/* Subroutine */ int dlatmr_(integer *m, integer *n, char *dist, integer * iseed, char *sym, doublereal *d__, integer *mode, doublereal *cond, doublereal *dmax__, char *rsign, char *grade, doublereal *dl, integer *model, doublereal *condl, doublereal *dr, integer *moder, doublereal *condr, char *pivtng, integer *ipivot, integer *kl, integer *ku, doublereal *sparse, doublereal *anorm, char *pack, doublereal *a, integer *lda, integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1, d__2, d__3; /* Local variables */ static integer isub, jsub; static doublereal temp; static integer isym, i__, j, k; static doublereal alpha; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); static integer ipack; extern logical lsame_(char *, char *); static doublereal tempa[1]; static integer iisub, idist, jjsub, mnmin; static logical dzero; static integer mnsub; static doublereal onorm; static integer mxsub, npvts; extern /* Subroutine */ int dlatm1_(integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *, integer *); extern doublereal dlatm2_(integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *) , dlatm3_(integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *), dlangb_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); static integer igrade; extern doublereal dlansb_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); static logical fulbnd; extern /* Subroutine */ int xerbla_(char *, integer *); static logical badpvt; extern doublereal dlansp_(char *, char *, integer *, doublereal *, doublereal *), dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *); static integer irsign, ipvtng, kll, kuu; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= DLATMR generates random matrices of various types for testing LAPACK programs. DLATMR operates by applying the following sequence of operations: Generate a matrix A with random entries of distribution DIST which is symmetric if SYM='S', and nonsymmetric if SYM='N'. Set the diagonal to D, where D may be input or computed according to MODE, COND, DMAX and RSIGN as described below. Grade the matrix, if desired, from the left and/or right as specified by GRADE. The inputs DL, MODEL, CONDL, DR, MODER and CONDR also determine the grading as described below. Permute, if desired, the rows and/or columns as specified by PIVTNG and IPIVOT. Set random entries to zero, if desired, to get a random sparse matrix as specified by SPARSE. Make A a band matrix, if desired, by zeroing out the matrix outside a band of lower bandwidth KL and upper bandwidth KU. Scale A, if desired, to have maximum entry ANORM. 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 square upper triangular) store the lower half columnwise (if symmetric or square lower triangular) same as upper half rowwise if symmetric store the lower triangle in banded format (if symmetric) store the upper triangle in banded format (if symmetric) store the entire matrix in banded format Note: If two calls to DLATMR differ only in the PACK parameter, they will generate mathematically equivalent matrices. If two calls to DLATMR both have full bandwidth (KL = M-1 and KU = N-1), and differ only in the PIVTNG and PACK parameters, then the matrices generated will differ only in the order of the rows and/or columns, and otherwise contain the same data. This consistency cannot be and is not maintained with less than full bandwidth. Arguments ========= M - INTEGER Number of rows of A. Not modified. N - INTEGER Number of columns of A. Not modified. DIST - CHARACTER*1 On entry, DIST specifies the type of distribution to be used to generate a random matrix . '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 DLATMR to continue the same random number sequence. Changed on exit. SYM - CHARACTER*1 If SYM='S' or 'H', generated matrix is symmetric. If SYM='N', generated matrix is nonsymmetric. Not modified. D - DOUBLE PRECISION array, dimension (min(M,N)) On entry this array specifies the diagonal entries of the diagonal of A. D may either be specified on entry, or set according to MODE and COND as described below. May be changed on exit if MODE is nonzero. MODE - INTEGER On entry describes how D is to be used: 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, Not modified. COND - DOUBLE PRECISION On entry, used as described under MODE above. If used, it must be >= 1. Not modified. DMAX - DOUBLE PRECISION If MODE neither -6, 0 nor 6, the diagonal is scaled by DMAX / max(abs(D(i))), so that maximum absolute entry of diagonal is abs(DMAX). If DMAX is negative (or zero), diagonal will be scaled by a negative number (or zero). RSIGN - CHARACTER*1 If MODE neither -6, 0 nor 6, specifies sign of diagonal as follows: 'T' => diagonal entries are multiplied by 1 or -1 with probability .5 'F' => diagonal unchanged Not modified. GRADE - CHARACTER*1 Specifies grading of matrix as follows: 'N' => no grading 'L' => matrix premultiplied by diag( DL ) (only if matrix nonsymmetric) 'R' => matrix postmultiplied by diag( DR ) (only if matrix nonsymmetric) 'B' => matrix premultiplied by diag( DL ) and postmultiplied by diag( DR ) (only if matrix nonsymmetric) 'S' or 'H' => matrix premultiplied by diag( DL ) and postmultiplied by diag( DL ) ('S' for symmetric, or 'H' for Hermitian) 'E' => matrix premultiplied by diag( DL ) and postmultiplied by inv( diag( DL ) ) ( 'E' for eigenvalue invariance) (only if matrix nonsymmetric) Note: if GRADE='E', then M must equal N. Not modified. DL - DOUBLE PRECISION array, dimension (M) If MODEL=0, then on entry this array specifies the diagonal entries of a diagonal matrix used as described under GRADE above. If MODEL is not zero, then DL will be set according to MODEL and CONDL, analogous to the way D is set according to MODE and COND (except there is no DMAX parameter for DL). If GRADE='E', then DL cannot have zero entries. Not referenced if GRADE = 'N' or 'R'. Changed on exit. MODEL - INTEGER This specifies how the diagonal array DL is to be computed, just as MODE specifies how D is to be computed. Not modified. CONDL - DOUBLE PRECISION When MODEL is not zero, this specifies the condition number of the computed DL. Not modified. DR - DOUBLE PRECISION array, dimension (N) If MODER=0, then on entry this array specifies the diagonal entries of a diagonal matrix used as described under GRADE above. If MODER is not zero, then DR will be set according to MODER and CONDR, analogous to the way D is set according to MODE and COND (except there is no DMAX parameter for DR). Not referenced if GRADE = 'N', 'L', 'H', 'S' or 'E'. Changed on exit. MODER - INTEGER This specifies how the diagonal array DR is to be computed, just as MODE specifies how D is to be computed. Not modified. CONDR - DOUBLE PRECISION When MODER is not zero, this specifies the condition number of the computed DR. Not modified. PIVTNG - CHARACTER*1 On entry specifies pivoting permutations as follows: 'N' or ' ' => none. 'L' => left or row pivoting (matrix must be nonsymmetric). 'R' => right or column pivoting (matrix must be nonsymmetric). 'B' or 'F' => both or full pivoting, i.e., on both sides. In this case, M must equal N If two calls to DLATMR both have full bandwidth (KL = M-1 and KU = N-1), and differ only in the PIVTNG and PACK parameters, then the matrices generated will differ only in the order of the rows and/or columns, and otherwise contain the same data. This consistency cannot be maintained with less than full bandwidth. IPIVOT - INTEGER array, dimension (N or M) This array specifies the permutation used. After the basic matrix is generated, the rows, columns, or both are permuted. If, say, row pivoting is selected, DLATMR starts with the *last* row and interchanges the M-th and IPIVOT(M)-th rows, then moves to the next-to-last row, interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, and so on. In terms of "2-cycles", the permutation is (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) where the rightmost cycle is applied first. This is the *inverse* of the effect of pivoting in LINPACK. The idea is that factoring (with pivoting) an identity matrix which has been inverse-pivoted in this way should result in a pivot vector identical to IPIVOT. Not referenced if PIVTNG = 'N'. Not modified. SPARSE - DOUBLE PRECISION On entry specifies the sparsity of the matrix if a sparse matrix is to be generated. SPARSE should lie between 0 and 1. To generate a sparse matrix, for each matrix entry a uniform ( 0, 1 ) random number x is generated and compared to SPARSE; if x is larger the matrix entry is unchanged and if x is smaller the entry is set to zero. Thus on the average a fraction SPARSE of the entries will be set to zero. Not modified. KL - INTEGER On entry specifies the lower bandwidth of the matrix. For example, KL=0 implies upper triangular, KL=1 implies upper Hessenberg, and KL at least M-1 implies the matrix is not banded. Must equal KU if matrix is symmetric. Not modified. KU - INTEGER On entry specifies the upper bandwidth of the matrix. For example, KU=0 implies lower triangular, KU=1 implies lower Hessenberg, and KU at least N-1 implies the matrix is not banded. Must equal KL if matrix is symmetric. Not modified. ANORM - DOUBLE PRECISION On entry specifies maximum entry of output matrix (output matrix will by multiplied by a constant so that its largest absolute entry equal ANORM) if ANORM is nonnegative. If ANORM is negative no scaling is done. Not modified. PACK - CHARACTER*1 On entry 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 matrix symmetric or square upper triangular) 'R' => store the lower triangle columnwise (only if matrix symmetric or square lower triangular) (same as upper half rowwise if symmetric) 'B' => store the lower triangle in band storage scheme (only if matrix symmetric) 'Q' => store the upper triangle in band storage scheme (only if matrix symmetric) '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 DLATMR 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. Only those entries of A which are significant on output will be referenced (even if A is in packed or band storage format). The 'unoccupied corners' of A in band format will be zeroed out. LDA - INTEGER on entry LDA specifies the first dimension of A as declared in the calling program. If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). If PACK='C' or 'R', LDA must be at least 1. If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) If PACK='Z', LDA must be at least KUU+KLL+1, where KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) Not modified. IWORK - INTEGER array, dimension ( N or M) Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. INFO - INTEGER Error parameter on exit: 0 => normal return -1 => M negative or unequal to N and SYM='S' or 'H' -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 => MODE neither -6, 0 nor 6 and RSIGN illegal string -11 => GRADE illegal string, or GRADE='E' and M not equal to N, or GRADE='L', 'R', 'B' or 'E' and SYM = 'S' or 'H' -12 => GRADE = 'E' and DL contains zero -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', 'S' or 'E' -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', and MODEL neither -6, 0 nor 6 -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' -17 => CONDR less than 1.0, GRADE='R' or 'B', and MODER neither -6, 0 nor 6 -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and M not equal to N, or PIVTNG='L' or 'R' and SYM='S' or 'H' -19 => IPIVOT contains out of range number and PIVTNG not equal to 'N' -20 => KL negative -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL -22 => SPARSE not in range 0. to 1. -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' and SYM='N', or PACK='C' and SYM='N' and either KL not equal to 0 or N not equal to M, or PACK='R' and SYM='N', and either KU not equal to 0 or N not equal to M -26 => LDA too small 1 => Error return from DLATM1 (computing D) 2 => Cannot scale diagonal to DMAX (max. entry is 0) 3 => Error return from DLATM1 (computing DL) 4 => Error return from DLATM1 (computing DR) 5 => ANORM is positive, but matrix constructed prior to attempting to scale it to have norm ANORM, is zero ===================================================================== 1) Decode and Test the input parameters. Initialize flags & seed. Parameter adjustments */ --iseed; --d__; --dl; --dr; --ipivot; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --iwork; /* 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, "S")) { isym = 0; } else if (lsame_(sym, "N")) { isym = 1; } else if (lsame_(sym, "H")) { isym = 0; } else { isym = -1; } /* Decode RSIGN */ if (lsame_(rsign, "F")) { irsign = 0; } else if (lsame_(rsign, "T")) { irsign = 1; } else { irsign = -1; } /* Decode PIVTNG */ if (lsame_(pivtng, "N")) { ipvtng = 0; } else if (lsame_(pivtng, " ")) { ipvtng = 0; } else if (lsame_(pivtng, "L")) { ipvtng = 1; npvts = *m; } else if (lsame_(pivtng, "R")) { ipvtng = 2; npvts = *n; } else if (lsame_(pivtng, "B")) { ipvtng = 3; npvts = min(*n,*m); } else if (lsame_(pivtng, "F")) { ipvtng = 3; npvts = min(*n,*m); } else { ipvtng = -1; } /* Decode GRADE */ if (lsame_(grade, "N")) { igrade = 0; } else if (lsame_(grade, "L")) { igrade = 1; } else if (lsame_(grade, "R")) { igrade = 2; } else if (lsame_(grade, "B")) { igrade = 3; } else if (lsame_(grade, "E")) { igrade = 4; } else if (lsame_(grade, "H") || lsame_(grade, "S")) { igrade = 5; } else { igrade = -1; } /* Decode PACK */ if (lsame_(pack, "N")) { ipack = 0; } else if (lsame_(pack, "U")) { ipack = 1; } else if (lsame_(pack, "L")) { ipack = 2; } else if (lsame_(pack, "C")) { ipack = 3; } else if (lsame_(pack, "R")) { ipack = 4; } else if (lsame_(pack, "B")) { ipack = 5; } else if (lsame_(pack, "Q")) { ipack = 6; } 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; kll = min(i__1,i__2); /* Computing MIN */ i__1 = *ku, i__2 = *n - 1; kuu = min(i__1,i__2); /* If inv(DL) is used, check to see if DL has a zero entry. */ dzero = FALSE_; if (igrade == 4 && *model == 0) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { if (dl[i__] == 0.) { dzero = TRUE_; } /* L10: */ } } /* Check values in IPIVOT */ badpvt = FALSE_; if (ipvtng > 0) { i__1 = npvts; for (j = 1; j <= i__1; ++j) { if (ipivot[j] <= 0 || ipivot[j] > npvts) { badpvt = TRUE_; } /* L20: */ } } /* Set INFO if an error */ if (*m < 0) { *info = -1; } else if (*m != *n && isym == 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (idist == -1) { *info = -3; } else if (isym == -1) { *info = -5; } else if (*mode < -6 || *mode > 6) { *info = -7; } else if (*mode != -6 && *mode != 0 && *mode != 6 && *cond < 1.) { *info = -8; } else if (*mode != -6 && *mode != 0 && *mode != 6 && irsign == -1) { *info = -10; } else if (igrade == -1 || igrade == 4 && *m != *n || igrade >= 1 && igrade <= 4 && isym == 0) { *info = -11; } else if (igrade == 4 && dzero) { *info = -12; } else if ((igrade == 1 || igrade == 3 || igrade == 4 || igrade == 5) && ( *model < -6 || *model > 6)) { *info = -13; } else if ((igrade == 1 || igrade == 3 || igrade == 4 || igrade == 5) && ( *model != -6 && *model != 0 && *model != 6) && *condl < 1.) { *info = -14; } else if ((igrade == 2 || igrade == 3) && (*moder < -6 || *moder > 6)) { *info = -16; } else if ((igrade == 2 || igrade == 3) && (*moder != -6 && *moder != 0 && *moder != 6) && *condr < 1.) { *info = -17; } else if (ipvtng == -1 || ipvtng == 3 && *m != *n || (ipvtng == 1 || ipvtng == 2) && isym == 0) { *info = -18; } else if (ipvtng != 0 && badpvt) { *info = -19; } else if (*kl < 0) { *info = -20; } else if (*ku < 0 || isym == 0 && *kl != *ku) { *info = -21; } else if (*sparse < 0. || *sparse > 1.) { *info = -22; } else if (ipack == -1 || (ipack == 1 || ipack == 2 || ipack == 5 || ipack == 6) && isym == 1 || ipack == 3 && isym == 1 && (*kl != 0 || *m != *n) || ipack == 4 && isym == 1 && (*ku != 0 || *m != *n)) { *info = -24; } else if ((ipack == 0 || ipack == 1 || ipack == 2) && *lda < max(1,*m) || (ipack == 3 || ipack == 4) && *lda < 1 || (ipack == 5 || ipack == 6) && *lda < kuu + 1 || ipack == 7 && *lda < kll + kuu + 1) { *info = -26; } if (*info != 0) { i__1 = -(*info); xerbla_("DLATMR", &i__1); return 0; } /* Decide if we can pivot consistently */ fulbnd = FALSE_; if (kuu == *n - 1 && kll == *m - 1) { fulbnd = TRUE_; } /* Initialize random number generator */ for (i__ = 1; i__ <= 4; ++i__) { iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096; /* L30: */ } iseed[4] = (iseed[4] / 2 << 1) + 1; /* 2) Set up D, DL, and DR, if indicated. Compute D according to COND and MODE */ dlatm1_(mode, cond, &irsign, &idist, &iseed[1], &d__[1], &mnmin, info); if (*info != 0) { *info = 1; return 0; } if (*mode != 0 && *mode != -6 && *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); /* L40: */ } if (temp == 0. && *dmax__ != 0.) { *info = 2; return 0; } if (temp != 0.) { alpha = *dmax__ / temp; } else { alpha = 1.; } i__1 = mnmin; for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = alpha * d__[i__]; /* L50: */ } } /* Compute DL if grading set */ if (igrade == 1 || igrade == 3 || igrade == 4 || igrade == 5) { dlatm1_(model, condl, &c__0, &idist, &iseed[1], &dl[1], m, info); if (*info != 0) { *info = 3; return 0; } } /* Compute DR if grading set */ if (igrade == 2 || igrade == 3) { dlatm1_(moder, condr, &c__0, &idist, &iseed[1], &dr[1], n, info); if (*info != 0) { *info = 4; return 0; } } /* 3) Generate IWORK if pivoting */ if (ipvtng > 0) { i__1 = npvts; for (i__ = 1; i__ <= i__1; ++i__) { iwork[i__] = i__; /* L60: */ } if (fulbnd) { i__1 = npvts; for (i__ = 1; i__ <= i__1; ++i__) { k = ipivot[i__]; j = iwork[i__]; iwork[i__] = iwork[k]; iwork[k] = j; /* L70: */ } } else { for (i__ = npvts; i__ >= 1; --i__) { k = ipivot[i__]; j = iwork[i__]; iwork[i__] = iwork[k]; iwork[k] = j; /* L80: */ } } } /* 4) Generate matrices for each kind of PACKing Always sweep matrix columnwise (if symmetric, upper half only) so that matrix generated does not depend on PACK */ if (fulbnd) { /* Use DLATM3 so matrices generated with differing PIVOTing only differ only in the order of their rows and/or columns. */ if (ipack == 0) { if (isym == 0) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); a_ref(isub, jsub) = temp; a_ref(jsub, isub) = temp; /* L90: */ } /* L100: */ } } else if (isym == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); a_ref(isub, jsub) = temp; /* L110: */ } /* L120: */ } } } else if (ipack == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], &dr[1] , &ipvtng, &iwork[1], sparse); mnsub = min(isub,jsub); mxsub = max(isub,jsub); a_ref(mnsub, mxsub) = temp; if (mnsub != mxsub) { a_ref(mxsub, mnsub) = 0.; } /* L130: */ } /* L140: */ } } else if (ipack == 2) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], &dr[1] , &ipvtng, &iwork[1], sparse); mnsub = min(isub,jsub); mxsub = max(isub,jsub); a_ref(mxsub, mnsub) = temp; if (mnsub != mxsub) { a_ref(mnsub, mxsub) = 0.; } /* L150: */ } /* L160: */ } } else if (ipack == 3) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], &dr[1] , &ipvtng, &iwork[1], sparse); /* Compute K = location of (ISUB,JSUB) entry in packed array */ mnsub = min(isub,jsub); mxsub = max(isub,jsub); k = mxsub * (mxsub - 1) / 2 + mnsub; /* Convert K to (IISUB,JJSUB) location */ jjsub = (k - 1) / *lda + 1; iisub = k - *lda * (jjsub - 1); a_ref(iisub, jjsub) = temp; /* L170: */ } /* L180: */ } } else if (ipack == 4) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], &dr[1] , &ipvtng, &iwork[1], sparse); /* Compute K = location of (I,J) entry in packed array */ mnsub = min(isub,jsub); mxsub = max(isub,jsub); if (mnsub == 1) { k = mxsub; } else { k = *n * (*n + 1) / 2 - (*n - mnsub + 1) * (*n - mnsub + 2) / 2 + mxsub - mnsub + 1; } /* Convert K to (IISUB,JJSUB) location */ jjsub = (k - 1) / *lda + 1; iisub = k - *lda * (jjsub - 1); a_ref(iisub, jjsub) = temp; /* L190: */ } /* L200: */ } } else if (ipack == 5) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = j - kuu; i__ <= i__2; ++i__) { if (i__ < 1) { a_ref(j - i__ + 1, i__ + *n) = 0.; } else { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); mnsub = min(isub,jsub); mxsub = max(isub,jsub); a_ref(mxsub - mnsub + 1, mnsub) = temp; } /* L210: */ } /* L220: */ } } else if (ipack == 6) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = j - kuu; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], &dr[1] , &ipvtng, &iwork[1], sparse); mnsub = min(isub,jsub); mxsub = max(isub,jsub); a_ref(mnsub - mxsub + kuu + 1, mxsub) = temp; /* L230: */ } /* L240: */ } } else if (ipack == 7) { if (isym == 0) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = j - kuu; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); mnsub = min(isub,jsub); mxsub = max(isub,jsub); a_ref(mnsub - mxsub + kuu + 1, mxsub) = temp; if (i__ < 1) { a_ref(j - i__ + 1 + kuu, i__ + *n) = 0.; } if (i__ >= 1 && mnsub != mxsub) { a_ref(mxsub - mnsub + 1 + kuu, mnsub) = temp; } /* L250: */ } /* L260: */ } } else if (isym == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j + kll; for (i__ = j - kuu; i__ <= i__2; ++i__) { temp = dlatm3_(m, n, &i__, &j, &isub, &jsub, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); a_ref(isub - jsub + kuu + 1, jsub) = temp; /* L270: */ } /* L280: */ } } } } else { /* Use DLATM2 */ if (ipack == 0) { if (isym == 0) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { a_ref(i__, j) = dlatm2_(m, n, &i__, &j, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); a_ref(j, i__) = a_ref(i__, j); /* L290: */ } /* L300: */ } } else if (isym == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { a_ref(i__, j) = dlatm2_(m, n, &i__, &j, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); /* L310: */ } /* L320: */ } } } else if (ipack == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { a_ref(i__, j) = dlatm2_(m, n, &i__, &j, kl, ku, &idist, & iseed[1], &d__[1], &igrade, &dl[1], &dr[1], & ipvtng, &iwork[1], sparse); if (i__ != j) { a_ref(j, i__) = 0.; } /* L330: */ } /* L340: */ } } else if (ipack == 2) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { a_ref(j, i__) = dlatm2_(m, n, &i__, &j, kl, ku, &idist, & iseed[1], &d__[1], &igrade, &dl[1], &dr[1], & ipvtng, &iwork[1], sparse); if (i__ != j) { a_ref(i__, j) = 0.; } /* L350: */ } /* L360: */ } } else if (ipack == 3) { isub = 0; jsub = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { ++isub; if (isub > *lda) { isub = 1; ++jsub; } a_ref(isub, jsub) = dlatm2_(m, n, &i__, &j, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], &dr[1] , &ipvtng, &iwork[1], sparse); /* L370: */ } /* L380: */ } } else if (ipack == 4) { if (isym == 0) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { /* Compute K = location of (I,J) entry in packed array */ if (i__ == 1) { k = j; } else { k = *n * (*n + 1) / 2 - (*n - i__ + 1) * (*n - i__ + 2) / 2 + j - i__ + 1; } /* Convert K to (ISUB,JSUB) location */ jsub = (k - 1) / *lda + 1; isub = k - *lda * (jsub - 1); a_ref(isub, jsub) = dlatm2_(m, n, &i__, &j, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); /* L390: */ } /* L400: */ } } else { isub = 0; jsub = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = j; i__ <= i__2; ++i__) { ++isub; if (isub > *lda) { isub = 1; ++jsub; } a_ref(isub, jsub) = dlatm2_(m, n, &i__, &j, kl, ku, & idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); /* L410: */ } /* L420: */ } } } else if (ipack == 5) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = j - kuu; i__ <= i__2; ++i__) { if (i__ < 1) { a_ref(j - i__ + 1, i__ + *n) = 0.; } else { a_ref(j - i__ + 1, i__) = dlatm2_(m, n, &i__, &j, kl, ku, &idist, &iseed[1], &d__[1], &igrade, &dl[ 1], &dr[1], &ipvtng, &iwork[1], sparse); } /* L430: */ } /* L440: */ } } else if (ipack == 6) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = j - kuu; i__ <= i__2; ++i__) { a_ref(i__ - j + kuu + 1, j) = dlatm2_(m, n, &i__, &j, kl, ku, &idist, &iseed[1], &d__[1], &igrade, &dl[1], & dr[1], &ipvtng, &iwork[1], sparse); /* L450: */ } /* L460: */ } } else if (ipack == 7) { if (isym == 0) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = j - kuu; i__ <= i__2; ++i__) { a_ref(i__ - j + kuu + 1, j) = dlatm2_(m, n, &i__, &j, kl, ku, &idist, &iseed[1], &d__[1], &igrade, & dl[1], &dr[1], &ipvtng, &iwork[1], sparse); if (i__ < 1) { a_ref(j - i__ + 1 + kuu, i__ + *n) = 0.; } if (i__ >= 1 && i__ != j) { a_ref(j - i__ + 1 + kuu, i__) = a_ref(i__ - j + kuu + 1, j); } /* L470: */ } /* L480: */ } } else if (isym == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j + kll; for (i__ = j - kuu; i__ <= i__2; ++i__) { a_ref(i__ - j + kuu + 1, j) = dlatm2_(m, n, &i__, &j, kl, ku, &idist, &iseed[1], &d__[1], &igrade, & dl[1], &dr[1], &ipvtng, &iwork[1], sparse); /* L490: */ } /* L500: */ } } } } /* 5) Scaling the norm */ if (ipack == 0) { onorm = dlange_("M", m, n, &a[a_offset], lda, tempa); } else if (ipack == 1) { onorm = dlansy_("M", "U", n, &a[a_offset], lda, tempa); } else if (ipack == 2) { onorm = dlansy_("M", "L", n, &a[a_offset], lda, tempa); } else if (ipack == 3) { onorm = dlansp_("M", "U", n, &a[a_offset], tempa); } else if (ipack == 4) { onorm = dlansp_("M", "L", n, &a[a_offset], tempa); } else if (ipack == 5) { onorm = dlansb_("M", "L", n, &kll, &a[a_offset], lda, tempa); } else if (ipack == 6) { onorm = dlansb_("M", "U", n, &kuu, &a[a_offset], lda, tempa); } else if (ipack == 7) { onorm = dlangb_("M", n, &kll, &kuu, &a[a_offset], lda, tempa); } if (*anorm >= 0.) { if (*anorm > 0. && onorm == 0.) { /* Desired scaling impossible */ *info = 5; return 0; } else if (*anorm > 1. && onorm < 1. || *anorm < 1. && onorm > 1.) { /* Scale carefully to avoid over / underflow */ if (ipack <= 2) { i__1 = *n; for (j = 1; j <= i__1; ++j) { d__1 = 1. / onorm; dscal_(m, &d__1, &a_ref(1, j), &c__1); dscal_(m, anorm, &a_ref(1, j), &c__1); /* L510: */ } } else if (ipack == 3 || ipack == 4) { i__1 = *n * (*n + 1) / 2; d__1 = 1. / onorm; dscal_(&i__1, &d__1, &a[a_offset], &c__1); i__1 = *n * (*n + 1) / 2; dscal_(&i__1, anorm, &a[a_offset], &c__1); } else if (ipack >= 5) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = kll + kuu + 1; d__1 = 1. / onorm; dscal_(&i__2, &d__1, &a_ref(1, j), &c__1); i__2 = kll + kuu + 1; dscal_(&i__2, anorm, &a_ref(1, j), &c__1); /* L520: */ } } } else { /* Scale straightforwardly */ if (ipack <= 2) { i__1 = *n; for (j = 1; j <= i__1; ++j) { d__1 = *anorm / onorm; dscal_(m, &d__1, &a_ref(1, j), &c__1); /* L530: */ } } else if (ipack == 3 || ipack == 4) { i__1 = *n * (*n + 1) / 2; d__1 = *anorm / onorm; dscal_(&i__1, &d__1, &a[a_offset], &c__1); } else if (ipack >= 5) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = kll + kuu + 1; d__1 = *anorm / onorm; dscal_(&i__2, &d__1, &a_ref(1, j), &c__1); /* L540: */ } } } } /* End of DLATMR */ return 0; } /* dlatmr_ */
/* Subroutine */ int dlatme_(integer *n, char *dist, integer *iseed, doublereal *d__, integer *mode, doublereal *cond, doublereal *dmax__, char *ei, char *rsign, char *upper, char *sim, doublereal *ds, integer *modes, doublereal *conds, integer *kl, integer *ku, doublereal *anorm, doublereal *a, integer *lda, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1, d__2, d__3; /* Local variables */ integer i__, j, ic, jc, ir, jr, jcr; doublereal tau; logical bads; extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *); integer isim; doublereal temp; logical badei; doublereal alpha; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); integer iinfo; doublereal tempa[1]; integer icols; logical useei; integer idist; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer irows; extern /* Subroutine */ int dlatm1_(integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *, integer *); extern doublereal dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dlarge_(integer *, doublereal *, integer *, integer *, doublereal *, integer *), dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *); extern doublereal dlaran_(integer *); extern /* Subroutine */ int dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *), dlarnv_(integer *, integer *, integer *, doublereal *); integer irsign, iupper; doublereal xnorms; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DLATME generates random non-symmetric square matrices with */ /* specified eigenvalues for testing LAPACK programs. */ /* DLATME operates by applying the following sequence of */ /* operations: */ /* 1. Set the diagonal to D, where D may be input or */ /* computed according to MODE, COND, DMAX, and RSIGN */ /* as described below. */ /* 2. If complex conjugate pairs are desired (MODE=0 and EI(1)='R', */ /* or MODE=5), certain pairs of adjacent elements of D are */ /* interpreted as the real and complex parts of a complex */ /* conjugate pair; A thus becomes block diagonal, with 1x1 */ /* and 2x2 blocks. */ /* 3. If UPPER='T', the upper triangle of A is set to random values */ /* out of distribution DIST. */ /* 4. If SIM='T', A is multiplied on the left by a random matrix */ /* X, whose singular values are specified by DS, MODES, and */ /* CONDS, and on the right by X inverse. */ /* 5. If KL < N-1, the lower bandwidth is reduced to KL using */ /* Householder transformations. If KU < N-1, the upper */ /* bandwidth is reduced to KU. */ /* 6. If ANORM is not negative, the matrix is scaled to have */ /* maximum-element-norm ANORM. */ /* (Note: since the matrix cannot be reduced beyond Hessenberg form, */ /* no packing options are available.) */ /* Arguments */ /* ========= */ /* N - INTEGER */ /* The number of columns (or rows) 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, and for the */ /* upper triangle (see UPPER). */ /* '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 DLATME */ /* to continue the same random number sequence. */ /* Changed on exit. */ /* D - DOUBLE PRECISION array, dimension ( N ) */ /* This array is used to specify the eigenvalues of A. If */ /* MODE=0, then D is assumed to contain the eigenvalues (but */ /* see the description of EI), otherwise they will be */ /* computed according to MODE, COND, DMAX, and RSIGN and */ /* placed in D. */ /* Modified if MODE is nonzero. */ /* MODE - INTEGER */ /* On entry this describes how the eigenvalues are to */ /* be specified: */ /* MODE = 0 means use D (with EI) 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. Each odd-even pair */ /* of elements will be either used as two real */ /* eigenvalues or as the real and imaginary part */ /* of a complex conjugate pair of eigenvalues; */ /* the choice of which is done is random, with */ /* 50-50 probability, for each pair. */ /* 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 between 1 and 4, D has entries ranging */ /* from 1 to 1/COND, if between -1 and -4, D has entries */ /* ranging from 1/COND to 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))). 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. */ /* EI - CHARACTER*1 array, dimension ( N ) */ /* If MODE is 0, and EI(1) is not ' ' (space character), */ /* this array specifies which elements of D (on input) are */ /* real eigenvalues and which are the real and imaginary parts */ /* of a complex conjugate pair of eigenvalues. The elements */ /* of EI may then only have the values 'R' and 'I'. If */ /* EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is */ /* CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex */ /* conjugate thereof. If EI(j)=EI(j+1)='R', then the j-th */ /* eigenvalue is D(j) (i.e., real). EI(1) may not be 'I', */ /* nor may two adjacent elements of EI both have the value 'I'. */ /* If MODE is not 0, then EI is ignored. If MODE is 0 and */ /* EI(1)=' ', then the eigenvalues will all be real. */ /* Not modified. */ /* RSIGN - CHARACTER*1 */ /* If MODE is not 0, 6, or -6, and RSIGN='T', then the */ /* elements of D, as computed according to MODE and COND, will */ /* be multiplied by a random sign (+1 or -1). If RSIGN='F', */ /* they will not be. RSIGN may only have the values 'T' or */ /* 'F'. */ /* Not modified. */ /* UPPER - CHARACTER*1 */ /* If UPPER='T', then the elements of A above the diagonal */ /* (and above the 2x2 diagonal blocks, if A has complex */ /* eigenvalues) will be set to random numbers out of DIST. */ /* If UPPER='F', they will not. UPPER may only have the */ /* values 'T' or 'F'. */ /* Not modified. */ /* SIM - CHARACTER*1 */ /* If SIM='T', then A will be operated on by a "similarity */ /* transform", i.e., multiplied on the left by a matrix X and */ /* on the right by X inverse. X = U S V, where U and V are */ /* random unitary matrices and S is a (diagonal) matrix of */ /* singular values specified by DS, MODES, and CONDS. If */ /* SIM='F', then A will not be transformed. */ /* Not modified. */ /* DS - DOUBLE PRECISION array, dimension ( N ) */ /* This array is used to specify the singular values of X, */ /* in the same way that D specifies the eigenvalues of A. */ /* If MODE=0, the DS contains the singular values, which */ /* may not be zero. */ /* Modified if MODE is nonzero. */ /* MODES - INTEGER */ /* CONDS - DOUBLE PRECISION */ /* Same as MODE and COND, but for specifying the diagonal */ /* of S. MODES=-6 and +6 are not allowed (since they would */ /* result in randomly ill-conditioned eigenvalues.) */ /* KL - INTEGER */ /* This specifies the lower bandwidth of the matrix. KL=1 */ /* specifies upper Hessenberg form. If KL is at least N-1, */ /* then A will have full lower bandwidth. KL must be at */ /* least 1. */ /* Not modified. */ /* KU - INTEGER */ /* This specifies the upper bandwidth of the matrix. KU=1 */ /* specifies lower Hessenberg form. If KU is at least N-1, */ /* then A will have full upper bandwidth; if KU and KL */ /* are both at least N-1, then A will be dense. Only one of */ /* KU and KL may be less than N-1. KU must be at least 1. */ /* Not modified. */ /* ANORM - DOUBLE PRECISION */ /* If ANORM is not negative, then A will be scaled by a non- */ /* negative real number to make the maximum-element-norm of A */ /* to be ANORM. */ /* Not modified. */ /* A - DOUBLE PRECISION array, dimension ( LDA, N ) */ /* On exit A is the desired test matrix. */ /* Modified. */ /* LDA - INTEGER */ /* LDA specifies the first dimension of A as declared in the */ /* calling program. LDA must be at least N. */ /* Not modified. */ /* WORK - DOUBLE PRECISION array, dimension ( 3*N ) */ /* Workspace. */ /* Modified. */ /* INFO - INTEGER */ /* Error code. On exit, INFO will be set to one of the */ /* following values: */ /* 0 => normal return */ /* -1 => N negative */ /* -2 => DIST illegal string */ /* -5 => MODE not in range -6 to 6 */ /* -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 */ /* -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or */ /* two adjacent elements of EI are 'I'. */ /* -9 => RSIGN is not 'T' or 'F' */ /* -10 => UPPER is not 'T' or 'F' */ /* -11 => SIM is not 'T' or 'F' */ /* -12 => MODES=0 and DS has a zero singular value. */ /* -13 => MODES is not in the range -5 to 5. */ /* -14 => MODES is nonzero and CONDS is less than 1. */ /* -15 => KL is less than 1. */ /* -16 => KU is less than 1, or KL and KU are both less than */ /* N-1. */ /* -19 => LDA is less than N. */ /* 1 => Error return from DLATM1 (computing D) */ /* 2 => Cannot scale to DMAX (max. eigenvalue is 0) */ /* 3 => Error return from DLATM1 (computing DS) */ /* 4 => Error return from DLARGE */ /* 5 => Zero singular value from DLATM1. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* 1) Decode and Test the input parameters. */ /* Initialize flags & seed. */ /* Parameter adjustments */ --iseed; --d__; --ei; --ds; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; /* Function Body */ *info = 0; /* Quick return if possible */ if (*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; } /* Check EI */ useei = TRUE_; badei = FALSE_; if (lsame_(ei + 1, " ") || *mode != 0) { useei = FALSE_; } else { if (lsame_(ei + 1, "R")) { i__1 = *n; for (j = 2; j <= i__1; ++j) { if (lsame_(ei + j, "I")) { if (lsame_(ei + (j - 1), "I")) { badei = TRUE_; } } else { if (! lsame_(ei + j, "R")) { badei = TRUE_; } } /* L10: */ } } else { badei = TRUE_; } } /* Decode RSIGN */ if (lsame_(rsign, "T")) { irsign = 1; } else if (lsame_(rsign, "F")) { irsign = 0; } else { irsign = -1; } /* Decode UPPER */ if (lsame_(upper, "T")) { iupper = 1; } else if (lsame_(upper, "F")) { iupper = 0; } else { iupper = -1; } /* Decode SIM */ if (lsame_(sim, "T")) { isim = 1; } else if (lsame_(sim, "F")) { isim = 0; } else { isim = -1; } /* Check DS, if MODES=0 and ISIM=1 */ bads = FALSE_; if (*modes == 0 && isim == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (ds[j] == 0.) { bads = TRUE_; } /* L20: */ } } /* Set INFO if an error */ if (*n < 0) { *info = -1; } else if (idist == -1) { *info = -2; } else if (abs(*mode) > 6) { *info = -5; } else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.) { *info = -6; } else if (badei) { *info = -8; } else if (irsign == -1) { *info = -9; } else if (iupper == -1) { *info = -10; } else if (isim == -1) { *info = -11; } else if (bads) { *info = -12; } else if (isim == 1 && abs(*modes) > 5) { *info = -13; } else if (isim == 1 && *modes != 0 && *conds < 1.) { *info = -14; } else if (*kl < 1) { *info = -15; } else if (*ku < 1 || *ku < *n - 1 && *kl < *n - 1) { *info = -16; } else if (*lda < max(1,*n)) { *info = -19; } if (*info != 0) { i__1 = -(*info); xerbla_("DLATME", &i__1); return 0; } /* Initialize random number generator */ for (i__ = 1; i__ <= 4; ++i__) { iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096; /* L30: */ } if (iseed[4] % 2 != 1) { ++iseed[4]; } /* 2) Set up diagonal of A */ /* Compute D according to COND and MODE */ dlatm1_(mode, cond, &irsign, &idist, &iseed[1], &d__[1], n, &iinfo); if (iinfo != 0) { *info = 1; return 0; } if (*mode != 0 && abs(*mode) != 6) { /* Scale by DMAX */ temp = abs(d__[1]); i__1 = *n; 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); /* L40: */ } if (temp > 0.) { alpha = *dmax__ / temp; } else if (*dmax__ != 0.) { *info = 2; return 0; } else { alpha = 0.; } dscal_(n, &alpha, &d__[1], &c__1); } dlaset_("Full", n, n, &c_b23, &c_b23, &a[a_offset], lda); i__1 = *lda + 1; dcopy_(n, &d__[1], &c__1, &a[a_offset], &i__1); /* Set up complex conjugate pairs */ if (*mode == 0) { if (useei) { i__1 = *n; for (j = 2; j <= i__1; ++j) { if (lsame_(ei + j, "I")) { a[j - 1 + j * a_dim1] = a[j + j * a_dim1]; a[j + (j - 1) * a_dim1] = -a[j + j * a_dim1]; a[j + j * a_dim1] = a[j - 1 + (j - 1) * a_dim1]; } /* L50: */ } } } else if (abs(*mode) == 5) { i__1 = *n; for (j = 2; j <= i__1; j += 2) { if (dlaran_(&iseed[1]) > .5) { a[j - 1 + j * a_dim1] = a[j + j * a_dim1]; a[j + (j - 1) * a_dim1] = -a[j + j * a_dim1]; a[j + j * a_dim1] = a[j - 1 + (j - 1) * a_dim1]; } /* L60: */ } } /* 3) If UPPER='T', set upper triangle of A to random numbers. */ /* (but don't modify the corners of 2x2 blocks.) */ if (iupper != 0) { i__1 = *n; for (jc = 2; jc <= i__1; ++jc) { if (a[jc - 1 + jc * a_dim1] != 0.) { jr = jc - 2; } else { jr = jc - 1; } dlarnv_(&idist, &iseed[1], &jr, &a[jc * a_dim1 + 1]); /* L70: */ } } /* 4) If SIM='T', apply similarity transformation. */ /* -1 */ /* Transform is X A X , where X = U S V, thus */ /* it is U S V A V' (1/S) U' */ if (isim != 0) { /* Compute S (singular values of the eigenvector matrix) */ /* according to CONDS and MODES */ dlatm1_(modes, conds, &c__0, &c__0, &iseed[1], &ds[1], n, &iinfo); if (iinfo != 0) { *info = 3; return 0; } /* Multiply by V and V' */ dlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo); if (iinfo != 0) { *info = 4; return 0; } /* Multiply by S and (1/S) */ i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(n, &ds[j], &a[j + a_dim1], lda); if (ds[j] != 0.) { d__1 = 1. / ds[j]; dscal_(n, &d__1, &a[j * a_dim1 + 1], &c__1); } else { *info = 5; return 0; } /* L80: */ } /* Multiply by U and U' */ dlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo); if (iinfo != 0) { *info = 4; return 0; } } /* 5) Reduce the bandwidth. */ if (*kl < *n - 1) { /* Reduce bandwidth -- kill column */ i__1 = *n - 1; for (jcr = *kl + 1; jcr <= i__1; ++jcr) { ic = jcr - *kl; irows = *n + 1 - jcr; icols = *n + *kl - jcr; dcopy_(&irows, &a[jcr + ic * a_dim1], &c__1, &work[1], &c__1); xnorms = work[1]; dlarfg_(&irows, &xnorms, &work[2], &c__1, &tau); work[1] = 1.; dgemv_("T", &irows, &icols, &c_b39, &a[jcr + (ic + 1) * a_dim1], lda, &work[1], &c__1, &c_b23, &work[irows + 1], &c__1); d__1 = -tau; dger_(&irows, &icols, &d__1, &work[1], &c__1, &work[irows + 1], & c__1, &a[jcr + (ic + 1) * a_dim1], lda); dgemv_("N", n, &irows, &c_b39, &a[jcr * a_dim1 + 1], lda, &work[1] , &c__1, &c_b23, &work[irows + 1], &c__1); d__1 = -tau; dger_(n, &irows, &d__1, &work[irows + 1], &c__1, &work[1], &c__1, &a[jcr * a_dim1 + 1], lda); a[jcr + ic * a_dim1] = xnorms; i__2 = irows - 1; dlaset_("Full", &i__2, &c__1, &c_b23, &c_b23, &a[jcr + 1 + ic * a_dim1], lda); /* L90: */ } } else if (*ku < *n - 1) { /* Reduce upper bandwidth -- kill a row at a time. */ i__1 = *n - 1; for (jcr = *ku + 1; jcr <= i__1; ++jcr) { ir = jcr - *ku; irows = *n + *ku - jcr; icols = *n + 1 - jcr; dcopy_(&icols, &a[ir + jcr * a_dim1], lda, &work[1], &c__1); xnorms = work[1]; dlarfg_(&icols, &xnorms, &work[2], &c__1, &tau); work[1] = 1.; dgemv_("N", &irows, &icols, &c_b39, &a[ir + 1 + jcr * a_dim1], lda, &work[1], &c__1, &c_b23, &work[icols + 1], &c__1); d__1 = -tau; dger_(&irows, &icols, &d__1, &work[icols + 1], &c__1, &work[1], & c__1, &a[ir + 1 + jcr * a_dim1], lda); dgemv_("C", &icols, n, &c_b39, &a[jcr + a_dim1], lda, &work[1], & c__1, &c_b23, &work[icols + 1], &c__1); d__1 = -tau; dger_(&icols, n, &d__1, &work[1], &c__1, &work[icols + 1], &c__1, &a[jcr + a_dim1], lda); a[ir + jcr * a_dim1] = xnorms; i__2 = icols - 1; dlaset_("Full", &c__1, &i__2, &c_b23, &c_b23, &a[ir + (jcr + 1) * a_dim1], lda); /* L100: */ } } /* Scale the matrix to have norm ANORM */ if (*anorm >= 0.) { temp = dlange_("M", n, n, &a[a_offset], lda, tempa); if (temp > 0.) { alpha = *anorm / temp; i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(n, &alpha, &a[j * a_dim1 + 1], &c__1); /* L110: */ } } } return 0; /* End of DLATME */ } /* dlatme_ */
/* Subroutine */ int zlatme_(integer *n, char *dist, integer *iseed, doublecomplex *d, integer *mode, doublereal *cond, doublecomplex * dmax__, char *ei, char *rsign, char *upper, char *sim, doublereal *ds, integer *modes, doublereal *conds, integer *kl, integer *ku, doublereal *anorm, doublecomplex *a, integer *lda, doublecomplex * work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1, d__2; doublecomplex z__1, z__2; /* Builtin functions */ double z_abs(doublecomplex *); void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static logical bads; static integer isim; static doublereal temp; static integer i, j; static doublecomplex alpha; extern logical lsame_(char *, char *); static integer iinfo; static doublereal tempa[1]; static integer icols; extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); static integer idist; extern /* Subroutine */ int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); static integer irows; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), dlatm1_(integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *, integer *), zlatm1_(integer *, doublereal *, integer *, integer *, integer *, doublecomplex *, integer *, integer *); static integer ic, jc, ir; static doublereal ralpha; extern /* Subroutine */ int xerbla_(char *, integer *); extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zdscal_(integer *, doublereal *, doublecomplex *, integer *), zlarge_(integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *), zlarfg_( integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *, integer *); extern /* Double Complex */ void zlarnd_(doublecomplex *, integer *, integer *); static integer irsign; extern /* Subroutine */ int zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); static integer iupper; extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *, doublecomplex *); static doublecomplex xnorms; static integer jcr; static doublecomplex tau; /* -- LAPACK test routine (version 2.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= ZLATME generates random non-symmetric square matrices with specified eigenvalues for testing LAPACK programs. ZLATME operates by applying the following sequence of operations: 1. Set the diagonal to D, where D may be input or computed according to MODE, COND, DMAX, and RSIGN as described below. 2. If UPPER='T', the upper triangle of A is set to random values out of distribution DIST. 3. If SIM='T', A is multiplied on the left by a random matrix X, whose singular values are specified by DS, MODES, and CONDS, and on the right by X inverse. 4. If KL < N-1, the lower bandwidth is reduced to KL using Householder transformations. If KU < N-1, the upper bandwidth is reduced to KU. 5. If ANORM is not negative, the matrix is scaled to have maximum-element-norm ANORM. (Note: since the matrix cannot be reduced beyond Hessenberg form, no packing options are available.) Arguments ========= N - INTEGER The number of columns (or rows) 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, and on the upper triangle (see UPPER). 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) 'D' => uniform on the complex disc |z| < 1. 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 ZLATME to continue the same random number sequence. Changed on exit. D - COMPLEX*16 array, dimension ( N ) This array is used to specify the eigenvalues of A. If MODE=0, then D is assumed to contain the eigenvalues otherwise they will be computed according to MODE, COND, DMAX, and RSIGN and placed in D. Modified if MODE is nonzero. MODE - INTEGER On entry this describes how the 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 between 1 and 4, D has entries ranging from 1 to 1/COND, if between -1 and -4, D has entries ranging from 1/COND to 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 - COMPLEX*16 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))). Note that DMAX need not be positive or real: if DMAX is negative or complex (or zero), D will be scaled by a negative or complex number (or zero). If RSIGN='F' then the largest (absolute) eigenvalue will be equal to DMAX. Not modified. EI - CHARACTER*1 (ignored) Not modified. RSIGN - CHARACTER*1 If MODE is not 0, 6, or -6, and RSIGN='T', then the elements of D, as computed according to MODE and COND, will be multiplied by a random complex number from the unit circle |z| = 1. If RSIGN='F', they will not be. RSIGN may only have the values 'T' or 'F'. Not modified. UPPER - CHARACTER*1 If UPPER='T', then the elements of A above the diagonal will be set to random numbers out of DIST. If UPPER='F', they will not. UPPER may only have the values 'T' or 'F'. Not modified. SIM - CHARACTER*1 If SIM='T', then A will be operated on by a "similarity transform", i.e., multiplied on the left by a matrix X and on the right by X inverse. X = U S V, where U and V are random unitary matrices and S is a (diagonal) matrix of singular values specified by DS, MODES, and CONDS. If SIM='F', then A will not be transformed. Not modified. DS - DOUBLE PRECISION array, dimension ( N ) This array is used to specify the singular values of X, in the same way that D specifies the eigenvalues of A. If MODE=0, the DS contains the singular values, which may not be zero. Modified if MODE is nonzero. MODES - INTEGER CONDS - DOUBLE PRECISION Similar to MODE and COND, but for specifying the diagonal of S. MODES=-6 and +6 are not allowed (since they would result in randomly ill-conditioned eigenvalues.) KL - INTEGER This specifies the lower bandwidth of the matrix. KL=1 specifies upper Hessenberg form. If KL is at least N-1, then A will have full lower bandwidth. Not modified. KU - INTEGER This specifies the upper bandwidth of the matrix. KU=1 specifies lower Hessenberg form. If KU is at least N-1, then A will have full upper bandwidth; if KU and KL are both at least N-1, then A will be dense. Only one of KU and KL may be less than N-1. Not modified. ANORM - DOUBLE PRECISION If ANORM is not negative, then A will be scaled by a non- negative real number to make the maximum-element-norm of A to be ANORM. Not modified. A - COMPLEX*16 array, dimension ( LDA, N ) On exit A is the desired test matrix. Modified. LDA - INTEGER LDA specifies the first dimension of A as declared in the calling program. LDA must be at least M. Not modified. WORK - COMPLEX*16 array, dimension ( 3*N ) Workspace. Modified. INFO - INTEGER Error code. On exit, INFO will be set to one of the following values: 0 => normal return -1 => N negative -2 => DIST illegal string -5 => MODE not in range -6 to 6 -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 -9 => RSIGN is not 'T' or 'F' -10 => UPPER is not 'T' or 'F' -11 => SIM is not 'T' or 'F' -12 => MODES=0 and DS has a zero singular value. -13 => MODES is not in the range -5 to 5. -14 => MODES is nonzero and CONDS is less than 1. -15 => KL is less than 1. -16 => KU is less than 1, or KL and KU are both less than N-1. -19 => LDA is less than M. 1 => Error return from ZLATM1 (computing D) 2 => Cannot scale to DMAX (max. eigenvalue is 0) 3 => Error return from DLATM1 (computing DS) 4 => Error return from ZLARGE 5 => Zero singular value from DLATM1. ===================================================================== 1) Decode and Test the input parameters. Initialize flags & seed. Parameter adjustments */ --iseed; --d; --ds; a_dim1 = *lda; a_offset = a_dim1 + 1; a -= a_offset; --work; /* Function Body */ *info = 0; /* Quick return if possible */ if (*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 if (lsame_(dist, "D")) { idist = 4; } else { idist = -1; } /* Decode RSIGN */ if (lsame_(rsign, "T")) { irsign = 1; } else if (lsame_(rsign, "F")) { irsign = 0; } else { irsign = -1; } /* Decode UPPER */ if (lsame_(upper, "T")) { iupper = 1; } else if (lsame_(upper, "F")) { iupper = 0; } else { iupper = -1; } /* Decode SIM */ if (lsame_(sim, "T")) { isim = 1; } else if (lsame_(sim, "F")) { isim = 0; } else { isim = -1; } /* Check DS, if MODES=0 and ISIM=1 */ bads = FALSE_; if (*modes == 0 && isim == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (ds[j] == 0.) { bads = TRUE_; } /* L10: */ } } /* Set INFO if an error */ if (*n < 0) { *info = -1; } else if (idist == -1) { *info = -2; } else if (abs(*mode) > 6) { *info = -5; } else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.) { *info = -6; } else if (irsign == -1) { *info = -9; } else if (iupper == -1) { *info = -10; } else if (isim == -1) { *info = -11; } else if (bads) { *info = -12; } else if (isim == 1 && abs(*modes) > 5) { *info = -13; } else if (isim == 1 && *modes != 0 && *conds < 1.) { *info = -14; } else if (*kl < 1) { *info = -15; } else if (*ku < 1 || *ku < *n - 1 && *kl < *n - 1) { *info = -16; } else if (*lda < max(1,*n)) { *info = -19; } if (*info != 0) { i__1 = -(*info); xerbla_("ZLATME", &i__1); return 0; } /* Initialize random number generator */ for (i = 1; i <= 4; ++i) { iseed[i] = (i__1 = iseed[i], abs(i__1)) % 4096; /* L20: */ } if (iseed[4] % 2 != 1) { ++iseed[4]; } /* 2) Set up diagonal of A Compute D according to COND and MODE */ zlatm1_(mode, cond, &irsign, &idist, &iseed[1], &d[1], n, &iinfo); if (iinfo != 0) { *info = 1; return 0; } if (*mode != 0 && abs(*mode) != 6) { /* Scale by DMAX */ temp = z_abs(&d[1]); i__1 = *n; for (i = 2; i <= i__1; ++i) { /* Computing MAX */ d__1 = temp, d__2 = z_abs(&d[i]); temp = max(d__1,d__2); /* L30: */ } if (temp > 0.) { z__1.r = dmax__->r / temp, z__1.i = dmax__->i / temp; alpha.r = z__1.r, alpha.i = z__1.i; } else { *info = 2; return 0; } zscal_(n, &alpha, &d[1], &c__1); } zlaset_("Full", n, n, &c_b1, &c_b1, &a[a_offset], lda); i__1 = *lda + 1; zcopy_(n, &d[1], &c__1, &a[a_offset], &i__1); /* 3) If UPPER='T', set upper triangle of A to random numbers. */ if (iupper != 0) { i__1 = *n; for (jc = 2; jc <= i__1; ++jc) { i__2 = jc - 1; zlarnv_(&idist, &iseed[1], &i__2, &a[jc * a_dim1 + 1]); /* L40: */ } } /* 4) If SIM='T', apply similarity transformation. -1 Transform is X A X , where X = U S V, thus it is U S V A V' (1/S) U' */ if (isim != 0) { /* Compute S (singular values of the eigenvector matrix) according to CONDS and MODES */ dlatm1_(modes, conds, &c__0, &c__0, &iseed[1], &ds[1], n, &iinfo); if (iinfo != 0) { *info = 3; return 0; } /* Multiply by V and V' */ zlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo); if (iinfo != 0) { *info = 4; return 0; } /* Multiply by S and (1/S) */ i__1 = *n; for (j = 1; j <= i__1; ++j) { zdscal_(n, &ds[j], &a[j + a_dim1], lda); if (ds[j] != 0.) { d__1 = 1. / ds[j]; zdscal_(n, &d__1, &a[j * a_dim1 + 1], &c__1); } else { *info = 5; return 0; } /* L50: */ } /* Multiply by U and U' */ zlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo); if (iinfo != 0) { *info = 4; return 0; } } /* 5) Reduce the bandwidth. */ if (*kl < *n - 1) { /* Reduce bandwidth -- kill column */ i__1 = *n - 1; for (jcr = *kl + 1; jcr <= i__1; ++jcr) { ic = jcr - *kl; irows = *n + 1 - jcr; icols = *n + *kl - jcr; zcopy_(&irows, &a[jcr + ic * a_dim1], &c__1, &work[1], &c__1); xnorms.r = work[1].r, xnorms.i = work[1].i; zlarfg_(&irows, &xnorms, &work[2], &c__1, &tau); d_cnjg(&z__1, &tau); tau.r = z__1.r, tau.i = z__1.i; work[1].r = 1., work[1].i = 0.; zlarnd_(&z__1, &c__5, &iseed[1]); alpha.r = z__1.r, alpha.i = z__1.i; zgemv_("C", &irows, &icols, &c_b2, &a[jcr + (ic + 1) * a_dim1], lda, &work[1], &c__1, &c_b1, &work[irows + 1], &c__1); z__1.r = -tau.r, z__1.i = -tau.i; zgerc_(&irows, &icols, &z__1, &work[1], &c__1, &work[irows + 1], & c__1, &a[jcr + (ic + 1) * a_dim1], lda); zgemv_("N", n, &irows, &c_b2, &a[jcr * a_dim1 + 1], lda, &work[1], &c__1, &c_b1, &work[irows + 1], &c__1); d_cnjg(&z__2, &tau); z__1.r = -z__2.r, z__1.i = -z__2.i; zgerc_(n, &irows, &z__1, &work[irows + 1], &c__1, &work[1], &c__1, &a[jcr * a_dim1 + 1], lda); i__2 = jcr + ic * a_dim1; a[i__2].r = xnorms.r, a[i__2].i = xnorms.i; i__2 = irows - 1; zlaset_("Full", &i__2, &c__1, &c_b1, &c_b1, &a[jcr + 1 + ic * a_dim1], lda); i__2 = icols + 1; zscal_(&i__2, &alpha, &a[jcr + ic * a_dim1], lda); d_cnjg(&z__1, &alpha); zscal_(n, &z__1, &a[jcr * a_dim1 + 1], &c__1); /* L60: */ } } else if (*ku < *n - 1) { /* Reduce upper bandwidth -- kill a row at a time. */ i__1 = *n - 1; for (jcr = *ku + 1; jcr <= i__1; ++jcr) { ir = jcr - *ku; irows = *n + *ku - jcr; icols = *n + 1 - jcr; zcopy_(&icols, &a[ir + jcr * a_dim1], lda, &work[1], &c__1); xnorms.r = work[1].r, xnorms.i = work[1].i; zlarfg_(&icols, &xnorms, &work[2], &c__1, &tau); d_cnjg(&z__1, &tau); tau.r = z__1.r, tau.i = z__1.i; work[1].r = 1., work[1].i = 0.; i__2 = icols - 1; zlacgv_(&i__2, &work[2], &c__1); zlarnd_(&z__1, &c__5, &iseed[1]); alpha.r = z__1.r, alpha.i = z__1.i; zgemv_("N", &irows, &icols, &c_b2, &a[ir + 1 + jcr * a_dim1], lda, &work[1], &c__1, &c_b1, &work[icols + 1], &c__1); z__1.r = -tau.r, z__1.i = -tau.i; zgerc_(&irows, &icols, &z__1, &work[icols + 1], &c__1, &work[1], & c__1, &a[ir + 1 + jcr * a_dim1], lda); zgemv_("C", &icols, n, &c_b2, &a[jcr + a_dim1], lda, &work[1], & c__1, &c_b1, &work[icols + 1], &c__1); d_cnjg(&z__2, &tau); z__1.r = -z__2.r, z__1.i = -z__2.i; zgerc_(&icols, n, &z__1, &work[1], &c__1, &work[icols + 1], &c__1, &a[jcr + a_dim1], lda); i__2 = ir + jcr * a_dim1; a[i__2].r = xnorms.r, a[i__2].i = xnorms.i; i__2 = icols - 1; zlaset_("Full", &c__1, &i__2, &c_b1, &c_b1, &a[ir + (jcr + 1) * a_dim1], lda); i__2 = irows + 1; zscal_(&i__2, &alpha, &a[ir + jcr * a_dim1], &c__1); d_cnjg(&z__1, &alpha); zscal_(n, &z__1, &a[jcr + a_dim1], lda); /* L70: */ } } /* Scale the matrix to have norm ANORM */ if (*anorm >= 0.) { temp = zlange_("M", n, n, &a[a_offset], lda, tempa); if (temp > 0.) { ralpha = *anorm / temp; i__1 = *n; for (j = 1; j <= i__1; ++j) { zdscal_(n, &ralpha, &a[j * a_dim1 + 1], &c__1); /* L80: */ } } } return 0; /* End of ZLATME */ } /* zlatme_ */