/* 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 sgelsx_(integer *m, integer *n, integer *nrhs, real *a, integer *lda, real *b, integer *ldb, integer *jpvt, real *rcond, integer *rank, real *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; real r__1; /* Local variables */ static integer i__, j, k; static real c1, c2, s1, s2, t1, t2; static integer mn; static real anrm, bnrm, smin, smax; static integer iascl, ibscl, ismin, ismax; extern /* Subroutine */ int strsm_(char *, char *, char *, char *, integer *, integer *, real *, real *, integer *, real *, integer * , ftnlen, ftnlen, ftnlen, ftnlen), slaic1_(integer *, integer *, real *, real *, real *, real *, real *, real *, real *), sorm2r_( char *, char *, integer *, integer *, integer *, real *, integer * , real *, real *, integer *, real *, integer *, ftnlen, ftnlen), slabad_(real *, real *); extern doublereal slamch_(char *, ftnlen), slange_(char *, integer *, integer *, real *, integer *, real *, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); static real bignum; extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *, ftnlen), sgeqpf_(integer *, integer *, real *, integer *, integer *, real *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *, ftnlen); static real sminpr, smaxpr, smlnum; extern /* Subroutine */ int slatzm_(char *, integer *, integer *, real *, integer *, real *, real *, real *, integer *, real *, ftnlen), stzrqf_(integer *, integer *, real *, integer *, real *, integer * ); /* -- LAPACK driver routine (version 3.0) -- */ /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */ /* Courant Institute, Argonne National Lab, and Rice University */ /* March 31, 1993 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* This routine is deprecated and has been replaced by routine SGELSY. */ /* SGELSX computes the minimum-norm solution to a real 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 orthogonal 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) REAL 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) REAL 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) REAL array, dimension */ /* (max( min(M,N)+3*N, 2*min(M,N)+NRHS )), */ /* 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 .. */ /* 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; /* 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_("SGELSX", &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 = slange_("M", m, n, &a[a_offset], lda, &work[1], (ftnlen)1); iascl = 0; if (anrm > 0.f && anrm < smlnum) { /* Scale matrix norm up to SMLNUM */ slascl_("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 */ slascl_("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); slaset_("F", &i__1, nrhs, &c_b13, &c_b13, &b[b_offset], ldb, (ftnlen) 1); *rank = 0; goto L100; } bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1], (ftnlen)1); ibscl = 0; if (bnrm > 0.f && bnrm < smlnum) { /* Scale matrix norm up to SMLNUM */ slascl_("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 */ slascl_("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 */ sgeqpf_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], info); /* workspace 3*N. Details of Householder rotations stored */ /* in WORK(1:MN). */ /* Determine RANK using incremental condition estimation */ work[ismin] = 1.f; work[ismax] = 1.f; smax = (r__1 = a[a_dim1 + 1], dabs(r__1)); smin = smax; if ((r__1 = a[a_dim1 + 1], dabs(r__1)) == 0.f) { *rank = 0; i__1 = max(*m,*n); slaset_("F", &i__1, nrhs, &c_b13, &c_b13, &b[b_offset], ldb, (ftnlen) 1); goto L100; } else { *rank = 1; } L10: if (*rank < mn) { i__ = *rank + 1; slaic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[ i__ + i__ * a_dim1], &sminpr, &s1, &c1); slaic1_(&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__) { work[ismin + i__ - 1] = s1 * work[ismin + i__ - 1]; work[ismax + i__ - 1] = s2 * work[ismax + i__ - 1]; /* L20: */ } work[ismin + *rank] = c1; work[ismax + *rank] = c2; 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) { stzrqf_(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) */ sorm2r_("Left", "Transpose", m, nrhs, &mn, &a[a_offset], lda, &work[1], & b[b_offset], ldb, &work[(mn << 1) + 1], info, (ftnlen)4, (ftnlen) 9); /* workspace NRHS */ /* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */ strsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b36, & 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) { b[i__ + j * b_dim1] = 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; slatzm_("Left", &i__2, nrhs, &a[i__ + (*rank + 1) * a_dim1], lda, &work[mn + i__], &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__) { work[(mn << 1) + i__] = 1.f; /* L60: */ } i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (work[(mn << 1) + i__] == 1.f) { if (jpvt[i__] != i__) { k = i__; t1 = b[k + j * b_dim1]; t2 = b[jpvt[k] + j * b_dim1]; L70: b[jpvt[k] + j * b_dim1] = t1; work[(mn << 1) + k] = 0.f; t1 = t2; k = jpvt[k]; t2 = b[jpvt[k] + j * b_dim1]; if (jpvt[k] != i__) { goto L70; } b[i__ + j * b_dim1] = t1; work[(mn << 1) + k] = 0.f; } } /* L80: */ } /* L90: */ } /* Undo scaling */ if (iascl == 1) { slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); slascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset], lda, info, (ftnlen)1); } else if (iascl == 2) { slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); slascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset], lda, info, (ftnlen)1); } if (ibscl == 1) { slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); } else if (ibscl == 2) { slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); } L100: return 0; /* End of SGELSX */ } /* sgelsx_ */