#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static integer c__1 = 1; static doublereal c_b22 = 0.; static logical c_true = TRUE_; static logical c_false = FALSE_; /* Subroutine */ int dlatms_(integer *m, integer *n, char *dist, integer * iseed, char *sym, doublereal *d__, integer *mode, doublereal *cond, doublereal *dmax__, integer *kl, integer *ku, char *pack, doublereal * a, integer *lda, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublereal d__1, d__2, d__3; logical L__1; /* Builtin functions */ double cos(doublereal), sin(doublereal); /* Local variables */ doublereal c__; integer i__, j, k; doublereal s; integer ic, jc, nc, il, ir, jr, mr, ir1, ir2, jch, llb, jkl, jku, uub, ilda, icol; doublereal temp; integer irow, isym; doublereal alpha, angle; integer ipack; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); integer ioffg; extern logical lsame_(char *, char *); integer iinfo, idist, mnmin; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer iskew; doublereal extra, dummy; extern /* Subroutine */ int dlatm1_(integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *, integer *), dlagge_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *); integer iendch, ipackg, minlda; extern doublereal dlarnd_(integer *, integer *); extern /* Subroutine */ int dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), xerbla_(char *, integer *), dlagsy_( integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *), dlarot_(logical *, logical *, logical *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *); logical iltemp, givens; integer ioffst, irsign; logical ilextr, topdwn; integer isympk; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DLATMS generates random matrices with specified singular values */ /* (or symmetric/hermitian with specified eigenvalues) */ /* for testing LAPACK programs. */ /* DLATMS operates by applying the following sequence of */ /* operations: */ /* Set the diagonal to D, where D may be input or */ /* computed according to MODE, COND, DMAX, and SYM */ /* as described below. */ /* Generate a matrix with the appropriate band structure, by one */ /* of two methods: */ /* Method A: */ /* Generate a dense M x N matrix by multiplying D on the left */ /* and the right by random unitary matrices, then: */ /* Reduce the bandwidth according to KL and KU, using */ /* Householder transformations. */ /* Method B: */ /* Convert the bandwidth-0 (i.e., diagonal) matrix to a */ /* bandwidth-1 matrix using Givens rotations, "chasing" */ /* out-of-band elements back, much as in QR; then */ /* convert the bandwidth-1 to a bandwidth-2 matrix, etc. */ /* Note that for reasonably small bandwidths (relative to */ /* M and N) this requires less storage, as a dense matrix */ /* is not generated. Also, for symmetric matrices, only */ /* one triangle is generated. */ /* Method A is chosen if the bandwidth is a large fraction of the */ /* order of the matrix, and LDA is at least M (so a dense */ /* matrix can be stored.) Method B is chosen if the bandwidth */ /* is small (< 1/2 N for symmetric, < .3 N+M for */ /* non-symmetric), or LDA is less than M and not less than the */ /* bandwidth. */ /* Pack the matrix if desired. Options specified by PACK are: */ /* no packing */ /* zero out upper half (if symmetric) */ /* zero out lower half (if symmetric) */ /* store the upper half columnwise (if symmetric or upper */ /* triangular) */ /* store the lower half columnwise (if symmetric or lower */ /* triangular) */ /* store the lower triangle in banded format (if symmetric */ /* or lower triangular) */ /* store the upper triangle in banded format (if symmetric */ /* or upper triangular) */ /* store the entire matrix in banded format */ /* If Method B is chosen, and band format is specified, then the */ /* matrix will be generated in the band format, so no repacking */ /* will be necessary. */ /* Arguments */ /* ========= */ /* M - INTEGER */ /* The number of rows of A. Not modified. */ /* N - INTEGER */ /* The number of columns of A. Not modified. */ /* DIST - CHARACTER*1 */ /* On entry, DIST specifies the type of distribution to be used */ /* to generate the random eigen-/singular values. */ /* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) */ /* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) */ /* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) */ /* Not modified. */ /* ISEED - INTEGER array, dimension ( 4 ) */ /* On entry ISEED specifies the seed of the random number */ /* generator. They should lie between 0 and 4095 inclusive, */ /* and ISEED(4) should be odd. The random number generator */ /* uses a linear congruential sequence limited to small */ /* integers, and so should produce machine independent */ /* random numbers. The values of ISEED are changed on */ /* exit, and can be used in the next call to DLATMS */ /* to continue the same random number sequence. */ /* Changed on exit. */ /* SYM - CHARACTER*1 */ /* If SYM='S' or 'H', the generated matrix is symmetric, with */ /* eigenvalues specified by D, COND, MODE, and DMAX; they */ /* may be positive, negative, or zero. */ /* If SYM='P', the generated matrix is symmetric, with */ /* eigenvalues (= singular values) specified by D, COND, */ /* MODE, and DMAX; they will not be negative. */ /* If SYM='N', the generated matrix is nonsymmetric, with */ /* singular values specified by D, COND, MODE, and DMAX; */ /* they will not be negative. */ /* Not modified. */ /* D - DOUBLE PRECISION array, dimension ( MIN( M , N ) ) */ /* This array is used to specify the singular values or */ /* eigenvalues of A (see SYM, above.) If MODE=0, then D is */ /* assumed to contain the singular/eigenvalues, otherwise */ /* they will be computed according to MODE, COND, and DMAX, */ /* and placed in D. */ /* Modified if MODE is nonzero. */ /* MODE - INTEGER */ /* On entry this describes how the singular/eigenvalues are to */ /* be specified: */ /* MODE = 0 means use D as input */ /* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND */ /* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND */ /* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) */ /* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) */ /* MODE = 5 sets D to random numbers in the range */ /* ( 1/COND , 1 ) such that their logarithms */ /* are uniformly distributed. */ /* MODE = 6 set D to random numbers from same distribution */ /* as the rest of the matrix. */ /* MODE < 0 has the same meaning as ABS(MODE), except that */ /* the order of the elements of D is reversed. */ /* Thus if MODE is positive, D has entries ranging from */ /* 1 to 1/COND, if negative, from 1/COND to 1, */ /* If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then */ /* the elements of D will also be multiplied by a random */ /* sign (i.e., +1 or -1.) */ /* Not modified. */ /* COND - DOUBLE PRECISION */ /* On entry, this is used as described under MODE above. */ /* If used, it must be >= 1. Not modified. */ /* DMAX - DOUBLE PRECISION */ /* If MODE is neither -6, 0 nor 6, the contents of D, as */ /* computed according to MODE and COND, will be scaled by */ /* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or */ /* singular value (which is to say the norm) will be abs(DMAX). */ /* Note that DMAX need not be positive: if DMAX is negative */ /* (or zero), D will be scaled by a negative number (or zero). */ /* Not modified. */ /* KL - INTEGER */ /* This specifies the lower bandwidth of the matrix. For */ /* example, KL=0 implies upper triangular, KL=1 implies upper */ /* Hessenberg, and KL being at least M-1 means that the matrix */ /* has full lower bandwidth. KL must equal KU if the matrix */ /* is symmetric. */ /* Not modified. */ /* KU - INTEGER */ /* This specifies the upper bandwidth of the matrix. For */ /* example, KU=0 implies lower triangular, KU=1 implies lower */ /* Hessenberg, and KU being at least N-1 means that the matrix */ /* has full upper bandwidth. KL must equal KU if the matrix */ /* is symmetric. */ /* Not modified. */ /* PACK - CHARACTER*1 */ /* This specifies packing of matrix as follows: */ /* 'N' => no packing */ /* 'U' => zero out all subdiagonal entries (if symmetric) */ /* 'L' => zero out all superdiagonal entries (if symmetric) */ /* 'C' => store the upper triangle columnwise */ /* (only if the matrix is symmetric or upper triangular) */ /* 'R' => store the lower triangle columnwise */ /* (only if the matrix is symmetric or lower triangular) */ /* 'B' => store the lower triangle in band storage scheme */ /* (only if matrix symmetric or lower triangular) */ /* 'Q' => store the upper triangle in band storage scheme */ /* (only if matrix symmetric or upper triangular) */ /* 'Z' => store the entire matrix in band storage scheme */ /* (pivoting can be provided for by using this */ /* option to store A in the trailing rows of */ /* the allocated storage) */ /* Using these options, the various LAPACK packed and banded */ /* storage schemes can be obtained: */ /* GB - use 'Z' */ /* PB, SB or TB - use 'B' or 'Q' */ /* PP, SP or TP - use 'C' or 'R' */ /* If two calls to DLATMS differ only in the PACK parameter, */ /* they will generate mathematically equivalent matrices. */ /* Not modified. */ /* A - DOUBLE PRECISION array, dimension ( LDA, N ) */ /* On exit A is the desired test matrix. A is first generated */ /* in full (unpacked) form, and then packed, if so specified */ /* by PACK. Thus, the first M elements of the first N */ /* columns will always be modified. If PACK specifies a */ /* packed or banded storage scheme, all LDA elements of the */ /* first N columns will be modified; the elements of the */ /* array which do not correspond to elements of the generated */ /* matrix are set to zero. */ /* Modified. */ /* LDA - INTEGER */ /* LDA specifies the first dimension of A as declared in the */ /* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then */ /* LDA must be at least M. If PACK='B' or 'Q', then LDA must */ /* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). */ /* If PACK='Z', LDA must be large enough to hold the packed */ /* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. */ /* Not modified. */ /* WORK - DOUBLE PRECISION array, dimension ( 3*MAX( N , M ) ) */ /* Workspace. */ /* Modified. */ /* INFO - INTEGER */ /* Error code. On exit, INFO will be set to one of the */ /* following values: */ /* 0 => normal return */ /* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' */ /* -2 => N negative */ /* -3 => DIST illegal string */ /* -5 => SYM illegal string */ /* -7 => MODE not in range -6 to 6 */ /* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 */ /* -10 => KL negative */ /* -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL */ /* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; */ /* or PACK='C' or 'Q' and SYM='N' and KL is not zero; */ /* or PACK='R' or 'B' and SYM='N' and KU is not zero; */ /* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not */ /* N. */ /* -14 => LDA is less than M, or PACK='Z' and LDA is less than */ /* MIN(KU,N-1) + MIN(KL,M-1) + 1. */ /* 1 => Error return from DLATM1 */ /* 2 => Cannot scale to DMAX (max. sing. value is 0) */ /* 3 => Error return from DLAGGE or SLAGSY */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* 1) Decode and Test the input parameters. */ /* Initialize flags & seed. */ /* Parameter adjustments */ --iseed; --d__; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; /* Function Body */ *info = 0; /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } /* Decode DIST */ if (lsame_(dist, "U")) { idist = 1; } else if (lsame_(dist, "S")) { idist = 2; } else if (lsame_(dist, "N")) { idist = 3; } else { idist = -1; } /* Decode SYM */ if (lsame_(sym, "N")) { isym = 1; irsign = 0; } else if (lsame_(sym, "P")) { isym = 2; irsign = 0; } else if (lsame_(sym, "S")) { isym = 2; irsign = 1; } else if (lsame_(sym, "H")) { isym = 2; irsign = 1; } else { isym = -1; } /* Decode PACK */ isympk = 0; if (lsame_(pack, "N")) { ipack = 0; } else if (lsame_(pack, "U")) { ipack = 1; isympk = 1; } else if (lsame_(pack, "L")) { ipack = 2; isympk = 1; } else if (lsame_(pack, "C")) { ipack = 3; isympk = 2; } else if (lsame_(pack, "R")) { ipack = 4; isympk = 3; } else if (lsame_(pack, "B")) { ipack = 5; isympk = 3; } else if (lsame_(pack, "Q")) { ipack = 6; isympk = 2; } else if (lsame_(pack, "Z")) { ipack = 7; } else { ipack = -1; } /* Set certain internal parameters */ mnmin = min(*m,*n); /* Computing MIN */ i__1 = *kl, i__2 = *m - 1; llb = min(i__1,i__2); /* Computing MIN */ i__1 = *ku, i__2 = *n - 1; uub = min(i__1,i__2); /* Computing MIN */ i__1 = *m, i__2 = *n + llb; mr = min(i__1,i__2); /* Computing MIN */ i__1 = *n, i__2 = *m + uub; nc = min(i__1,i__2); if (ipack == 5 || ipack == 6) { minlda = uub + 1; } else if (ipack == 7) { minlda = llb + uub + 1; } else { minlda = *m; } /* Use Givens rotation method if bandwidth small enough, */ /* or if LDA is too small to store the matrix unpacked. */ givens = FALSE_; if (isym == 1) { /* Computing MAX */ i__1 = 1, i__2 = mr + nc; if ((doublereal) (llb + uub) < (doublereal) max(i__1,i__2) * .3) { givens = TRUE_; } } else { if (llb << 1 < *m) { givens = TRUE_; } } if (*lda < *m && *lda >= minlda) { givens = TRUE_; } /* Set INFO if an error */ if (*m < 0) { *info = -1; } else if (*m != *n && isym != 1) { *info = -1; } else if (*n < 0) { *info = -2; } else if (idist == -1) { *info = -3; } else if (isym == -1) { *info = -5; } else if (abs(*mode) > 6) { *info = -7; } else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.) { *info = -8; } else if (*kl < 0) { *info = -10; } else if (*ku < 0 || isym != 1 && *kl != *ku) { *info = -11; } else if (ipack == -1 || isympk == 1 && isym == 1 || isympk == 2 && isym == 1 && *kl > 0 || isympk == 3 && isym == 1 && *ku > 0 || isympk != 0 && *m != *n) { *info = -12; } else if (*lda < max(1,minlda)) { *info = -14; } if (*info != 0) { i__1 = -(*info); xerbla_("DLATMS", &i__1); return 0; } /* Initialize random number generator */ for (i__ = 1; i__ <= 4; ++i__) { iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096; /* L10: */ } if (iseed[4] % 2 != 1) { ++iseed[4]; } /* 2) Set up D if indicated. */ /* Compute D according to COND and MODE */ dlatm1_(mode, cond, &irsign, &idist, &iseed[1], &d__[1], &mnmin, &iinfo); if (iinfo != 0) { *info = 1; return 0; } /* Choose Top-Down if D is (apparently) increasing, */ /* Bottom-Up if D is (apparently) decreasing. */ if (abs(d__[1]) <= (d__1 = d__[mnmin], abs(d__1))) { topdwn = TRUE_; } else { topdwn = FALSE_; } if (*mode != 0 && abs(*mode) != 6) { /* Scale by DMAX */ temp = abs(d__[1]); i__1 = mnmin; for (i__ = 2; i__ <= i__1; ++i__) { /* Computing MAX */ d__2 = temp, d__3 = (d__1 = d__[i__], abs(d__1)); temp = max(d__2,d__3); /* L20: */ } if (temp > 0.) { alpha = *dmax__ / temp; } else { *info = 2; return 0; } dscal_(&mnmin, &alpha, &d__[1], &c__1); } /* 3) Generate Banded Matrix using Givens rotations. */ /* Also the special case of UUB=LLB=0 */ /* Compute Addressing constants to cover all */ /* storage formats. Whether GE, SY, GB, or SB, */ /* upper or lower triangle or both, */ /* the (i,j)-th element is in */ /* A( i - ISKEW*j + IOFFST, j ) */ if (ipack > 4) { ilda = *lda - 1; iskew = 1; if (ipack > 5) { ioffst = uub + 1; } else { ioffst = 1; } } else { ilda = *lda; iskew = 0; ioffst = 0; } /* IPACKG is the format that the matrix is generated in. If this is */ /* different from IPACK, then the matrix must be repacked at the */ /* end. It also signals how to compute the norm, for scaling. */ ipackg = 0; dlaset_("Full", lda, n, &c_b22, &c_b22, &a[a_offset], lda); /* Diagonal Matrix -- We are done, unless it */ /* is to be stored SP/PP/TP (PACK='R' or 'C') */ if (llb == 0 && uub == 0) { i__1 = ilda + 1; dcopy_(&mnmin, &d__[1], &c__1, &a[1 - iskew + ioffst + a_dim1], &i__1) ; if (ipack <= 2 || ipack >= 5) { ipackg = ipack; } } else if (givens) { /* Check whether to use Givens rotations, */ /* Householder transformations, or nothing. */ if (isym == 1) { /* Non-symmetric -- A = U D V */ if (ipack > 4) { ipackg = ipack; } else { ipackg = 0; } i__1 = ilda + 1; dcopy_(&mnmin, &d__[1], &c__1, &a[1 - iskew + ioffst + a_dim1], & i__1); if (topdwn) { jkl = 0; i__1 = uub; for (jku = 1; jku <= i__1; ++jku) { /* Transform from bandwidth JKL, JKU-1 to JKL, JKU */ /* Last row actually rotated is M */ /* Last column actually rotated is MIN( M+JKU, N ) */ /* Computing MIN */ i__3 = *m + jku; i__2 = min(i__3,*n) + jkl - 1; for (jr = 1; jr <= i__2; ++jr) { extra = 0.; angle = dlarnd_(&c__1, &iseed[1]) * 6.2831853071795864769252867663; c__ = cos(angle); s = sin(angle); /* Computing MAX */ i__3 = 1, i__4 = jr - jkl; icol = max(i__3,i__4); if (jr < *m) { /* Computing MIN */ i__3 = *n, i__4 = jr + jku; il = min(i__3,i__4) + 1 - icol; L__1 = jr > jkl; dlarot_(&c_true, &L__1, &c_false, &il, &c__, &s, & a[jr - iskew * icol + ioffst + icol * a_dim1], &ilda, &extra, &dummy); } /* Chase "EXTRA" back up */ ir = jr; ic = icol; i__3 = -jkl - jku; for (jch = jr - jkl; i__3 < 0 ? jch >= 1 : jch <= 1; jch += i__3) { if (ir < *m) { dlartg_(&a[ir + 1 - iskew * (ic + 1) + ioffst + (ic + 1) * a_dim1], &extra, &c__, & s, &dummy); } /* Computing MAX */ i__4 = 1, i__5 = jch - jku; irow = max(i__4,i__5); il = ir + 2 - irow; temp = 0.; iltemp = jch > jku; d__1 = -s; dlarot_(&c_false, &iltemp, &c_true, &il, &c__, & d__1, &a[irow - iskew * ic + ioffst + ic * a_dim1], &ilda, &temp, &extra); if (iltemp) { dlartg_(&a[irow + 1 - iskew * (ic + 1) + ioffst + (ic + 1) * a_dim1], &temp, & c__, &s, &dummy); /* Computing MAX */ i__4 = 1, i__5 = jch - jku - jkl; icol = max(i__4,i__5); il = ic + 2 - icol; extra = 0.; L__1 = jch > jku + jkl; d__1 = -s; dlarot_(&c_true, &L__1, &c_true, &il, &c__, & d__1, &a[irow - iskew * icol + ioffst + icol * a_dim1], &ilda, &extra, & temp); ic = icol; ir = irow; } /* L30: */ } /* L40: */ } /* L50: */ } jku = uub; i__1 = llb; for (jkl = 1; jkl <= i__1; ++jkl) { /* Transform from bandwidth JKL-1, JKU to JKL, JKU */ /* Computing MIN */ i__3 = *n + jkl; i__2 = min(i__3,*m) + jku - 1; for (jc = 1; jc <= i__2; ++jc) { extra = 0.; angle = dlarnd_(&c__1, &iseed[1]) * 6.2831853071795864769252867663; c__ = cos(angle); s = sin(angle); /* Computing MAX */ i__3 = 1, i__4 = jc - jku; irow = max(i__3,i__4); if (jc < *n) { /* Computing MIN */ i__3 = *m, i__4 = jc + jkl; il = min(i__3,i__4) + 1 - irow; L__1 = jc > jku; dlarot_(&c_false, &L__1, &c_false, &il, &c__, &s, &a[irow - iskew * jc + ioffst + jc * a_dim1], &ilda, &extra, &dummy); } /* Chase "EXTRA" back up */ ic = jc; ir = irow; i__3 = -jkl - jku; for (jch = jc - jku; i__3 < 0 ? jch >= 1 : jch <= 1; jch += i__3) { if (ic < *n) { dlartg_(&a[ir + 1 - iskew * (ic + 1) + ioffst + (ic + 1) * a_dim1], &extra, &c__, & s, &dummy); } /* Computing MAX */ i__4 = 1, i__5 = jch - jkl; icol = max(i__4,i__5); il = ic + 2 - icol; temp = 0.; iltemp = jch > jkl; d__1 = -s; dlarot_(&c_true, &iltemp, &c_true, &il, &c__, & d__1, &a[ir - iskew * icol + ioffst + icol * a_dim1], &ilda, &temp, &extra); if (iltemp) { dlartg_(&a[ir + 1 - iskew * (icol + 1) + ioffst + (icol + 1) * a_dim1], &temp, &c__, &s, &dummy); /* Computing MAX */ i__4 = 1, i__5 = jch - jkl - jku; irow = max(i__4,i__5); il = ir + 2 - irow; extra = 0.; L__1 = jch > jkl + jku; d__1 = -s; dlarot_(&c_false, &L__1, &c_true, &il, &c__, & d__1, &a[irow - iskew * icol + ioffst + icol * a_dim1], &ilda, &extra, & temp); ic = icol; ir = irow; } /* L60: */ } /* L70: */ } /* L80: */ } } else { /* Bottom-Up -- Start at the bottom right. */ jkl = 0; i__1 = uub; for (jku = 1; jku <= i__1; ++jku) { /* Transform from bandwidth JKL, JKU-1 to JKL, JKU */ /* First row actually rotated is M */ /* First column actually rotated is MIN( M+JKU, N ) */ /* Computing MIN */ i__2 = *m, i__3 = *n + jkl; iendch = min(i__2,i__3) - 1; /* Computing MIN */ i__2 = *m + jku; i__3 = 1 - jkl; for (jc = min(i__2,*n) - 1; jc >= i__3; --jc) { extra = 0.; angle = dlarnd_(&c__1, &iseed[1]) * 6.2831853071795864769252867663; c__ = cos(angle); s = sin(angle); /* Computing MAX */ i__2 = 1, i__4 = jc - jku + 1; irow = max(i__2,i__4); if (jc > 0) { /* Computing MIN */ i__2 = *m, i__4 = jc + jkl + 1; il = min(i__2,i__4) + 1 - irow; L__1 = jc + jkl < *m; dlarot_(&c_false, &c_false, &L__1, &il, &c__, &s, &a[irow - iskew * jc + ioffst + jc * a_dim1], &ilda, &dummy, &extra); } /* Chase "EXTRA" back down */ ic = jc; i__2 = iendch; i__4 = jkl + jku; for (jch = jc + jkl; i__4 < 0 ? jch >= i__2 : jch <= i__2; jch += i__4) { ilextr = ic > 0; if (ilextr) { dlartg_(&a[jch - iskew * ic + ioffst + ic * a_dim1], &extra, &c__, &s, &dummy); } ic = max(1,ic); /* Computing MIN */ i__5 = *n - 1, i__6 = jch + jku; icol = min(i__5,i__6); iltemp = jch + jku < *n; temp = 0.; i__5 = icol + 2 - ic; dlarot_(&c_true, &ilextr, &iltemp, &i__5, &c__, & s, &a[jch - iskew * ic + ioffst + ic * a_dim1], &ilda, &extra, &temp); if (iltemp) { dlartg_(&a[jch - iskew * icol + ioffst + icol * a_dim1], &temp, &c__, &s, &dummy); /* Computing MIN */ i__5 = iendch, i__6 = jch + jkl + jku; il = min(i__5,i__6) + 2 - jch; extra = 0.; L__1 = jch + jkl + jku <= iendch; dlarot_(&c_false, &c_true, &L__1, &il, &c__, & s, &a[jch - iskew * icol + ioffst + icol * a_dim1], &ilda, &temp, &extra); ic = icol; } /* L90: */ } /* L100: */ } /* L110: */ } jku = uub; i__1 = llb; for (jkl = 1; jkl <= i__1; ++jkl) { /* Transform from bandwidth JKL-1, JKU to JKL, JKU */ /* First row actually rotated is MIN( N+JKL, M ) */ /* First column actually rotated is N */ /* Computing MIN */ i__3 = *n, i__4 = *m + jku; iendch = min(i__3,i__4) - 1; /* Computing MIN */ i__3 = *n + jkl; i__4 = 1 - jku; for (jr = min(i__3,*m) - 1; jr >= i__4; --jr) { extra = 0.; angle = dlarnd_(&c__1, &iseed[1]) * 6.2831853071795864769252867663; c__ = cos(angle); s = sin(angle); /* Computing MAX */ i__3 = 1, i__2 = jr - jkl + 1; icol = max(i__3,i__2); if (jr > 0) { /* Computing MIN */ i__3 = *n, i__2 = jr + jku + 1; il = min(i__3,i__2) + 1 - icol; L__1 = jr + jku < *n; dlarot_(&c_true, &c_false, &L__1, &il, &c__, &s, & a[jr - iskew * icol + ioffst + icol * a_dim1], &ilda, &dummy, &extra); } /* Chase "EXTRA" back down */ ir = jr; i__3 = iendch; i__2 = jkl + jku; for (jch = jr + jku; i__2 < 0 ? jch >= i__3 : jch <= i__3; jch += i__2) { ilextr = ir > 0; if (ilextr) { dlartg_(&a[ir - iskew * jch + ioffst + jch * a_dim1], &extra, &c__, &s, &dummy); } ir = max(1,ir); /* Computing MIN */ i__5 = *m - 1, i__6 = jch + jkl; irow = min(i__5,i__6); iltemp = jch + jkl < *m; temp = 0.; i__5 = irow + 2 - ir; dlarot_(&c_false, &ilextr, &iltemp, &i__5, &c__, & s, &a[ir - iskew * jch + ioffst + jch * a_dim1], &ilda, &extra, &temp); if (iltemp) { dlartg_(&a[irow - iskew * jch + ioffst + jch * a_dim1], &temp, &c__, &s, &dummy); /* Computing MIN */ i__5 = iendch, i__6 = jch + jkl + jku; il = min(i__5,i__6) + 2 - jch; extra = 0.; L__1 = jch + jkl + jku <= iendch; dlarot_(&c_true, &c_true, &L__1, &il, &c__, & s, &a[irow - iskew * jch + ioffst + jch * a_dim1], &ilda, &temp, &extra); ir = irow; } /* L120: */ } /* L130: */ } /* L140: */ } } } else { /* Symmetric -- A = U D U' */ ipackg = ipack; ioffg = ioffst; if (topdwn) { /* Top-Down -- Generate Upper triangle only */ if (ipack >= 5) { ipackg = 6; ioffg = uub + 1; } else { ipackg = 1; } i__1 = ilda + 1; dcopy_(&mnmin, &d__[1], &c__1, &a[1 - iskew + ioffg + a_dim1], &i__1); i__1 = uub; for (k = 1; k <= i__1; ++k) { i__4 = *n - 1; for (jc = 1; jc <= i__4; ++jc) { /* Computing MAX */ i__2 = 1, i__3 = jc - k; irow = max(i__2,i__3); /* Computing MIN */ i__2 = jc + 1, i__3 = k + 2; il = min(i__2,i__3); extra = 0.; temp = a[jc - iskew * (jc + 1) + ioffg + (jc + 1) * a_dim1]; angle = dlarnd_(&c__1, &iseed[1]) * 6.2831853071795864769252867663; c__ = cos(angle); s = sin(angle); L__1 = jc > k; dlarot_(&c_false, &L__1, &c_true, &il, &c__, &s, &a[ irow - iskew * jc + ioffg + jc * a_dim1], & ilda, &extra, &temp); /* Computing MIN */ i__3 = k, i__5 = *n - jc; i__2 = min(i__3,i__5) + 1; dlarot_(&c_true, &c_true, &c_false, &i__2, &c__, &s, & a[(1 - iskew) * jc + ioffg + jc * a_dim1], & ilda, &temp, &dummy); /* Chase EXTRA back up the matrix */ icol = jc; i__2 = -k; for (jch = jc - k; i__2 < 0 ? jch >= 1 : jch <= 1; jch += i__2) { dlartg_(&a[jch + 1 - iskew * (icol + 1) + ioffg + (icol + 1) * a_dim1], &extra, &c__, &s, & dummy); temp = a[jch - iskew * (jch + 1) + ioffg + (jch + 1) * a_dim1]; i__3 = k + 2; d__1 = -s; dlarot_(&c_true, &c_true, &c_true, &i__3, &c__, & d__1, &a[(1 - iskew) * jch + ioffg + jch * a_dim1], &ilda, &temp, &extra); /* Computing MAX */ i__3 = 1, i__5 = jch - k; irow = max(i__3,i__5); /* Computing MIN */ i__3 = jch + 1, i__5 = k + 2; il = min(i__3,i__5); extra = 0.; L__1 = jch > k; d__1 = -s; dlarot_(&c_false, &L__1, &c_true, &il, &c__, & d__1, &a[irow - iskew * jch + ioffg + jch * a_dim1], &ilda, &extra, &temp); icol = jch; /* L150: */ } /* L160: */ } /* L170: */ } /* If we need lower triangle, copy from upper. Note that */ /* the order of copying is chosen to work for 'q' -> 'b' */ if (ipack != ipackg && ipack != 3) { i__1 = *n; for (jc = 1; jc <= i__1; ++jc) { irow = ioffst - iskew * jc; /* Computing MIN */ i__2 = *n, i__3 = jc + uub; i__4 = min(i__2,i__3); for (jr = jc; jr <= i__4; ++jr) { a[jr + irow + jc * a_dim1] = a[jc - iskew * jr + ioffg + jr * a_dim1]; /* L180: */ } /* L190: */ } if (ipack == 5) { i__1 = *n; for (jc = *n - uub + 1; jc <= i__1; ++jc) { i__4 = uub + 1; for (jr = *n + 2 - jc; jr <= i__4; ++jr) { a[jr + jc * a_dim1] = 0.; /* L200: */ } /* L210: */ } } if (ipackg == 6) { ipackg = ipack; } else { ipackg = 0; } } } else { /* Bottom-Up -- Generate Lower triangle only */ if (ipack >= 5) { ipackg = 5; if (ipack == 6) { ioffg = 1; } } else { ipackg = 2; } i__1 = ilda + 1; dcopy_(&mnmin, &d__[1], &c__1, &a[1 - iskew + ioffg + a_dim1], &i__1); i__1 = uub; for (k = 1; k <= i__1; ++k) { for (jc = *n - 1; jc >= 1; --jc) { /* Computing MIN */ i__4 = *n + 1 - jc, i__2 = k + 2; il = min(i__4,i__2); extra = 0.; temp = a[(1 - iskew) * jc + 1 + ioffg + jc * a_dim1]; angle = dlarnd_(&c__1, &iseed[1]) * 6.2831853071795864769252867663; c__ = cos(angle); s = -sin(angle); L__1 = *n - jc > k; dlarot_(&c_false, &c_true, &L__1, &il, &c__, &s, &a[( 1 - iskew) * jc + ioffg + jc * a_dim1], &ilda, &temp, &extra); /* Computing MAX */ i__4 = 1, i__2 = jc - k + 1; icol = max(i__4,i__2); i__4 = jc + 2 - icol; dlarot_(&c_true, &c_false, &c_true, &i__4, &c__, &s, & a[jc - iskew * icol + ioffg + icol * a_dim1], &ilda, &dummy, &temp); /* Chase EXTRA back down the matrix */ icol = jc; i__4 = *n - 1; i__2 = k; for (jch = jc + k; i__2 < 0 ? jch >= i__4 : jch <= i__4; jch += i__2) { dlartg_(&a[jch - iskew * icol + ioffg + icol * a_dim1], &extra, &c__, &s, &dummy); temp = a[(1 - iskew) * jch + 1 + ioffg + jch * a_dim1]; i__3 = k + 2; dlarot_(&c_true, &c_true, &c_true, &i__3, &c__, & s, &a[jch - iskew * icol + ioffg + icol * a_dim1], &ilda, &extra, &temp); /* Computing MIN */ i__3 = *n + 1 - jch, i__5 = k + 2; il = min(i__3,i__5); extra = 0.; L__1 = *n - jch > k; dlarot_(&c_false, &c_true, &L__1, &il, &c__, &s, & a[(1 - iskew) * jch + ioffg + jch * a_dim1], &ilda, &temp, &extra); icol = jch; /* L220: */ } /* L230: */ } /* L240: */ } /* If we need upper triangle, copy from lower. Note that */ /* the order of copying is chosen to work for 'b' -> 'q' */ if (ipack != ipackg && ipack != 4) { for (jc = *n; jc >= 1; --jc) { irow = ioffst - iskew * jc; /* Computing MAX */ i__2 = 1, i__4 = jc - uub; i__1 = max(i__2,i__4); for (jr = jc; jr >= i__1; --jr) { a[jr + irow + jc * a_dim1] = a[jc - iskew * jr + ioffg + jr * a_dim1]; /* L250: */ } /* L260: */ } if (ipack == 6) { i__1 = uub; for (jc = 1; jc <= i__1; ++jc) { i__2 = uub + 1 - jc; for (jr = 1; jr <= i__2; ++jr) { a[jr + jc * a_dim1] = 0.; /* L270: */ } /* L280: */ } } if (ipackg == 5) { ipackg = ipack; } else { ipackg = 0; } } } } } else { /* 4) Generate Banded Matrix by first */ /* Rotating by random Unitary matrices, */ /* then reducing the bandwidth using Householder */ /* transformations. */ /* Note: we should get here only if LDA .ge. N */ if (isym == 1) { /* Non-symmetric -- A = U D V */ dlagge_(&mr, &nc, &llb, &uub, &d__[1], &a[a_offset], lda, &iseed[ 1], &work[1], &iinfo); } else { /* Symmetric -- A = U D U' */ dlagsy_(m, &llb, &d__[1], &a[a_offset], lda, &iseed[1], &work[1], &iinfo); } if (iinfo != 0) { *info = 3; return 0; } } /* 5) Pack the matrix */ if (ipack != ipackg) { if (ipack == 1) { /* 'U' -- Upper triangular, not packed */ i__1 = *m; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = j + 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = 0.; /* L290: */ } /* L300: */ } } else if (ipack == 2) { /* 'L' -- Lower triangular, not packed */ i__1 = *m; for (j = 2; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = 0.; /* L310: */ } /* L320: */ } } else if (ipack == 3) { /* 'C' -- Upper triangle packed Columnwise. */ icol = 1; irow = 0; i__1 = *m; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { ++irow; if (irow > *lda) { irow = 1; ++icol; } a[irow + icol * a_dim1] = a[i__ + j * a_dim1]; /* L330: */ } /* L340: */ } } else if (ipack == 4) { /* 'R' -- Lower triangle packed Columnwise. */ icol = 1; irow = 0; i__1 = *m; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = j; i__ <= i__2; ++i__) { ++irow; if (irow > *lda) { irow = 1; ++icol; } a[irow + icol * a_dim1] = a[i__ + j * a_dim1]; /* L350: */ } /* L360: */ } } else if (ipack >= 5) { /* 'B' -- The lower triangle is packed as a band matrix. */ /* 'Q' -- The upper triangle is packed as a band matrix. */ /* 'Z' -- The whole matrix is packed as a band matrix. */ if (ipack == 5) { uub = 0; } if (ipack == 6) { llb = 0; } i__1 = uub; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ i__2 = j + llb; for (i__ = min(i__2,*m); i__ >= 1; --i__) { a[i__ - j + uub + 1 + j * a_dim1] = a[i__ + j * a_dim1]; /* L370: */ } /* L380: */ } i__1 = *n; for (j = uub + 2; j <= i__1; ++j) { /* Computing MIN */ i__4 = j + llb; i__2 = min(i__4,*m); for (i__ = j - uub; i__ <= i__2; ++i__) { a[i__ - j + uub + 1 + j * a_dim1] = a[i__ + j * a_dim1]; /* L390: */ } /* L400: */ } } /* If packed, zero out extraneous elements. */ /* Symmetric/Triangular Packed -- */ /* zero out everything after A(IROW,ICOL) */ if (ipack == 3 || ipack == 4) { i__1 = *m; for (jc = icol; jc <= i__1; ++jc) { i__2 = *lda; for (jr = irow + 1; jr <= i__2; ++jr) { a[jr + jc * a_dim1] = 0.; /* L410: */ } irow = 0; /* L420: */ } } else if (ipack >= 5) { /* Packed Band -- */ /* 1st row is now in A( UUB+2-j, j), zero above it */ /* m-th row is now in A( M+UUB-j,j), zero below it */ /* last non-zero diagonal is now in A( UUB+LLB+1,j ), */ /* zero below it, too. */ ir1 = uub + llb + 2; ir2 = uub + *m + 2; i__1 = *n; for (jc = 1; jc <= i__1; ++jc) { i__2 = uub + 1 - jc; for (jr = 1; jr <= i__2; ++jr) { a[jr + jc * a_dim1] = 0.; /* L430: */ } /* Computing MAX */ /* Computing MIN */ i__3 = ir1, i__5 = ir2 - jc; i__2 = 1, i__4 = min(i__3,i__5); i__6 = *lda; for (jr = max(i__2,i__4); jr <= i__6; ++jr) { a[jr + jc * a_dim1] = 0.; /* L440: */ } /* L450: */ } } } return 0; /* End of DLATMS */ } /* dlatms_ */