doublereal ctzt01_(integer *m, integer *n, complex *a, complex *af, integer *
lda, complex *tau, complex *work, integer *lwork)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2, i__3, i__4;
real ret_val;
/* Local variables */
integer i__, j;
real norma;
real rwork[1];
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTZT01 returns */
/* || A - R*Q || / ( M * eps * ||A|| ) */
/* for an upper trapezoidal A that was factored with CTZRQF. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrices A and AF. */
/* N (input) INTEGER */
/* The number of columns of the matrices A and AF. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The original upper trapezoidal M by N matrix A. */
/* AF (input) COMPLEX array, dimension (LDA,N) */
/* The output of CTZRQF for input matrix A. */
/* The lower triangle is not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays A and AF. */
/* TAU (input) COMPLEX array, dimension (M) */
/* Details of the Householder transformations as returned by */
/* CTZRQF. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The length of the array WORK. LWORK >= m*n + m. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
af_dim1 = *lda;
af_offset = 1 + af_dim1;
af -= af_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
ret_val = 0.f;
if (*lwork < *m * *n + *m) {
this_xerbla_("CTZT01", &c__8);
return ret_val;
}
/* Quick return if possible */
if (*m <= 0 || *n <= 0) {
return ret_val;
}
norma = clange_("One-norm", m, n, &a[a_offset], lda, rwork);
/* Copy upper triangle R */
claset_("Full", m, n, &c_b6, &c_b6, &work[1], m);
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = (j - 1) * *m + i__;
i__4 = i__ + j * af_dim1;
work[i__3].r = af[i__4].r, work[i__3].i = af[i__4].i;
/* L10: */
}
/* L20: */
}
/* R = R * P(1) * ... *P(m) */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n - *m + 1;
clatzm_("Right", &i__, &i__2, &af[i__ + (*m + 1) * af_dim1], lda, &
tau[i__], &work[(i__ - 1) * *m + 1], &work[*m * *m + 1], m, &
work[*m * *n + 1]);
/* L30: */
}
/* R = R - A */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
caxpy_(m, &c_b15, &a[i__ * a_dim1 + 1], &c__1, &work[(i__ - 1) * *m +
1], &c__1);
/* L40: */
}
ret_val = clange_("One-norm", m, n, &work[1], m, rwork);
ret_val /= slamch_("Epsilon") * (real) max(*m,*n);
if (norma != 0.f) {
ret_val /= norma;
}
return ret_val;
/* End of CTZT01 */
} /* ctzt01_ */
/* Subroutine */ int cgelsx_(integer *m, integer *n, integer *nrhs, complex *
a, integer *lda, complex *b, integer *ldb, integer *jpvt, real *rcond,
integer *rank, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
complex q__1;
/* Builtin functions */
double c_abs(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
static integer i__, j, k;
static complex c1, c2, s1, s2, t1, t2;
static integer mn;
static real anrm, bnrm, smin, smax;
static integer iascl, ibscl, ismin, ismax;
extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *,
integer *, integer *, complex *, complex *, integer *, complex *,
integer *, ftnlen, ftnlen, ftnlen, ftnlen), claic1_(integer *,
integer *, complex *, real *, complex *, complex *, real *,
complex *, complex *), cunm2r_(char *, char *, integer *, integer
*, integer *, complex *, integer *, complex *, complex *, integer
*, complex *, integer *, ftnlen, ftnlen), slabad_(real *, real *);
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *, ftnlen);
extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *,
ftnlen), cgeqpf_(integer *, integer *, complex *, integer *,
integer *, complex *, complex *, real *, integer *);
extern doublereal slamch_(char *, ftnlen);
extern /* Subroutine */ int claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *, ftnlen), xerbla_(char *,
integer *, ftnlen);
static real bignum;
extern /* Subroutine */ int clatzm_(char *, integer *, integer *, complex
*, integer *, complex *, complex *, complex *, integer *, complex
*, ftnlen);
static real sminpr;
extern /* Subroutine */ int ctzrqf_(integer *, integer *, complex *,
integer *, complex *, integer *);
static real smaxpr, smlnum;
/* -- LAPACK driver 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 .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* This routine is deprecated and has been replaced by routine CGELSY. */
/* CGELSX computes the minimum-norm solution to a complex linear least */
/* squares problem: */
/* minimize || A * X - B || */
/* using a complete orthogonal factorization of A. A is an M-by-N */
/* matrix which may be rank-deficient. */
/* Several right hand side vectors b and solution vectors x can be */
/* handled in a single call; they are stored as the columns of the */
/* M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
/* matrix X. */
/* The routine first computes a QR factorization with column pivoting: */
/* A * P = Q * [ R11 R12 ] */
/* [ 0 R22 ] */
/* with R11 defined as the largest leading submatrix whose estimated */
/* condition number is less than 1/RCOND. The order of R11, RANK, */
/* is the effective rank of A. */
/* Then, R22 is considered to be negligible, and R12 is annihilated */
/* by unitary transformations from the right, arriving at the */
/* complete orthogonal factorization: */
/* A * P = Q * [ T11 0 ] * Z */
/* [ 0 0 ] */
/* The minimum-norm solution is then */
/* X = P * Z' [ inv(T11)*Q1'*B ] */
/* [ 0 ] */
/* where Q1 consists of the first RANK columns of Q. */
/* 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. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of */
/* columns of matrices B and X. NRHS >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, A has been overwritten by details of its */
/* complete orthogonal factorization. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the M-by-NRHS right hand side matrix B. */
/* On exit, the N-by-NRHS solution matrix X. */
/* If m >= n and RANK = n, the residual sum-of-squares for */
/* the solution in the i-th column is given by the sum of */
/* squares of elements N+1:M in that column. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,M,N). */
/* JPVT (input/output) INTEGER array, dimension (N) */
/* On entry, if JPVT(i) .ne. 0, the i-th column of A is an */
/* initial column, otherwise it is a free column. Before */
/* the QR factorization of A, all initial columns are */
/* permuted to the leading positions; only the remaining */
/* free columns are moved as a result of column pivoting */
/* during the factorization. */
/* On exit, if JPVT(i) = k, then the i-th column of A*P */
/* was the k-th column of A. */
/* RCOND (input) REAL */
/* RCOND is used to determine the effective rank of A, which */
/* is defined as the order of the largest leading triangular */
/* submatrix R11 in the QR factorization with pivoting of A, */
/* whose estimated condition number < 1/RCOND. */
/* RANK (output) INTEGER */
/* The effective rank of A, i.e., the order of the submatrix */
/* R11. This is the same as the order of the submatrix T11 */
/* in the complete orthogonal factorization of A. */
/* WORK (workspace) COMPLEX array, dimension */
/* (min(M,N) + max( N, 2*min(M,N)+NRHS )), */
/* RWORK (workspace) REAL array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. 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;
--jpvt;
--work;
--rwork;
/* Function Body */
mn = min(*m,*n);
ismin = mn + 1;
ismax = (mn << 1) + 1;
/* Test the input arguments. */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m);
if (*ldb < max(i__1,*n)) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGELSX", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
/* Computing MIN */
i__1 = min(*m,*n);
if (min(i__1,*nrhs) == 0) {
*rank = 0;
return 0;
}
/* Get machine parameters */
smlnum = slamch_("S", (ftnlen)1) / slamch_("P", (ftnlen)1);
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Scale A, B if max elements outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", m, n, &a[a_offset], lda, &rwork[1], (ftnlen)1);
iascl = 0;
if (anrm > 0.f && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info, (ftnlen)1);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM */
clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info, (ftnlen)1);
iascl = 2;
} else if (anrm == 0.f) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb, (ftnlen)1);
*rank = 0;
goto L100;
}
bnrm = clange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1], (ftnlen)1);
ibscl = 0;
if (bnrm > 0.f && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
clascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM */
clascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
ibscl = 2;
}
/* Compute QR factorization with column pivoting of A: */
/* A * P = Q * R */
cgeqpf_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &
rwork[1], info);
/* complex workspace MN+N. Real workspace 2*N. Details of Householder */
/* rotations stored in WORK(1:MN). */
/* Determine RANK using incremental condition estimation */
i__1 = ismin;
work[i__1].r = 1.f, work[i__1].i = 0.f;
i__1 = ismax;
work[i__1].r = 1.f, work[i__1].i = 0.f;
smax = c_abs(&a[a_dim1 + 1]);
smin = smax;
if (c_abs(&a[a_dim1 + 1]) == 0.f) {
*rank = 0;
i__1 = max(*m,*n);
claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb, (ftnlen)1);
goto L100;
} else {
*rank = 1;
}
L10:
if (*rank < mn) {
i__ = *rank + 1;
claic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
i__ + i__ * a_dim1], &sminpr, &s1, &c1);
claic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
if (smaxpr * *rcond <= sminpr) {
i__1 = *rank;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ismin + i__ - 1;
i__3 = ismin + i__ - 1;
q__1.r = s1.r * work[i__3].r - s1.i * work[i__3].i, q__1.i =
s1.r * work[i__3].i + s1.i * work[i__3].r;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
i__2 = ismax + i__ - 1;
i__3 = ismax + i__ - 1;
q__1.r = s2.r * work[i__3].r - s2.i * work[i__3].i, q__1.i =
s2.r * work[i__3].i + s2.i * work[i__3].r;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L20: */
}
i__1 = ismin + *rank;
work[i__1].r = c1.r, work[i__1].i = c1.i;
i__1 = ismax + *rank;
work[i__1].r = c2.r, work[i__1].i = c2.i;
smin = sminpr;
smax = smaxpr;
++(*rank);
goto L10;
}
}
/* Logically partition R = [ R11 R12 ] */
/* [ 0 R22 ] */
/* where R11 = R(1:RANK,1:RANK) */
/* [R11,R12] = [ T11, 0 ] * Y */
if (*rank < *n) {
ctzrqf_(rank, n, &a[a_offset], lda, &work[mn + 1], info);
}
/* Details of Householder rotations stored in WORK(MN+1:2*MN) */
/* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
cunm2r_("Left", "Conjugate transpose", m, nrhs, &mn, &a[a_offset], lda, &
work[1], &b[b_offset], ldb, &work[(mn << 1) + 1], info, (ftnlen)4,
(ftnlen)19);
/* workspace NRHS */
/* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
ctrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b2, &a[
a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)
12, (ftnlen)8);
i__1 = *n;
for (i__ = *rank + 1; i__ <= i__1; ++i__) {
i__2 = *nrhs;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L30: */
}
/* L40: */
}
/* B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS) */
if (*rank < *n) {
i__1 = *rank;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n - *rank + 1;
r_cnjg(&q__1, &work[mn + i__]);
clatzm_("Left", &i__2, nrhs, &a[i__ + (*rank + 1) * a_dim1], lda,
&q__1, &b[i__ + b_dim1], &b[*rank + 1 + b_dim1], ldb, &
work[(mn << 1) + 1], (ftnlen)4);
/* L50: */
}
}
/* workspace NRHS */
/* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = (mn << 1) + i__;
work[i__3].r = 1.f, work[i__3].i = 0.f;
/* L60: */
}
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = (mn << 1) + i__;
if (work[i__3].r == 1.f && work[i__3].i == 0.f) {
if (jpvt[i__] != i__) {
k = i__;
i__3 = k + j * b_dim1;
t1.r = b[i__3].r, t1.i = b[i__3].i;
i__3 = jpvt[k] + j * b_dim1;
t2.r = b[i__3].r, t2.i = b[i__3].i;
L70:
i__3 = jpvt[k] + j * b_dim1;
b[i__3].r = t1.r, b[i__3].i = t1.i;
i__3 = (mn << 1) + k;
work[i__3].r = 0.f, work[i__3].i = 0.f;
t1.r = t2.r, t1.i = t2.i;
k = jpvt[k];
i__3 = jpvt[k] + j * b_dim1;
t2.r = b[i__3].r, t2.i = b[i__3].i;
if (jpvt[k] != i__) {
goto L70;
}
i__3 = i__ + j * b_dim1;
b[i__3].r = t1.r, b[i__3].i = t1.i;
i__3 = (mn << 1) + k;
work[i__3].r = 0.f, work[i__3].i = 0.f;
}
}
/* L80: */
}
/* L90: */
}
/* Undo scaling */
if (iascl == 1) {
clascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
clascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset],
lda, info, (ftnlen)1);
} else if (iascl == 2) {
clascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
clascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset],
lda, info, (ftnlen)1);
}
if (ibscl == 1) {
clascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
} else if (ibscl == 2) {
clascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
}
L100:
return 0;
/* End of CGELSX */
} /* cgelsx_ */