/*< SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) >*/
/* Subroutine */ int dorgqr_(integer *m, integer *n, integer *k, doublereal *
a, integer *lda, doublereal *tau, doublereal *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, j, l, ib, nb, ki=0, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int dorg2r_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *),
dlarfb_(char *, char *, char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen,
ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< INTEGER INFO, K, LDA, LWORK, M, N >*/
/* .. */
/* .. Array Arguments .. */
/*< DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* DORGQR generates an M-by-N real matrix Q with orthonormal columns, */
/* which is defined as the first N columns of a product of K elementary */
/* reflectors of order M */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by DGEQRF. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix Q. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix Q. M >= N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* matrix Q. N >= K >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the i-th column must contain the vector which */
/* defines the elementary reflector H(i), for i = 1,2,...,k, as */
/* returned by DGEQRF in the first k columns of its array */
/* argument A. */
/* On exit, the M-by-N matrix Q. */
/* LDA (input) INTEGER */
/* The first dimension of the array A. LDA >= max(1,M). */
/* TAU (input) DOUBLE PRECISION array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by DGEQRF. */
/* WORK (workspace/output) DOUBLE PRECISION 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. */
/* 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 has an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ZERO >*/
/*< PARAMETER ( ZERO = 0.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY >*/
/*< >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DLARFB, DLARFT, DORG2R, XERBLA >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ILAENV >*/
/*< EXTERNAL ILAENV >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) >*/
nb = ilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
/*< LWKOPT = MAX( 1, N )*NB >*/
lwkopt = max(1,*n) * nb;
/*< WORK( 1 ) = LWKOPT >*/
work[1] = (doublereal) lwkopt;
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( M.LT.0 ) THEN >*/
if (*m < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( N.LT.0 .OR. N.GT.M ) THEN >*/
} else if (*n < 0 || *n > *m) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( K.LT.0 .OR. K.GT.N ) THEN >*/
} else if (*k < 0 || *k > *n) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -5 >*/
*info = -5;
/*< ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < max(1,*n) && ! lquery) {
/*< INFO = -8 >*/
*info = -8;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'DORGQR', -INFO ) >*/
i__1 = -(*info);
xerbla_("DORGQR", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Quick return if possible */
/*< IF( N.LE.0 ) THEN >*/
if (*n <= 0) {
/*< WORK( 1 ) = 1 >*/
work[1] = 1.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< NBMIN = 2 >*/
nbmin = 2;
/*< NX = 0 >*/
nx = 0;
/*< IWS = N >*/
iws = *n;
/*< IF( NB.GT.1 .AND. NB.LT.K ) THEN >*/
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code. */
/*< NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) ) >*/
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "DORGQR", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
/*< IF( NX.LT.K ) THEN >*/
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
/*< LDWORK = N >*/
ldwork = *n;
/*< IWS = LDWORK*NB >*/
iws = ldwork * nb;
/*< IF( LWORK.LT.IWS ) THEN >*/
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
/*< NB = LWORK / LDWORK >*/
nb = *lwork / ldwork;
/*< NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) ) >*/
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "DORGQR", " ", m, n, k, &c_n1,
(ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN >*/
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the last block. */
/* The first kk columns are handled by the block method. */
/*< KI = ( ( K-NX-1 ) / NB )*NB >*/
ki = (*k - nx - 1) / nb * nb;
/*< KK = MIN( K, KI+NB ) >*/
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = min(i__1,i__2);
/* Set A(1:kk,kk+1:n) to zero. */
/*< DO 20 J = KK + 1, N >*/
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
/*< DO 10 I = 1, KK >*/
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
a[i__ + j * a_dim1] = 0.;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< 20 CONTINUE >*/
/* L20: */
}
/*< ELSE >*/
} else {
/*< KK = 0 >*/
kk = 0;
/*< END IF >*/
}
/* Use unblocked code for the last or only block. */
/*< >*/
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
tau[kk + 1], &work[1], &iinfo);
}
/*< IF( KK.GT.0 ) THEN >*/
if (kk > 0) {
/* Use blocked code */
/*< DO 50 I = KI + 1, 1, -NB >*/
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/*< IB = MIN( NB, K-I+1 ) >*/
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = min(i__2,i__3);
/*< IF( I+IB.LE.N ) THEN >*/
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
/*< >*/
i__2 = *m - i__ + 1;
dlarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7,
(ftnlen)10);
/* Apply H to A(i:m,i+ib:n) from the left */
/*< >*/
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
dlarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &
work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)
7, (ftnlen)10);
/*< END IF >*/
}
/* Apply H to rows i:m of current block */
/*< >*/
i__2 = *m - i__ + 1;
dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[1], &iinfo);
/* Set rows 1:i-1 of current block to zero */
/*< DO 40 J = I, I + IB - 1 >*/
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
/*< DO 30 L = 1, I - 1 >*/
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
/*< A( L, J ) = ZERO >*/
a[l + j * a_dim1] = 0.;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< 50 CONTINUE >*/
/* L50: */
}
/*< END IF >*/
}
/*< WORK( 1 ) = IWS >*/
work[1] = (doublereal) iws;
/*< RETURN >*/
return 0;
/* End of DORGQR */
/*< END >*/
} /* dorgqr_ */
/* Subroutine */ int dggsvp_(char *jobu, char *jobv, char *jobq, integer *m,
integer *p, integer *n, doublereal *a, integer *lda, doublereal *b,
integer *ldb, doublereal *tola, doublereal *tolb, integer *k, integer
*l, doublereal *u, integer *ldu, doublereal *v, integer *ldv,
doublereal *q, integer *ldq, integer *iwork, doublereal *tau,
doublereal *work, integer *info)
{
/* -- 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
Purpose
=======
DGGSVP 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
DGGSVD.
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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION
TOLB (input) DOUBLE PRECISION
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)*MAZHEPS,
TOLB = MAX(P,N)*norm(B)*MAZHEPS.
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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N)
WORK (workspace) DOUBLE PRECISION 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 DGEQPF 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.
=====================================================================
Test the input parameters
Parameter adjustments */
/* Table of constant values */
static doublereal c_b12 = 0.;
static doublereal c_b22 = 1.;
/* 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;
doublereal d__1;
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
static logical wantq, wantu, wantv;
extern /* Subroutine */ int dgeqr2_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *), dgerq2_(
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *), dorg2r_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *),
dorm2r_(char *, char *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *), dormr2_(char *, char *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *), dgeqpf_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, integer *),
dlacpy_(char *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *), dlaset_(char *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *), dlapmt_(logical *,
integer *, integer *, doublereal *, integer *, integer *);
static logical forwrd;
#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 u_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1]
#define v_ref(a_1,a_2) v[(a_2)*v_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
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_("DGGSVP", &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: */
}
dgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], info);
/* Update A := A*P */
dlapmt_(&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 ((d__1 = b_ref(i__, i__), abs(d__1)) > *tolb) {
++(*l);
}
/* L20: */
}
if (wantv) {
/* Copy the details of V, and form V. */
dlaset_("Full", p, p, &c_b12, &c_b12, &v[v_offset], ldv);
if (*p > 1) {
i__1 = *p - 1;
dlacpy_("Lower", &i__1, n, &b_ref(2, 1), ldb, &v_ref(2, 1), ldv);
}
i__1 = min(*p,*n);
dorg2r_(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_ref(i__, j) = 0.;
/* L30: */
}
/* L40: */
}
if (*p > *l) {
i__1 = *p - *l;
dlaset_("Full", &i__1, n, &c_b12, &c_b12, &b_ref(*l + 1, 1), ldb);
}
if (wantq) {
/* Set Q = I and Update Q := Q*P */
dlaset_("Full", n, n, &c_b12, &c_b22, &q[q_offset], ldq);
dlapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
}
if (*p >= *l && *n != *l) {
/* RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z */
dgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
/* Update A := A*Z' */
dormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[
a_offset], lda, &work[1], info);
if (wantq) {
/* Update Q := Q*Z' */
dormr2_("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;
dlaset_("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_ref(i__, j) = 0.;
/* 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;
dgeqpf_(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 ((d__1 = a_ref(i__, i__), abs(d__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);
dorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &
a_ref(1, *n - *l + 1), lda, &work[1], info);
if (wantu) {
/* Copy the details of U, and form U */
dlaset_("Full", m, m, &c_b12, &c_b12, &u[u_offset], ldu);
if (*m > 1) {
i__1 = *m - 1;
i__2 = *n - *l;
dlacpy_("Lower", &i__1, &i__2, &a_ref(2, 1), lda, &u_ref(2, 1),
ldu);
}
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
dorg2r_(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;
dlapmt_(&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_ref(i__, j) = 0.;
/* L90: */
}
/* L100: */
}
if (*m > *k) {
i__1 = *m - *k;
i__2 = *n - *l;
dlaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a_ref(*k + 1, 1), lda);
}
if (*n - *l > *k) {
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
i__1 = *n - *l;
dgerq2_(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;
dormr2_("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;
dlaset_("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_ref(i__, j) = 0.;
/* L110: */
}
/* L120: */
}
}
if (*m > *k) {
/* QR factorization of A( K+1:M,N-L+1:N ) */
i__1 = *m - *k;
dgeqr2_(&i__1, l, &a_ref(*k + 1, *n - *l + 1), 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);
dorm2r_("Right", "No transpose", m, &i__1, &i__2, &a_ref(*k + 1, *
n - *l + 1), lda, &tau[1], &u_ref(1, *k + 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_ref(i__, j) = 0.;
/* L130: */
}
/* L140: */
}
}
return 0;
/* End of DGGSVP */
} /* dggsvp_ */
/* Subroutine */ extern "C" int dorgqr_(integer *m, integer *n, integer *k, doublereal *
a, integer *lda, doublereal *tau, doublereal *work, integer *lwork,
integer *info)
{
/* -- LAPACK 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
=======
DORGQR generates an M-by-N real matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by DGEQRF in the first k columns of its array
argument A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
WORK (workspace/output) DOUBLE PRECISION 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.
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 has an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
/* 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;
/* Local variables */
static integer i__, j, l, nbmin, iinfo;
extern /* Subroutine */ int dorg2r_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *);
static integer ib, nb, ki, kk;
extern /* Subroutine */ int dlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
static integer nx;
extern /* Subroutine */ int dlarft_(char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ldwork, lwkopt;
static logical lquery;
static integer iws;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(1,*n) * nb;
work[1] = (doublereal) lwkopt;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DORGQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1] = 1.;
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, "DORGQR", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
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, "DORGQR", " ", m, n, k, &c_n1,
(ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the last block.
The first kk columns are handled by the block method. */
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = min(i__1,i__2);
/* Set A(1:kk,kk+1:n) to zero. */
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = 0.;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
dorg2r_(&i__1, &i__2, &i__3, &a_ref(kk + 1, kk + 1), lda, &tau[kk + 1]
, &work[1], &iinfo);
}
if (kk > 0) {
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = min(i__2,i__3);
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__2 = *m - i__ + 1;
dlarft_("Forward", "Columnwise", &i__2, &ib, &a_ref(i__, i__),
lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i:m,i+ib:n) from the left */
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
dlarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a_ref(i__, i__), lda, &work[1], &
ldwork, &a_ref(i__, i__ + ib), lda, &work[ib + 1], &
ldwork);
}
/* Apply H to rows i:m of current block */
i__2 = *m - i__ + 1;
dorg2r_(&i__2, &ib, &ib, &a_ref(i__, i__), lda, &tau[i__], &work[
1], &iinfo);
/* Set rows 1:i-1 of current block to zero */
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
a_ref(l, j) = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1] = (doublereal) iws;
return 0;
/* End of DORGQR */
} /* dorgqr_ */
/* Subroutine */ int dopgtr_(char *uplo, integer *n, doublereal *ap,
doublereal *tau, doublereal *q, integer *ldq, doublereal *work,
integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, j, ij;
extern logical lsame_(char *, char *);
integer iinfo;
logical upper;
extern /* Subroutine */ int dorg2l_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *),
dorg2r_(integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DOPGTR generates a real orthogonal matrix Q which is defined as the */
/* product of n-1 elementary reflectors H(i) of order n, as returned by */
/* DSPTRD using packed storage: */
/* if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), */
/* if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangular packed storage used in previous */
/* call to DSPTRD; */
/* = 'L': Lower triangular packed storage used in previous */
/* call to DSPTRD. */
/* N (input) INTEGER */
/* The order of the matrix Q. N >= 0. */
/* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* The vectors which define the elementary reflectors, as */
/* returned by DSPTRD. */
/* TAU (input) DOUBLE PRECISION array, dimension (N-1) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by DSPTRD. */
/* Q (output) DOUBLE PRECISION array, dimension (LDQ,N) */
/* The N-by-N orthogonal matrix Q. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,N). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N-1) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
--ap;
--tau;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--work;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldq < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DOPGTR", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (upper) {
/* Q was determined by a call to DSPTRD with UPLO = 'U' */
/* Unpack the vectors which define the elementary reflectors and */
/* set the last row and column of Q equal to those of the unit */
/* matrix */
ij = 2;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
q[i__ + j * q_dim1] = ap[ij];
++ij;
/* L10: */
}
ij += 2;
q[*n + j * q_dim1] = 0.;
/* L20: */
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
q[i__ + *n * q_dim1] = 0.;
/* L30: */
}
q[*n + *n * q_dim1] = 1.;
/* Generate Q(1:n-1,1:n-1) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
dorg2l_(&i__1, &i__2, &i__3, &q[q_offset], ldq, &tau[1], &work[1], &
iinfo);
} else {
/* Q was determined by a call to DSPTRD with UPLO = 'L'. */
/* Unpack the vectors which define the elementary reflectors and */
/* set the first row and column of Q equal to those of the unit */
/* matrix */
q[q_dim1 + 1] = 1.;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
q[i__ + q_dim1] = 0.;
/* L40: */
}
ij = 3;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
q[j * q_dim1 + 1] = 0.;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
q[i__ + j * q_dim1] = ap[ij];
++ij;
/* L50: */
}
ij += 2;
/* L60: */
}
if (*n > 1) {
/* Generate Q(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
dorg2r_(&i__1, &i__2, &i__3, &q[(q_dim1 << 1) + 2], ldq, &tau[1],
&work[1], &iinfo);
}
}
return 0;
/* End of DOPGTR */
} /* dopgtr_ */
/* Subroutine */ int derrqr_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublereal a[4] /* was [2][2] */, b[2];
integer i__, j;
doublereal w[2], x[2], af[4] /* was [2][2] */;
integer info;
extern /* Subroutine */ int dgeqr2_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *), dorg2r_(
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), dorm2r_(char *, char *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *), alaesm_(char *, logical *, integer *),
dgeqrf_(integer *, integer *, doublereal *, integer *, doublereal
*, doublereal *, integer *, integer *), chkxer_(char *, integer *,
integer *, logical *, logical *), dgeqrs_(integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *),
dorgqr_(integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *), dormqr_(char *,
char *, integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
integer *);
/* 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 */
/* ======= */
/* DERRQR tests the error exits for the DOUBLE PRECISION 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. / (doublereal) (i__ + j);
af[i__ + (j << 1) - 3] = 1. / (doublereal) (i__ + j);
/* L10: */
}
b[j - 1] = 0.;
w[j - 1] = 0.;
x[j - 1] = 0.;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QR factorization */
/* DGEQRF */
s_copy(srnamc_1.srnamt, "DGEQRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgeqrf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("DGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgeqrf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("DGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgeqrf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("DGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgeqrf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("DGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGEQR2 */
s_copy(srnamc_1.srnamt, "DGEQR2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgeqr2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("DGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgeqr2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("DGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgeqr2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("DGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGEQRS */
s_copy(srnamc_1.srnamt, "DGEQRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgeqrs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgeqrs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgeqrs_(&c__1, &c__2, &c__0, a, &c__2, x, b, &c__2, w, &c__1, &info);
chkxer_("DGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgeqrs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgeqrs_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("DGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dgeqrs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("DGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dgeqrs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DORGQR */
s_copy(srnamc_1.srnamt, "DORGQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dorgqr_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("DORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorgqr_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("DORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorgqr_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("DORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgqr_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("DORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgqr_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("DORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorgqr_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("DORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dorgqr_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("DORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DORG2R */
s_copy(srnamc_1.srnamt, "DORG2R", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dorg2r_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("DORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorg2r_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("DORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorg2r_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("DORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorg2r_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("DORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorg2r_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("DORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorg2r_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("DORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DORMQR */
s_copy(srnamc_1.srnamt, "DORMQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dormqr_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dormqr_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dormqr_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dormqr_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormqr_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormqr_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormqr_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dormqr_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dormqr_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dormqr_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("DORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DORM2R */
s_copy(srnamc_1.srnamt, "DORM2R", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dorm2r_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorm2r_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorm2r_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dorm2r_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorm2r_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorm2r_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorm2r_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dorm2r_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("DORM2R", &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 DERRQR */
} /* derrqr_ */
