} else if (! (wantv || lsame_(jobv, "N"))) {
*info = -2;
} else if (! (wantq || lsame_(jobq, "N"))) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*p < 0) {
*info = -5;
} else if (*n < 0) {
*info = -6;
} else if (*lda < max(1,*m)) {
*info = -8;
} else if (*ldb < max(1,*p)) {
*info = -10;
} else if (*ldu < 1 || wantu && *ldu < *m) {
*info = -16;
} else if (*ldv < 1 || wantv && *ldv < *p) {
*info = -18;
} else if (*ldq < 1 || wantq && *ldq < *n) {
*info = -20;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGSVP", &i__1);
return 0;
}
/* QR with column pivoting of B: B*P = V*( S11 S12 ) */
/* ( 0 0 ) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = 0;
/* L10: */
}
sgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], info);
/* Update A := A*P */
slapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);
/* Determine the effective rank of matrix B. */
*l = 0;
i__1 = min(*p,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
if ((r__1 = b[i__ + i__ * b_dim1], dabs(r__1)) > *tolb) {
++(*l);
}
/* L20: */
}
if (wantv) {
/* Copy the details of V, and form V. */
slaset_("Full", p, p, &c_b12, &c_b12, &v[v_offset], ldv);
if (*p > 1) {
i__1 = *p - 1;
slacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2],
ldv);
}
i__1 = min(*p,*n);
sorg2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
}
/* Clean up B */
i__1 = *l - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *l;
for (i__ = j + 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.f;
/* L30: */
}
/* L40: */
}
if (*p > *l) {
i__1 = *p - *l;
slaset_("Full", &i__1, n, &c_b12, &c_b12, &b[*l + 1 + b_dim1], ldb);
}
if (wantq) {
/* Set Q = I and Update Q := Q*P */
slaset_("Full", n, n, &c_b12, &c_b22, &q[q_offset], ldq);
slapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
}
if (*p >= *l && *n != *l) {
/* RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z */
sgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
/* Update A := A*Z' */
sormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[
a_offset], lda, &work[1], info);
if (wantq) {
/* Update Q := Q*Z' */
sormr2_("Right", "Transpose", n, n, l, &b[b_offset], ldb, &tau[1],
&q[q_offset], ldq, &work[1], info);
}
/* Clean up B */
i__1 = *n - *l;
slaset_("Full", l, &i__1, &c_b12, &c_b12, &b[b_offset], ldb);
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
i__2 = *l;
for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.f;
/* L50: */
}
/* L60: */
}
}
/* Let N-L L */
/* A = ( A11 A12 ) M, */
/* then the following does the complete QR decomposition of A11: */
/* A11 = U*( 0 T12 )*P1' */
/* ( 0 0 ) */
i__1 = *n - *l;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = 0;
/* L70: */
}
i__1 = *n - *l;
sgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], info);
/* Determine the effective rank of A11 */
*k = 0;
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
for (i__ = 1; i__ <= i__1; ++i__) {
if ((r__1 = a[i__ + i__ * a_dim1], dabs(r__1)) > *tola) {
++(*k);
}
/* L80: */
}
/* Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N ) */
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
sorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &a[(
*n - *l + 1) * a_dim1 + 1], lda, &work[1], info);
if (wantu) {
/* Copy the details of U, and form U */
slaset_("Full", m, m, &c_b12, &c_b12, &u[u_offset], ldu);
if (*m > 1) {
i__1 = *m - 1;
i__2 = *n - *l;
slacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2]
, ldu);
}
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
sorg2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
}
if (wantq) {
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
i__1 = *n - *l;
slapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
}
/* Clean up A: set the strictly lower triangular part of */
/* A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */
i__1 = *k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = 0.f;
/* L90: */
}
/* L100: */
}
if (*m > *k) {
i__1 = *m - *k;
i__2 = *n - *l;
slaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a[*k + 1 + a_dim1],
lda);
}
if (*n - *l > *k) {
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
i__1 = *n - *l;
sgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);
if (wantq) {
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1' */
i__1 = *n - *l;
sormr2_("Right", "Transpose", n, &i__1, k, &a[a_offset], lda, &
tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up A */
i__1 = *n - *l - *k;
slaset_("Full", k, &i__1, &c_b12, &c_b12, &a[a_offset], lda);
i__1 = *n - *l;
for (j = *n - *l - *k + 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = 0.f;
/* L110: */
}
/* L120: */
}
}
if (*m > *k) {
/* QR factorization of A( K+1:M,N-L+1:N ) */
i__1 = *m - *k;
sgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], &
work[1], info);
if (wantu) {
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
i__1 = *m - *k;
/* Computing MIN */
i__3 = *m - *k;
i__2 = min(i__3,*l);
sorm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n
- *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 +
1], ldu, &work[1], info);
}
/* Clean up */
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = 0.f;
/* L130: */
}
/* L140: */
}
}
return 0;
/* End of SGGSVP */
} /* sggsvp_ */
/* Subroutine */ int serrqr_(char *path, integer *nunit)
{
/* Local variables */
real a[4] /* was [2][2] */, b[2];
integer i__, j;
real w[2], x[2], af[4] /* was [2][2] */;
integer info;
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SERRQR tests the error exits for the REAL routines */
/* that use the QR decomposition of a general matrix. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
/* Set the variables to innocuous values. */
for (j = 1; j <= 2; ++j) {
for (i__ = 1; i__ <= 2; ++i__) {
a[i__ + (j << 1) - 3] = 1.f / (real) (i__ + j);
af[i__ + (j << 1) - 3] = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QR factorization */
/* SGEQRF */
s_copy(srnamc_1.srnamt, "SGEQRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgeqrf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeqrf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgeqrf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEQR2 */
s_copy(srnamc_1.srnamt, "SGEQR2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgeqr2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqr2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeqr2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEQRS */
s_copy(srnamc_1.srnamt, "SGEQRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgeqrs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrs_(&c__1, &c__2, &c__0, a, &c__2, x, b, &c__2, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgeqrs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgeqrs_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgeqrs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgeqrs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORGQR */
s_copy(srnamc_1.srnamt, "SORGQR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sorgqr_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorgqr_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorgqr_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorgqr_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorgqr_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorgqr_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sorgqr_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORG2R */
s_copy(srnamc_1.srnamt, "SORG2R", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sorg2r_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorg2r_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorg2r_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorg2r_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorg2r_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorg2r_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORMQR */
s_copy(srnamc_1.srnamt, "SORMQR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sormqr_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sormqr_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sormqr_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sormqr_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sormqr_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sormqr_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sormqr_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORM2R */
s_copy(srnamc_1.srnamt, "SORM2R", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sorm2r_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorm2r_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorm2r_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sorm2r_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sorm2r_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of SERRQR */
} /* serrqr_ */
/* Subroutine */ int stgex2_(logical *wantq, logical *wantz, integer *n, real
*a, integer *lda, real *b, integer *ldb, real *q, integer *ldq, real *
z__, integer *ldz, integer *j1, integer *n1, integer *n2, real *work,
integer *lwork, integer *info)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
(A, B) by an orthogonal equivalence transformation.
(A, B) must be in generalized real Schur canonical form (as returned
by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
diagonal blocks. B is upper triangular.
Optionally, the matrices Q and Z of generalized Schur vectors are
updated.
Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
Arguments
=========
WANTQ (input) LOGICAL
.TRUE. : update the left transformation matrix Q;
.FALSE.: do not update Q.
WANTZ (input) LOGICAL
.TRUE. : update the right transformation matrix Z;
.FALSE.: do not update Z.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input/output) REAL arrays, dimensions (LDA,N)
On entry, the matrix A in the pair (A, B).
On exit, the updated matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) REAL arrays, dimensions (LDB,N)
On entry, the matrix B in the pair (A, B).
On exit, the updated matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Q (input/output) REAL array, dimension (LDZ,N)
On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
On exit, the updated matrix Q.
Not referenced if WANTQ = .FALSE..
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= 1.
If WANTQ = .TRUE., LDQ >= N.
Z (input/output) REAL array, dimension (LDZ,N)
On entry, if WANTZ =.TRUE., the orthogonal matrix Z.
On exit, the updated matrix Z.
Not referenced if WANTZ = .FALSE..
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1.
If WANTZ = .TRUE., LDZ >= N.
J1 (input) INTEGER
The index to the first block (A11, B11). 1 <= J1 <= N.
N1 (input) INTEGER
The order of the first block (A11, B11). N1 = 0, 1 or 2.
N2 (input) INTEGER
The order of the second block (A22, B22). N2 = 0, 1 or 2.
WORK (workspace) REAL array, dimension (LWORK).
LWORK (input) INTEGER
The dimension of the array WORK.
LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )
INFO (output) INTEGER
=0: Successful exit
>0: If INFO = 1, the transformed matrix (A, B) would be
too far from generalized Schur form; the blocks are
not swapped and (A, B) and (Q, Z) are unchanged.
The problem of swapping is too ill-conditioned.
<0: If INFO = -16: LWORK is too small. Appropriate value
for LWORK is returned in WORK(1).
Further Details
===============
Based on contributions by
Bo Kagstrom and Peter Poromaa, Department of Computing Science,
Umea University, S-901 87 Umea, Sweden.
In the current code both weak and strong stability tests are
performed. The user can omit the strong stability test by changing
the internal logical parameter WANDS to .FALSE.. See ref. [2] for
details.
[1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
M.S. Moonen et al (eds), Linear Algebra for Large Scale and
Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
Eigenvalues of a Regular Matrix Pair (A, B) and Condition
Estimation: Theory, Algorithms and Software,
Report UMINF - 94.04, Department of Computing Science, Umea
University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
Note 87. To appear in Numerical Algorithms, 1996.
=====================================================================
Parameter adjustments */
/* Table of constant values */
static integer c__16 = 16;
static real c_b3 = 0.f;
static integer c__0 = 0;
static integer c__1 = 1;
static integer c__4 = 4;
static integer c__2 = 2;
static real c_b38 = 1.f;
static real c_b44 = -1.f;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
z_offset, i__1, i__2;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static logical weak;
static real ddum;
static integer idum;
static real taul[4], dsum, taur[4], scpy[16] /* was [4][4] */,
tcpy[16] /* was [4][4] */;
extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
integer *, real *, real *);
static real f, g;
static integer i__, m;
static real s[16] /* was [4][4] */, t[16] /* was [4][4] */, scale,
bqra21, brqa21;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
static real licop[16] /* was [4][4] */;
static integer linfo;
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
static real ircop[16] /* was [4][4] */, dnorm;
static integer iwork[4];
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), slagv2_(real *, integer *, real *, integer *, real *,
real *, real *, real *, real *, real *, real *), sgeqr2_(integer *
, integer *, real *, integer *, real *, real *, integer *),
sgerq2_(integer *, integer *, real *, integer *, real *, real *,
integer *);
static real be[2], ai[2];
extern /* Subroutine */ int sorg2r_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *), sorgr2_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
);
static real ar[2], sa, sb, li[16] /* was [4][4] */;
extern /* Subroutine */ int sorm2r_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *), sormr2_(char *, char *, integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, real *, integer *);
static real dscale, ir[16] /* was [4][4] */;
extern /* Subroutine */ int stgsy2_(char *, integer *, integer *, integer
*, real *, integer *, real *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *, integer *);
static real ss;
extern doublereal slamch_(char *);
static real ws;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slartg_(real *, real *,
real *, real *, real *);
static real thresh;
extern /* Subroutine */ int slassq_(integer *, real *, integer *, real *,
real *);
static real smlnum;
static logical strong;
static real eps;
#define scpy_ref(a_1,a_2) scpy[(a_2)*4 + a_1 - 5]
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
#define s_ref(a_1,a_2) s[(a_2)*4 + a_1 - 5]
#define t_ref(a_1,a_2) t[(a_2)*4 + a_1 - 5]
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
#define li_ref(a_1,a_2) li[(a_2)*4 + a_1 - 5]
#define ir_ref(a_1,a_2) ir[(a_2)*4 + a_1 - 5]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n <= 1 || *n1 <= 0 || *n2 <= 0) {
return 0;
}
if (*n1 > *n || *j1 + *n1 > *n) {
return 0;
}
m = *n1 + *n2;
/* Computing MAX */
i__1 = *n * m, i__2 = m * m << 1;
if (*lwork < max(i__1,i__2)) {
*info = -16;
/* Computing MAX */
i__1 = *n * m, i__2 = m * m << 1;
work[1] = (real) max(i__1,i__2);
return 0;
}
weak = FALSE_;
strong = FALSE_;
/* Make a local copy of selected block */
scopy_(&c__16, &c_b3, &c__0, li, &c__1);
scopy_(&c__16, &c_b3, &c__0, ir, &c__1);
slacpy_("Full", &m, &m, &a_ref(*j1, *j1), lda, s, &c__4);
slacpy_("Full", &m, &m, &b_ref(*j1, *j1), ldb, t, &c__4);
/* Compute threshold for testing acceptance of swapping. */
eps = slamch_("P");
smlnum = slamch_("S") / eps;
dscale = 0.f;
dsum = 1.f;
slacpy_("Full", &m, &m, s, &c__4, &work[1], &m);
i__1 = m * m;
slassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
slacpy_("Full", &m, &m, t, &c__4, &work[1], &m);
i__1 = m * m;
slassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
dnorm = dscale * sqrt(dsum);
/* Computing MAX */
r__1 = eps * 10.f * dnorm;
thresh = dmax(r__1,smlnum);
if (m == 2) {
/* CASE 1: Swap 1-by-1 and 1-by-1 blocks.
Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks
using Givens rotations and perform the swap tentatively. */
f = s_ref(2, 2) * t_ref(1, 1) - t_ref(2, 2) * s_ref(1, 1);
g = s_ref(2, 2) * t_ref(1, 2) - t_ref(2, 2) * s_ref(1, 2);
sb = (r__1 = t_ref(2, 2), dabs(r__1));
sa = (r__1 = s_ref(2, 2), dabs(r__1));
slartg_(&f, &g, &ir_ref(1, 2), &ir_ref(1, 1), &ddum);
ir_ref(2, 1) = -ir_ref(1, 2);
ir_ref(2, 2) = ir_ref(1, 1);
srot_(&c__2, &s_ref(1, 1), &c__1, &s_ref(1, 2), &c__1, &ir_ref(1, 1),
&ir_ref(2, 1));
srot_(&c__2, &t_ref(1, 1), &c__1, &t_ref(1, 2), &c__1, &ir_ref(1, 1),
&ir_ref(2, 1));
if (sa >= sb) {
slartg_(&s_ref(1, 1), &s_ref(2, 1), &li_ref(1, 1), &li_ref(2, 1),
&ddum);
} else {
slartg_(&t_ref(1, 1), &t_ref(2, 1), &li_ref(1, 1), &li_ref(2, 1),
&ddum);
}
srot_(&c__2, &s_ref(1, 1), &c__4, &s_ref(2, 1), &c__4, &li_ref(1, 1),
&li_ref(2, 1));
srot_(&c__2, &t_ref(1, 1), &c__4, &t_ref(2, 1), &c__4, &li_ref(1, 1),
&li_ref(2, 1));
li_ref(2, 2) = li_ref(1, 1);
li_ref(1, 2) = -li_ref(2, 1);
/* Weak stability test:
|S21| + |T21| <= O(EPS * F-norm((S, T))) */
ws = (r__1 = s_ref(2, 1), dabs(r__1)) + (r__2 = t_ref(2, 1), dabs(
r__2));
weak = ws <= thresh;
if (! weak) {
goto L70;
}
if (TRUE_) {
/* Strong stability test:
F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B))) */
slacpy_("Full", &m, &m, &a_ref(*j1, *j1), lda, &work[m * m + 1], &
m);
sgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, s, &c__4, &c_b3, &
work[1], &m);
sgemm_("N", "T", &m, &m, &m, &c_b44, &work[1], &m, ir, &c__4, &
c_b38, &work[m * m + 1], &m);
dscale = 0.f;
dsum = 1.f;
i__1 = m * m;
slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
slacpy_("Full", &m, &m, &b_ref(*j1, *j1), ldb, &work[m * m + 1], &
m);
sgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, t, &c__4, &c_b3, &
work[1], &m);
sgemm_("N", "T", &m, &m, &m, &c_b44, &work[1], &m, ir, &c__4, &
c_b38, &work[m * m + 1], &m);
i__1 = m * m;
slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
ss = dscale * sqrt(dsum);
strong = ss <= thresh;
if (! strong) {
goto L70;
}
}
/* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and
(A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
i__1 = *j1 + 1;
srot_(&i__1, &a_ref(1, *j1), &c__1, &a_ref(1, *j1 + 1), &c__1, &
ir_ref(1, 1), &ir_ref(2, 1));
i__1 = *j1 + 1;
srot_(&i__1, &b_ref(1, *j1), &c__1, &b_ref(1, *j1 + 1), &c__1, &
ir_ref(1, 1), &ir_ref(2, 1));
i__1 = *n - *j1 + 1;
srot_(&i__1, &a_ref(*j1, *j1), lda, &a_ref(*j1 + 1, *j1), lda, &
li_ref(1, 1), &li_ref(2, 1));
i__1 = *n - *j1 + 1;
srot_(&i__1, &b_ref(*j1, *j1), ldb, &b_ref(*j1 + 1, *j1), ldb, &
li_ref(1, 1), &li_ref(2, 1));
/* Set N1-by-N2 (2,1) - blocks to ZERO. */
a_ref(*j1 + 1, *j1) = 0.f;
b_ref(*j1 + 1, *j1) = 0.f;
/* Accumulate transformations into Q and Z if requested. */
if (*wantz) {
srot_(n, &z___ref(1, *j1), &c__1, &z___ref(1, *j1 + 1), &c__1, &
ir_ref(1, 1), &ir_ref(2, 1));
}
if (*wantq) {
srot_(n, &q_ref(1, *j1), &c__1, &q_ref(1, *j1 + 1), &c__1, &
li_ref(1, 1), &li_ref(2, 1));
}
/* Exit with INFO = 0 if swap was successfully performed. */
return 0;
} else {
/* CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2
and 2-by-2 blocks.
Solve the generalized Sylvester equation
S11 * R - L * S22 = SCALE * S12
T11 * R - L * T22 = SCALE * T12
for R and L. Solutions in LI and IR. */
slacpy_("Full", n1, n2, &t_ref(1, *n1 + 1), &c__4, li, &c__4);
slacpy_("Full", n1, n2, &s_ref(1, *n1 + 1), &c__4, &ir_ref(*n2 + 1, *
n1 + 1), &c__4);
stgsy2_("N", &c__0, n1, n2, s, &c__4, &s_ref(*n1 + 1, *n1 + 1), &c__4,
&ir_ref(*n2 + 1, *n1 + 1), &c__4, t, &c__4, &t_ref(*n1 + 1, *
n1 + 1), &c__4, li, &c__4, &scale, &dsum, &dscale, iwork, &
idum, &linfo);
/* Compute orthogonal matrix QL:
QL' * LI = [ TL ]
[ 0 ]
where
LI = [ -L ]
[ SCALE * identity(N2) ] */
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
sscal_(n1, &c_b44, &li_ref(1, i__), &c__1);
li_ref(*n1 + i__, i__) = scale;
/* L10: */
}
sgeqr2_(&m, n2, li, &c__4, taul, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
sorg2r_(&m, &m, n2, li, &c__4, taul, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
/* Compute orthogonal matrix RQ:
IR * RQ' = [ 0 TR],
where IR = [ SCALE * identity(N1), R ] */
i__1 = *n1;
for (i__ = 1; i__ <= i__1; ++i__) {
ir_ref(*n2 + i__, i__) = scale;
/* L20: */
}
sgerq2_(n1, &m, &ir_ref(*n2 + 1, 1), &c__4, taur, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
sorgr2_(&m, &m, n1, ir, &c__4, taur, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
/* Perform the swapping tentatively: */
sgemm_("T", "N", &m, &m, &m, &c_b38, li, &c__4, s, &c__4, &c_b3, &
work[1], &m);
sgemm_("N", "T", &m, &m, &m, &c_b38, &work[1], &m, ir, &c__4, &c_b3,
s, &c__4);
sgemm_("T", "N", &m, &m, &m, &c_b38, li, &c__4, t, &c__4, &c_b3, &
work[1], &m);
sgemm_("N", "T", &m, &m, &m, &c_b38, &work[1], &m, ir, &c__4, &c_b3,
t, &c__4);
slacpy_("F", &m, &m, s, &c__4, scpy, &c__4);
slacpy_("F", &m, &m, t, &c__4, tcpy, &c__4);
slacpy_("F", &m, &m, ir, &c__4, ircop, &c__4);
slacpy_("F", &m, &m, li, &c__4, licop, &c__4);
/* Triangularize the B-part by an RQ factorization.
Apply transformation (from left) to A-part, giving S. */
sgerq2_(&m, &m, t, &c__4, taur, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
sormr2_("R", "T", &m, &m, &m, t, &c__4, taur, s, &c__4, &work[1], &
linfo);
if (linfo != 0) {
goto L70;
}
sormr2_("L", "N", &m, &m, &m, t, &c__4, taur, ir, &c__4, &work[1], &
linfo);
if (linfo != 0) {
goto L70;
}
/* Compute F-norm(S21) in BRQA21. (T21 is 0.) */
dscale = 0.f;
dsum = 1.f;
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
slassq_(n1, &s_ref(*n2 + 1, i__), &c__1, &dscale, &dsum);
/* L30: */
}
brqa21 = dscale * sqrt(dsum);
/* Triangularize the B-part by a QR factorization.
Apply transformation (from right) to A-part, giving S. */
sgeqr2_(&m, &m, tcpy, &c__4, taul, &work[1], &linfo);
if (linfo != 0) {
goto L70;
}
sorm2r_("L", "T", &m, &m, &m, tcpy, &c__4, taul, scpy, &c__4, &work[1]
, info);
sorm2r_("R", "N", &m, &m, &m, tcpy, &c__4, taul, licop, &c__4, &work[
1], info);
if (linfo != 0) {
goto L70;
}
/* Compute F-norm(S21) in BQRA21. (T21 is 0.) */
dscale = 0.f;
dsum = 1.f;
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
slassq_(n1, &scpy_ref(*n2 + 1, i__), &c__1, &dscale, &dsum);
/* L40: */
}
bqra21 = dscale * sqrt(dsum);
/* Decide which method to use.
Weak stability test:
F-norm(S21) <= O(EPS * F-norm((S, T))) */
if (bqra21 <= brqa21 && bqra21 <= thresh) {
slacpy_("F", &m, &m, scpy, &c__4, s, &c__4);
slacpy_("F", &m, &m, tcpy, &c__4, t, &c__4);
slacpy_("F", &m, &m, ircop, &c__4, ir, &c__4);
slacpy_("F", &m, &m, licop, &c__4, li, &c__4);
} else if (brqa21 >= thresh) {
goto L70;
}
/* Set lower triangle of B-part to zero */
i__1 = m;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = m - i__ + 1;
scopy_(&i__2, &c_b3, &c__0, &t_ref(i__, i__ - 1), &c__1);
/* L50: */
}
if (TRUE_) {
/* Strong stability test:
F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B))) */
slacpy_("Full", &m, &m, &a_ref(*j1, *j1), lda, &work[m * m + 1], &
m);
sgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, s, &c__4, &c_b3, &
work[1], &m);
sgemm_("N", "N", &m, &m, &m, &c_b44, &work[1], &m, ir, &c__4, &
c_b38, &work[m * m + 1], &m);
dscale = 0.f;
dsum = 1.f;
i__1 = m * m;
slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
slacpy_("Full", &m, &m, &b_ref(*j1, *j1), ldb, &work[m * m + 1], &
m);
sgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, t, &c__4, &c_b3, &
work[1], &m);
sgemm_("N", "N", &m, &m, &m, &c_b44, &work[1], &m, ir, &c__4, &
c_b38, &work[m * m + 1], &m);
i__1 = m * m;
slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
ss = dscale * sqrt(dsum);
strong = ss <= thresh;
if (! strong) {
goto L70;
}
}
/* If the swap is accepted ("weakly" and "strongly"), apply the
transformations and set N1-by-N2 (2,1)-block to zero. */
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
scopy_(n1, &c_b3, &c__0, &s_ref(*n2 + 1, i__), &c__1);
/* L60: */
}
/* copy back M-by-M diagonal block starting at index J1 of (A, B) */
slacpy_("F", &m, &m, s, &c__4, &a_ref(*j1, *j1), lda);
slacpy_("F", &m, &m, t, &c__4, &b_ref(*j1, *j1), ldb);
scopy_(&c__16, &c_b3, &c__0, t, &c__1);
/* Standardize existing 2-by-2 blocks. */
i__1 = m * m;
scopy_(&i__1, &c_b3, &c__0, &work[1], &c__1);
work[1] = 1.f;
t_ref(1, 1) = 1.f;
idum = *lwork - m * m - 2;
if (*n2 > 1) {
slagv2_(&a_ref(*j1, *j1), lda, &b_ref(*j1, *j1), ldb, ar, ai, be,
&work[1], &work[2], &t_ref(1, 1), &t_ref(2, 1));
work[m + 1] = -work[2];
work[m + 2] = work[1];
t_ref(*n2, *n2) = t_ref(1, 1);
t_ref(1, 2) = -t_ref(2, 1);
}
work[m * m] = 1.f;
t_ref(m, m) = 1.f;
if (*n1 > 1) {
slagv2_(&a_ref(*j1 + *n2, *j1 + *n2), lda, &b_ref(*j1 + *n2, *j1
+ *n2), ldb, taur, taul, &work[m * m + 1], &work[*n2 * m
+ *n2 + 1], &work[*n2 * m + *n2 + 2], &t_ref(*n2 + 1, *n2
+ 1), &t_ref(m, m - 1));
work[m * m] = work[*n2 * m + *n2 + 1];
work[m * m - 1] = -work[*n2 * m + *n2 + 2];
t_ref(m, m) = t_ref(*n2 + 1, *n2 + 1);
t_ref(m - 1, m) = -t_ref(m, m - 1);
}
sgemm_("T", "N", n2, n1, n2, &c_b38, &work[1], &m, &a_ref(*j1, *j1 + *
n2), lda, &c_b3, &work[m * m + 1], n2);
slacpy_("Full", n2, n1, &work[m * m + 1], n2, &a_ref(*j1, *j1 + *n2),
lda);
sgemm_("T", "N", n2, n1, n2, &c_b38, &work[1], &m, &b_ref(*j1, *j1 + *
n2), ldb, &c_b3, &work[m * m + 1], n2);
slacpy_("Full", n2, n1, &work[m * m + 1], n2, &b_ref(*j1, *j1 + *n2),
ldb);
sgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, &work[1], &m, &c_b3, &
work[m * m + 1], &m);
slacpy_("Full", &m, &m, &work[m * m + 1], &m, li, &c__4);
sgemm_("N", "N", n2, n1, n1, &c_b38, &a_ref(*j1, *j1 + *n2), lda, &
t_ref(*n2 + 1, *n2 + 1), &c__4, &c_b3, &work[1], n2);
slacpy_("Full", n2, n1, &work[1], n2, &a_ref(*j1, *j1 + *n2), lda);
sgemm_("N", "N", n2, n1, n1, &c_b38, &b_ref(*j1, *j1 + *n2), lda, &
t_ref(*n2 + 1, *n2 + 1), &c__4, &c_b3, &work[1], n2);
slacpy_("Full", n2, n1, &work[1], n2, &b_ref(*j1, *j1 + *n2), ldb);
sgemm_("T", "N", &m, &m, &m, &c_b38, ir, &c__4, t, &c__4, &c_b3, &
work[1], &m);
slacpy_("Full", &m, &m, &work[1], &m, ir, &c__4);
/* Accumulate transformations into Q and Z if requested. */
if (*wantq) {
sgemm_("N", "N", n, &m, &m, &c_b38, &q_ref(1, *j1), ldq, li, &
c__4, &c_b3, &work[1], n);
slacpy_("Full", n, &m, &work[1], n, &q_ref(1, *j1), ldq);
}
if (*wantz) {
sgemm_("N", "N", n, &m, &m, &c_b38, &z___ref(1, *j1), ldz, ir, &
c__4, &c_b3, &work[1], n);
slacpy_("Full", n, &m, &work[1], n, &z___ref(1, *j1), ldz);
}
/* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and
(A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
i__ = *j1 + m;
if (i__ <= *n) {
i__1 = *n - i__ + 1;
sgemm_("T", "N", &m, &i__1, &m, &c_b38, li, &c__4, &a_ref(*j1,
i__), lda, &c_b3, &work[1], &m);
i__1 = *n - i__ + 1;
slacpy_("Full", &m, &i__1, &work[1], &m, &a_ref(*j1, i__), lda);
i__1 = *n - i__ + 1;
sgemm_("T", "N", &m, &i__1, &m, &c_b38, li, &c__4, &b_ref(*j1,
i__), lda, &c_b3, &work[1], &m);
i__1 = *n - i__ + 1;
slacpy_("Full", &m, &i__1, &work[1], &m, &b_ref(*j1, i__), lda);
}
i__ = *j1 - 1;
if (i__ > 0) {
sgemm_("N", "N", &i__, &m, &m, &c_b38, &a_ref(1, *j1), lda, ir, &
c__4, &c_b3, &work[1], &i__);
slacpy_("Full", &i__, &m, &work[1], &i__, &a_ref(1, *j1), lda);
sgemm_("N", "N", &i__, &m, &m, &c_b38, &b_ref(1, *j1), ldb, ir, &
c__4, &c_b3, &work[1], &i__);
slacpy_("Full", &i__, &m, &work[1], &i__, &b_ref(1, *j1), ldb);
}
/* Exit with INFO = 0 if swap was successfully performed. */
return 0;
}
/* Exit with INFO = 1 if swap was rejected. */
L70:
*info = 1;
return 0;
/* End of STGEX2 */
} /* stgex2_ */
/* Subroutine */ int serrqr_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
static real a[4] /* was [2][2] */, b[2];
static integer i__, j;
static real w[2], x[2];
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *);
static real af[4] /* was [2][2] */;
extern /* Subroutine */ int sorg2r_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *), sorm2r_(char *, char *,
integer *, integer *, integer *, real *, integer *, real *, real *
, integer *, real *, integer *), alaesm_(char *,
logical *, integer *), chkxer_(char *, integer *, integer
*, logical *, logical *), sgeqrf_(integer *, integer *,
real *, integer *, real *, real *, integer *, integer *), sgeqrs_(
integer *, integer *, integer *, real *, integer *, real *, real *
, integer *, real *, integer *, integer *), sorgqr_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, integer *), sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
#define a_ref(a_1,a_2) a[(a_2)*2 + a_1 - 3]
#define af_ref(a_1,a_2) af[(a_2)*2 + a_1 - 3]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
SERRQR tests the error exits for the REAL routines
that use the QR decomposition of a general matrix.
Arguments
=========
PATH (input) CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT (input) INTEGER
The unit number for output.
===================================================================== */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
/* Set the variables to innocuous values. */
for (j = 1; j <= 2; ++j) {
for (i__ = 1; i__ <= 2; ++i__) {
a_ref(i__, j) = 1.f / (real) (i__ + j);
af_ref(i__, j) = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QR factorization
SGEQRF */
s_copy(srnamc_1.srnamt, "SGEQRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgeqrf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeqrf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgeqrf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEQR2 */
s_copy(srnamc_1.srnamt, "SGEQR2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgeqr2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqr2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeqr2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEQRS */
s_copy(srnamc_1.srnamt, "SGEQRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgeqrs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrs_(&c__1, &c__2, &c__0, a, &c__2, x, b, &c__2, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgeqrs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgeqrs_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgeqrs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgeqrs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORGQR */
s_copy(srnamc_1.srnamt, "SORGQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sorgqr_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorgqr_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorgqr_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorgqr_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorgqr_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorgqr_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sorgqr_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORG2R */
s_copy(srnamc_1.srnamt, "SORG2R", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sorg2r_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorg2r_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorg2r_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorg2r_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorg2r_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorg2r_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORMQR */
s_copy(srnamc_1.srnamt, "SORMQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sormqr_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sormqr_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sormqr_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sormqr_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sormqr_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sormqr_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sormqr_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORM2R */
s_copy(srnamc_1.srnamt, "SORM2R", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sorm2r_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorm2r_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorm2r_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sorm2r_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sorm2r_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of SERRQR */
} /* serrqr_ */
/*< >*/
/* Subroutine */ int sggsvp_(char *jobu, char *jobv, char *jobq, integer *m,
integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb,
real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu,
real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real *
tau, real *work, integer *info, ftnlen jobu_len, ftnlen jobv_len,
ftnlen jobq_len)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
u_offset, v_dim1, v_offset, i__1, i__2, i__3;
real r__1;
/* Local variables */
integer i__, j;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
logical wantq, wantu, wantv;
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *), sgerq2_(integer *, integer *, real
*, integer *, real *, real *, integer *), sorg2r_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
), sorm2r_(char *, char *, integer *, integer *, integer *, real *
, integer *, real *, real *, integer *, real *, integer *, ftnlen,
ftnlen), sormr2_(char *, char *, integer *, integer *, integer *,
real *, integer *, real *, real *, integer *, real *, integer *,
ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen), sgeqpf_(
integer *, integer *, real *, integer *, integer *, real *, real *
, integer *), slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *, ftnlen), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *, ftnlen), slapmt_(
logical *, integer *, integer *, real *, integer *, integer *);
logical forwrd;
(void)jobu_len;
(void)jobv_len;
(void)jobq_len;
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/*< CHARACTER JOBQ, JOBU, JOBV >*/
/*< INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P >*/
/*< REAL TOLA, TOLB >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IWORK( * ) >*/
/*< >*/
/* .. */
/* Purpose */
/* ======= */
/* SGGSVP computes orthogonal matrices U, V and Q such that */
/* N-K-L K L */
/* U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; */
/* L ( 0 0 A23 ) */
/* M-K-L ( 0 0 0 ) */
/* N-K-L K L */
/* = K ( 0 A12 A13 ) if M-K-L < 0; */
/* M-K ( 0 0 A23 ) */
/* N-K-L K L */
/* V'*B*Q = L ( 0 0 B13 ) */
/* P-L ( 0 0 0 ) */
/* where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
/* upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
/* otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective */
/* numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the */
/* transpose of Z. */
/* This decomposition is the preprocessing step for computing the */
/* Generalized Singular Value Decomposition (GSVD), see subroutine */
/* SGGSVD. */
/* Arguments */
/* ========= */
/* JOBU (input) CHARACTER*1 */
/* = 'U': Orthogonal matrix U is computed; */
/* = 'N': U is not computed. */
/* JOBV (input) CHARACTER*1 */
/* = 'V': Orthogonal matrix V is computed; */
/* = 'N': V is not computed. */
/* JOBQ (input) CHARACTER*1 */
/* = 'Q': Orthogonal matrix Q is computed; */
/* = 'N': Q is not computed. */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* P (input) INTEGER */
/* The number of rows of the matrix B. P >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrices A and B. N >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, A contains the triangular (or trapezoidal) matrix */
/* described in the Purpose section. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* B (input/output) REAL array, dimension (LDB,N) */
/* On entry, the P-by-N matrix B. */
/* On exit, B contains the triangular matrix described in */
/* the Purpose section. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,P). */
/* TOLA (input) REAL */
/* TOLB (input) REAL */
/* TOLA and TOLB are the thresholds to determine the effective */
/* numerical rank of matrix B and a subblock of A. Generally, */
/* they are set to */
/* TOLA = MAX(M,N)*norm(A)*MACHEPS, */
/* TOLB = MAX(P,N)*norm(B)*MACHEPS. */
/* The size of TOLA and TOLB may affect the size of backward */
/* errors of the decomposition. */
/* K (output) INTEGER */
/* L (output) INTEGER */
/* On exit, K and L specify the dimension of the subblocks */
/* described in Purpose. */
/* K + L = effective numerical rank of (A',B')'. */
/* U (output) REAL array, dimension (LDU,M) */
/* If JOBU = 'U', U contains the orthogonal matrix U. */
/* If JOBU = 'N', U is not referenced. */
/* LDU (input) INTEGER */
/* The leading dimension of the array U. LDU >= max(1,M) if */
/* JOBU = 'U'; LDU >= 1 otherwise. */
/* V (output) REAL array, dimension (LDV,M) */
/* If JOBV = 'V', V contains the orthogonal matrix V. */
/* If JOBV = 'N', V is not referenced. */
/* LDV (input) INTEGER */
/* The leading dimension of the array V. LDV >= max(1,P) if */
/* JOBV = 'V'; LDV >= 1 otherwise. */
/* Q (output) REAL array, dimension (LDQ,N) */
/* If JOBQ = 'Q', Q contains the orthogonal matrix Q. */
/* If JOBQ = 'N', Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,N) if */
/* JOBQ = 'Q'; LDQ >= 1 otherwise. */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* TAU (workspace) REAL array, dimension (N) */
/* WORK (workspace) REAL array, dimension (max(3*N,M,P)) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The subroutine uses LAPACK subroutine SGEQPF for the QR factorization */
/* with column pivoting to detect the effective numerical rank of the */
/* a matrix. It may be replaced by a better rank determination strategy. */
/* ===================================================================== */
/* .. Parameters .. */
/*< REAL ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL FORWRD, WANTQ, WANTU, WANTV >*/
/*< INTEGER I, J >*/
/* .. */
/* .. External Functions .. */
/*< LOGICAL LSAME >*/
/*< EXTERNAL LSAME >*/
/* .. */
/* .. External Subroutines .. */
/*< >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, MAX, MIN >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/*< WANTU = LSAME( JOBU, 'U' ) >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--iwork;
--tau;
--work;
/* Function Body */
wantu = lsame_(jobu, "U", (ftnlen)1, (ftnlen)1);
/*< WANTV = LSAME( JOBV, 'V' ) >*/
wantv = lsame_(jobv, "V", (ftnlen)1, (ftnlen)1);
/*< WANTQ = LSAME( JOBQ, 'Q' ) >*/
wantq = lsame_(jobq, "Q", (ftnlen)1, (ftnlen)1);
/*< FORWRD = .TRUE. >*/
forwrd = TRUE_;
/*< INFO = 0 >*/
*info = 0;
/*< IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN >*/
if (! (wantu || lsame_(jobu, "N", (ftnlen)1, (ftnlen)1))) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN >*/
} else if (! (wantv || lsame_(jobv, "N", (ftnlen)1, (ftnlen)1))) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN >*/
} else if (! (wantq || lsame_(jobq, "N", (ftnlen)1, (ftnlen)1))) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( M.LT.0 ) THEN >*/
} else if (*m < 0) {
/*< INFO = -4 >*/
*info = -4;
/*< ELSE IF( P.LT.0 ) THEN >*/
} else if (*p < 0) {
/*< INFO = -5 >*/
*info = -5;
/*< ELSE IF( N.LT.0 ) THEN >*/
} else if (*n < 0) {
/*< INFO = -6 >*/
*info = -6;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -8 >*/
*info = -8;
/*< ELSE IF( LDB.LT.MAX( 1, P ) ) THEN >*/
} else if (*ldb < max(1,*p)) {
/*< INFO = -10 >*/
*info = -10;
/*< ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN >*/
} else if (*ldu < 1 || (wantu && *ldu < *m)) {
/*< INFO = -16 >*/
*info = -16;
/*< ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN >*/
} else if (*ldv < 1 || (wantv && *ldv < *p)) {
/*< INFO = -18 >*/
*info = -18;
/*< ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN >*/
} else if (*ldq < 1 || (wantq && *ldq < *n)) {
/*< INFO = -20 >*/
*info = -20;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'SGGSVP', -INFO ) >*/
i__1 = -(*info);
xerbla_("SGGSVP", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* QR with column pivoting of B: B*P = V*( S11 S12 ) */
/* ( 0 0 ) */
/*< DO 10 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< IWORK( I ) = 0 >*/
iwork[i__] = 0;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< CALL SGEQPF( P, N, B, LDB, IWORK, TAU, WORK, INFO ) >*/
sgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], info);
/* Update A := A*P */
/*< CALL SLAPMT( FORWRD, M, N, A, LDA, IWORK ) >*/
slapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);
/* Determine the effective rank of matrix B. */
/*< L = 0 >*/
*l = 0;
/*< DO 20 I = 1, MIN( P, N ) >*/
i__1 = min(*p,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
/*< >*/
if ((r__1 = b[i__ + i__ * b_dim1], dabs(r__1)) > *tolb) {
++(*l);
}
/*< 20 CONTINUE >*/
/* L20: */
}
/*< IF( WANTV ) THEN >*/
if (wantv) {
/* Copy the details of V, and form V. */
/*< CALL SLASET( 'Full', P, P, ZERO, ZERO, V, LDV ) >*/
slaset_("Full", p, p, &c_b12, &c_b12, &v[v_offset], ldv, (ftnlen)4);
/*< >*/
if (*p > 1) {
i__1 = *p - 1;
slacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2],
ldv, (ftnlen)5);
}
/*< CALL SORG2R( P, P, MIN( P, N ), V, LDV, TAU, WORK, INFO ) >*/
i__1 = min(*p,*n);
sorg2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
/*< END IF >*/
}
/* Clean up B */
/*< DO 40 J = 1, L - 1 >*/
i__1 = *l - 1;
for (j = 1; j <= i__1; ++j) {
/*< DO 30 I = J + 1, L >*/
i__2 = *l;
for (i__ = j + 1; i__ <= i__2; ++i__) {
/*< B( I, J ) = ZERO >*/
b[i__ + j * b_dim1] = (float)0.;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< >*/
if (*p > *l) {
i__1 = *p - *l;
slaset_("Full", &i__1, n, &c_b12, &c_b12, &b[*l + 1 + b_dim1], ldb, (
ftnlen)4);
}
/*< IF( WANTQ ) THEN >*/
if (wantq) {
/* Set Q = I and Update Q := Q*P */
/*< CALL SLASET( 'Full', N, N, ZERO, ONE, Q, LDQ ) >*/
slaset_("Full", n, n, &c_b12, &c_b22, &q[q_offset], ldq, (ftnlen)4);
/*< CALL SLAPMT( FORWRD, N, N, Q, LDQ, IWORK ) >*/
slapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
/*< END IF >*/
}
/*< IF( P.GE.L .AND. N.NE.L ) THEN >*/
if (*p >= *l && *n != *l) {
/* RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z */
/*< CALL SGERQ2( L, N, B, LDB, TAU, WORK, INFO ) >*/
sgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
/* Update A := A*Z' */
/*< >*/
sormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[
a_offset], lda, &work[1], info, (ftnlen)5, (ftnlen)9);
/*< IF( WANTQ ) THEN >*/
if (wantq) {
/* Update Q := Q*Z' */
/*< >*/
sormr2_("Right", "Transpose", n, n, l, &b[b_offset], ldb, &tau[1],
&q[q_offset], ldq, &work[1], info, (ftnlen)5, (ftnlen)9);
/*< END IF >*/
}
/* Clean up B */
/*< CALL SLASET( 'Full', L, N-L, ZERO, ZERO, B, LDB ) >*/
i__1 = *n - *l;
slaset_("Full", l, &i__1, &c_b12, &c_b12, &b[b_offset], ldb, (ftnlen)
4);
/*< DO 60 J = N - L + 1, N >*/
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
/*< DO 50 I = J - N + L + 1, L >*/
i__2 = *l;
for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
/*< B( I, J ) = ZERO >*/
b[i__ + j * b_dim1] = (float)0.;
/*< 50 CONTINUE >*/
/* L50: */
}
/*< 60 CONTINUE >*/
/* L60: */
}
/*< END IF >*/
}
/* Let N-L L */
/* A = ( A11 A12 ) M, */
/* then the following does the complete QR decomposition of A11: */
/* A11 = U*( 0 T12 )*P1' */
/* ( 0 0 ) */
/*< DO 70 I = 1, N - L >*/
i__1 = *n - *l;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< IWORK( I ) = 0 >*/
iwork[i__] = 0;
/*< 70 CONTINUE >*/
/* L70: */
}
/*< CALL SGEQPF( M, N-L, A, LDA, IWORK, TAU, WORK, INFO ) >*/
i__1 = *n - *l;
sgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], info);
/* Determine the effective rank of A11 */
/*< K = 0 >*/
*k = 0;
/*< DO 80 I = 1, MIN( M, N-L ) >*/
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
for (i__ = 1; i__ <= i__1; ++i__) {
/*< >*/
if ((r__1 = a[i__ + i__ * a_dim1], dabs(r__1)) > *tola) {
++(*k);
}
/*< 80 CONTINUE >*/
/* L80: */
}
/* Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N ) */
/*< >*/
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
sorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &a[(
*n - *l + 1) * a_dim1 + 1], lda, &work[1], info, (ftnlen)4, (
ftnlen)9);
/*< IF( WANTU ) THEN >*/
if (wantu) {
/* Copy the details of U, and form U */
/*< CALL SLASET( 'Full', M, M, ZERO, ZERO, U, LDU ) >*/
slaset_("Full", m, m, &c_b12, &c_b12, &u[u_offset], ldu, (ftnlen)4);
/*< >*/
if (*m > 1) {
i__1 = *m - 1;
i__2 = *n - *l;
slacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2]
, ldu, (ftnlen)5);
}
/*< CALL SORG2R( M, M, MIN( M, N-L ), U, LDU, TAU, WORK, INFO ) >*/
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
sorg2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
/*< END IF >*/
}
/*< IF( WANTQ ) THEN >*/
if (wantq) {
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
/*< CALL SLAPMT( FORWRD, N, N-L, Q, LDQ, IWORK ) >*/
i__1 = *n - *l;
slapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
/*< END IF >*/
}
/* Clean up A: set the strictly lower triangular part of */
/* A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */
/*< DO 100 J = 1, K - 1 >*/
i__1 = *k - 1;
for (j = 1; j <= i__1; ++j) {
/*< DO 90 I = J + 1, K >*/
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
a[i__ + j * a_dim1] = (float)0.;
/*< 90 CONTINUE >*/
/* L90: */
}
/*< 100 CONTINUE >*/
/* L100: */
}
/*< >*/
if (*m > *k) {
i__1 = *m - *k;
i__2 = *n - *l;
slaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a[*k + 1 + a_dim1],
lda, (ftnlen)4);
}
/*< IF( N-L.GT.K ) THEN >*/
if (*n - *l > *k) {
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
/*< CALL SGERQ2( K, N-L, A, LDA, TAU, WORK, INFO ) >*/
i__1 = *n - *l;
sgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);
/*< IF( WANTQ ) THEN >*/
if (wantq) {
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1' */
/*< >*/
i__1 = *n - *l;
sormr2_("Right", "Transpose", n, &i__1, k, &a[a_offset], lda, &
tau[1], &q[q_offset], ldq, &work[1], info, (ftnlen)5, (
ftnlen)9);
/*< END IF >*/
}
/* Clean up A */
/*< CALL SLASET( 'Full', K, N-L-K, ZERO, ZERO, A, LDA ) >*/
i__1 = *n - *l - *k;
slaset_("Full", k, &i__1, &c_b12, &c_b12, &a[a_offset], lda, (ftnlen)
4);
/*< DO 120 J = N - L - K + 1, N - L >*/
i__1 = *n - *l;
for (j = *n - *l - *k + 1; j <= i__1; ++j) {
/*< DO 110 I = J - N + L + K + 1, K >*/
i__2 = *k;
for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
a[i__ + j * a_dim1] = (float)0.;
/*< 110 CONTINUE >*/
/* L110: */
}
/*< 120 CONTINUE >*/
/* L120: */
}
/*< END IF >*/
}
/*< IF( M.GT.K ) THEN >*/
if (*m > *k) {
/* QR factorization of A( K+1:M,N-L+1:N ) */
/*< CALL SGEQR2( M-K, L, A( K+1, N-L+1 ), LDA, TAU, WORK, INFO ) >*/
i__1 = *m - *k;
sgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], &
work[1], info);
/*< IF( WANTU ) THEN >*/
if (wantu) {
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
/*< >*/
i__1 = *m - *k;
/* Computing MIN */
i__3 = *m - *k;
i__2 = min(i__3,*l);
sorm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n
- *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 +
1], ldu, &work[1], info, (ftnlen)5, (ftnlen)12);
/*< END IF >*/
}
/* Clean up */
/*< DO 140 J = N - L + 1, N >*/
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
/*< DO 130 I = J - N + K + L + 1, M >*/
i__2 = *m;
for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
a[i__ + j * a_dim1] = (float)0.;
/*< 130 CONTINUE >*/
/* L130: */
}
/*< 140 CONTINUE >*/
/* L140: */
}
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of SGGSVP */
/*< END >*/
} /* sggsvp_ */
/* Subroutine */ int sgeqpf_(integer *m, integer *n, real *a, integer *lda,
integer *jpvt, real *tau, real *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, ma, mn;
real aii;
integer pvt;
real temp, temp2;
extern doublereal snrm2_(integer *, real *, integer *);
real tol3z;
extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *,
integer *, real *, real *, integer *, real *);
integer itemp;
extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *,
integer *), sgeqr2_(integer *, integer *, real *, integer *, real
*, real *, integer *), sorm2r_(char *, char *, integer *, integer
*, integer *, real *, integer *, real *, real *, integer *, real *
, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *), slarfg_(
integer *, real *, real *, integer *, real *);
extern integer isamax_(integer *, real *, integer *);
/* -- LAPACK deprecated driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* This routine is deprecated and has been replaced by routine SGEQP3. */
/* SGEQPF computes a QR factorization with column pivoting of a */
/* real M-by-N matrix A: A*P = Q*R. */
/* Arguments */
/* ========= */
/* 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 */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, the upper triangle of the array contains the */
/* min(M,N)-by-N upper triangular matrix R; the elements */
/* below the diagonal, together with the array TAU, */
/* represent the orthogonal matrix Q as a product of */
/* min(m,n) elementary reflectors. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* JPVT (input/output) INTEGER array, dimension (N) */
/* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */
/* to the front of A*P (a leading column); if JPVT(i) = 0, */
/* the i-th column of A is a free column. */
/* On exit, if JPVT(i) = k, then the i-th column of A*P */
/* was the k-th column of A. */
/* TAU (output) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors. */
/* WORK (workspace) REAL array, dimension (3*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(1) H(2) . . . H(n) */
/* Each H(i) has the form */
/* H = I - tau * v * v' */
/* where tau is a real scalar, and v is a real vector with */
/* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i). */
/* The matrix P is represented in jpvt as follows: If */
/* jpvt(j) = i */
/* then the jth column of P is the ith canonical unit vector. */
/* Partial column norm updating strategy modified by */
/* Z. Drmac and Z. Bujanovic, Dept. of Mathematics, */
/* University of Zagreb, Croatia. */
/* June 2006. */
/* For more details see LAPACK Working Note 176. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--jpvt;
--tau;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEQPF", &i__1);
return 0;
}
mn = min(*m,*n);
tol3z = sqrt(slamch_("Epsilon"));
/* Move initial columns up front */
itemp = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (jpvt[i__] != 0) {
if (i__ != itemp) {
sswap_(m, &a[i__ * a_dim1 + 1], &c__1, &a[itemp * a_dim1 + 1],
&c__1);
jpvt[i__] = jpvt[itemp];
jpvt[itemp] = i__;
} else {
jpvt[i__] = i__;
}
++itemp;
} else {
jpvt[i__] = i__;
}
/* L10: */
}
--itemp;
/* Compute the QR factorization and update remaining columns */
if (itemp > 0) {
ma = min(itemp,*m);
sgeqr2_(m, &ma, &a[a_offset], lda, &tau[1], &work[1], info);
if (ma < *n) {
i__1 = *n - ma;
sorm2r_("Left", "Transpose", m, &i__1, &ma, &a[a_offset], lda, &
tau[1], &a[(ma + 1) * a_dim1 + 1], lda, &work[1], info);
}
}
if (itemp < mn) {
/* Initialize partial column norms. The first n elements of */
/* work store the exact column norms. */
i__1 = *n;
for (i__ = itemp + 1; i__ <= i__1; ++i__) {
i__2 = *m - itemp;
work[i__] = snrm2_(&i__2, &a[itemp + 1 + i__ * a_dim1], &c__1);
work[*n + i__] = work[i__];
/* L20: */
}
/* Compute factorization */
i__1 = mn;
for (i__ = itemp + 1; i__ <= i__1; ++i__) {
/* Determine ith pivot column and swap if necessary */
i__2 = *n - i__ + 1;
pvt = i__ - 1 + isamax_(&i__2, &work[i__], &c__1);
if (pvt != i__) {
sswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
c__1);
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[i__];
jpvt[i__] = itemp;
work[pvt] = work[i__];
work[*n + pvt] = work[*n + i__];
}
/* Generate elementary reflector H(i) */
if (i__ < *m) {
i__2 = *m - i__ + 1;
slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + 1 + i__ *
a_dim1], &c__1, &tau[i__]);
} else {
slarfg_(&c__1, &a[*m + *m * a_dim1], &a[*m + *m * a_dim1], &
c__1, &tau[*m]);
}
if (i__ < *n) {
/* Apply H(i) to A(i:m,i+1:n) from the left */
aii = a[i__ + i__ * a_dim1];
a[i__ + i__ * a_dim1] = 1.f;
i__2 = *m - i__ + 1;
i__3 = *n - i__;
slarf_("LEFT", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
tau[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[(*
n << 1) + 1]);
a[i__ + i__ * a_dim1] = aii;
}
/* Update partial column norms */
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
if (work[j] != 0.f) {
/* NOTE: The following 4 lines follow from the analysis in */
/* Lapack Working Note 176. */
temp = (r__1 = a[i__ + j * a_dim1], dabs(r__1)) / work[j];
/* Computing MAX */
r__1 = 0.f, r__2 = (temp + 1.f) * (1.f - temp);
temp = dmax(r__1,r__2);
/* Computing 2nd power */
r__1 = work[j] / work[*n + j];
temp2 = temp * (r__1 * r__1);
if (temp2 <= tol3z) {
if (*m - i__ > 0) {
i__3 = *m - i__;
work[j] = snrm2_(&i__3, &a[i__ + 1 + j * a_dim1],
&c__1);
work[*n + j] = work[j];
} else {
work[j] = 0.f;
work[*n + j] = 0.f;
}
} else {
work[j] *= sqrt(temp);
}
}
/* L30: */
}
/* L40: */
}
}
return 0;
/* End of SGEQPF */
} /* sgeqpf_ */
/* Subroutine */ int sgeqrf_(integer *m, integer *n, real *a, integer *lda,
real *tau, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, ib, nb, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *), slarfb_(char *, char *, char *,
char *, integer *, integer *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGEQRF computes a QR factorization of a real M-by-N matrix A: */
/* A = Q * R. */
/* Arguments */
/* ========= */
/* 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. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, the elements on and above the diagonal of the array */
/* contain the min(M,N)-by-N upper trapezoidal matrix R (R is */
/* upper triangular if m >= n); the elements below the diagonal, */
/* with the array TAU, represent the orthogonal matrix Q as a */
/* product of min(m,n) elementary reflectors (see Further */
/* Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) REAL 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,N). */
/* For optimum performance LWORK >= N*NB, where NB is */
/* the optimal blocksize. */
/* 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 */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(1) H(2) . . . H(k), where k = min(m,n). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a real scalar, and v is a real vector with */
/* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
/* and tau in TAU(i). */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1);
lwkopt = *n * nb;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEQRF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1] = 1.f;
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQRF", " ", m, n, &c_n1, &c_n1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQRF", " ", m, n, &c_n1, &
c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the QR factorization of the current block */
/* A(i:m,i:i+ib-1) */
i__3 = *m - i__ + 1;
sgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *m - i__ + 1;
slarft_("Forward", "Columnwise", &i__3, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H' to A(i:m,i+ib:n) from the left */
i__3 = *m - i__ + 1;
i__4 = *n - i__ - ib + 1;
slarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, &
i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib
+ 1], &ldwork);
}
/* L10: */
}
} else {
i__ = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i__ <= k) {
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
sgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
work[1] = (real) iws;
return 0;
/* End of SGEQRF */
} /* sgeqrf_ */
/* Subroutine */
int sggsvp_(char *jobu, char *jobv, char *jobq, integer *m, integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb, real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu, real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real * tau, real *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1, u_offset, v_dim1, v_offset, i__1, i__2, i__3;
real r__1;
/* Local variables */
integer i__, j;
extern logical lsame_(char *, char *);
logical wantq, wantu, wantv;
extern /* Subroutine */
int sgeqr2_(integer *, integer *, real *, integer *, real *, real *, integer *), sgerq2_(integer *, integer *, real *, integer *, real *, real *, integer *), sorg2r_(integer *, integer *, integer *, real *, integer *, real *, real *, integer * ), sorm2r_(char *, char *, integer *, integer *, integer *, real * , integer *, real *, real *, integer *, real *, integer *), sormr2_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *), xerbla_(char *, integer *), sgeqpf_( integer *, integer *, real *, integer *, integer *, real *, real * , integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), slapmt_( logical *, integer *, integer *, real *, integer *, integer *);
logical forwrd;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--iwork;
--tau;
--work;
/* Function Body */
wantu = lsame_(jobu, "U");
wantv = lsame_(jobv, "V");
wantq = lsame_(jobq, "Q");
forwrd = TRUE_;
*info = 0;
if (! (wantu || lsame_(jobu, "N")))
{
*info = -1;
}
else if (! (wantv || lsame_(jobv, "N")))
{
*info = -2;
}
else if (! (wantq || lsame_(jobq, "N")))
{
*info = -3;
}
else if (*m < 0)
{
*info = -4;
}
else if (*p < 0)
{
*info = -5;
}
else if (*n < 0)
{
*info = -6;
}
else if (*lda < max(1,*m))
{
*info = -8;
}
else if (*ldb < max(1,*p))
{
*info = -10;
}
else if (*ldu < 1 || wantu && *ldu < *m)
{
*info = -16;
}
else if (*ldv < 1 || wantv && *ldv < *p)
{
*info = -18;
}
else if (*ldq < 1 || wantq && *ldq < *n)
{
*info = -20;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SGGSVP", &i__1);
return 0;
}
/* QR with column pivoting of B: B*P = V*( S11 S12 ) */
/* ( 0 0 ) */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
iwork[i__] = 0;
/* L10: */
}
sgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], info);
/* Update A := A*P */
slapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);
/* Determine the effective rank of matrix B. */
*l = 0;
i__1 = min(*p,*n);
for (i__ = 1;
i__ <= i__1;
++i__)
{
if ((r__1 = b[i__ + i__ * b_dim1], f2c_abs(r__1)) > *tolb)
{
++(*l);
}
/* L20: */
}
if (wantv)
{
/* Copy the details of V, and form V. */
slaset_("Full", p, p, &c_b12, &c_b12, &v[v_offset], ldv);
if (*p > 1)
{
i__1 = *p - 1;
slacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2], ldv);
}
i__1 = min(*p,*n);
sorg2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
}
/* Clean up B */
i__1 = *l - 1;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *l;
for (i__ = j + 1;
i__ <= i__2;
++i__)
{
b[i__ + j * b_dim1] = 0.f;
/* L30: */
}
/* L40: */
}
if (*p > *l)
{
i__1 = *p - *l;
slaset_("Full", &i__1, n, &c_b12, &c_b12, &b[*l + 1 + b_dim1], ldb);
}
if (wantq)
{
/* Set Q = I and Update Q := Q*P */
slaset_("Full", n, n, &c_b12, &c_b22, &q[q_offset], ldq);
slapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
}
if (*p >= *l && *n != *l)
{
/* RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z */
sgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
/* Update A := A*Z**T */
sormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[ a_offset], lda, &work[1], info);
if (wantq)
{
/* Update Q := Q*Z**T */
sormr2_("Right", "Transpose", n, n, l, &b[b_offset], ldb, &tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up B */
i__1 = *n - *l;
slaset_("Full", l, &i__1, &c_b12, &c_b12, &b[b_offset], ldb);
i__1 = *n;
for (j = *n - *l + 1;
j <= i__1;
++j)
{
i__2 = *l;
for (i__ = j - *n + *l + 1;
i__ <= i__2;
++i__)
{
b[i__ + j * b_dim1] = 0.f;
/* L50: */
}
/* L60: */
}
}
/* Let N-L L */
/* A = ( A11 A12 ) M, */
/* then the following does the complete QR decomposition of A11: */
/* A11 = U*( 0 T12 )*P1**T */
/* ( 0 0 ) */
i__1 = *n - *l;
for (i__ = 1;
i__ <= i__1;
++i__)
{
iwork[i__] = 0;
/* L70: */
}
i__1 = *n - *l;
sgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], info);
/* Determine the effective rank of A11 */
*k = 0;
/* Computing MIN */
i__2 = *m;
i__3 = *n - *l; // , expr subst
i__1 = min(i__2,i__3);
for (i__ = 1;
i__ <= i__1;
++i__)
{
if ((r__1 = a[i__ + i__ * a_dim1], f2c_abs(r__1)) > *tola)
{
++(*k);
}
/* L80: */
}
/* Update A12 := U**T*A12, where A12 = A( 1:M, N-L+1:N ) */
/* Computing MIN */
i__2 = *m;
i__3 = *n - *l; // , expr subst
i__1 = min(i__2,i__3);
sorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &a[( *n - *l + 1) * a_dim1 + 1], lda, &work[1], info);
if (wantu)
{
/* Copy the details of U, and form U */
slaset_("Full", m, m, &c_b12, &c_b12, &u[u_offset], ldu);
if (*m > 1)
{
i__1 = *m - 1;
i__2 = *n - *l;
slacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2] , ldu);
}
/* Computing MIN */
i__2 = *m;
i__3 = *n - *l; // , expr subst
i__1 = min(i__2,i__3);
sorg2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
}
if (wantq)
{
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
i__1 = *n - *l;
slapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
}
/* Clean up A: set the strictly lower triangular part of */
/* A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */
i__1 = *k - 1;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *k;
for (i__ = j + 1;
i__ <= i__2;
++i__)
{
a[i__ + j * a_dim1] = 0.f;
/* L90: */
}
/* L100: */
}
if (*m > *k)
{
i__1 = *m - *k;
i__2 = *n - *l;
slaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a[*k + 1 + a_dim1], lda);
}
if (*n - *l > *k)
{
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
i__1 = *n - *l;
sgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);
if (wantq)
{
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**T */
i__1 = *n - *l;
sormr2_("Right", "Transpose", n, &i__1, k, &a[a_offset], lda, & tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up A */
i__1 = *n - *l - *k;
slaset_("Full", k, &i__1, &c_b12, &c_b12, &a[a_offset], lda);
i__1 = *n - *l;
for (j = *n - *l - *k + 1;
j <= i__1;
++j)
{
i__2 = *k;
for (i__ = j - *n + *l + *k + 1;
i__ <= i__2;
++i__)
{
a[i__ + j * a_dim1] = 0.f;
/* L110: */
}
/* L120: */
}
}
if (*m > *k)
{
/* QR factorization of A( K+1:M,N-L+1:N ) */
i__1 = *m - *k;
sgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], & work[1], info);
if (wantu)
{
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
i__1 = *m - *k;
/* Computing MIN */
i__3 = *m - *k;
i__2 = min(i__3,*l);
sorm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 + 1], ldu, &work[1], info);
}
/* Clean up */
i__1 = *n;
for (j = *n - *l + 1;
j <= i__1;
++j)
{
i__2 = *m;
for (i__ = j - *n + *k + *l + 1;
i__ <= i__2;
++i__)
{
a[i__ + j * a_dim1] = 0.f;
/* L130: */
}
/* L140: */
}
}
return 0;
/* End of SGGSVP */
}
