#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static integer c__5 = 5; static integer c__2 = 2; static integer c__1 = 1; static integer c__4 = 4; static doublereal c_b92 = 2.; static integer c_n1 = -1; /* Subroutine */ int zlattr_(integer *imat, char *uplo, char *trans, char * diag, integer *iseed, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, doublecomplex *work, doublereal *rwork, integer * info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2; doublecomplex z__1, z__2; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); void z_div(doublecomplex *, doublecomplex *, doublecomplex *); double pow_dd(doublereal *, doublereal *), sqrt(doublereal); void d_cnjg(doublecomplex *, doublecomplex *); double z_abs(doublecomplex *); /* Local variables */ doublereal c__; integer i__, j; doublecomplex s; doublereal x, y, z__; doublecomplex ra, rb; integer kl, ku, iy; doublereal ulp, sfac; integer mode; char path[3], dist[1]; doublereal unfl, rexp; char type__[1]; doublereal texp; extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublecomplex *); doublecomplex star1, plus1, plus2; doublereal bscal; extern logical lsame_(char *, char *); doublereal tscal, anorm, bnorm, tleft; logical upper; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zrotg_(doublecomplex *, doublecomplex *, doublereal *, doublecomplex *), zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlatb4_( char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *), dlabad_(doublereal *, doublereal *); extern doublereal dlamch_(char *), dlarnd_(integer *, integer *); extern /* Subroutine */ int zdscal_(integer *, doublereal *, doublecomplex *, integer *); doublereal bignum, cndnum; extern /* Subroutine */ int dlarnv_(integer *, integer *, integer *, doublereal *); extern integer izamax_(integer *, doublecomplex *, integer *); extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *, integer *); integer jcount; extern /* Subroutine */ int zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal smlnum; extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *, doublecomplex *); /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZLATTR generates a triangular test matrix in 2-dimensional storage. */ /* IMAT and UPLO uniquely specify the properties of the test matrix, */ /* which is returned in the array A. */ /* Arguments */ /* ========= */ /* IMAT (input) INTEGER */ /* An integer key describing which matrix to generate for this */ /* path. */ /* UPLO (input) CHARACTER*1 */ /* Specifies whether the matrix A will be upper or lower */ /* triangular. */ /* = 'U': Upper triangular */ /* = 'L': Lower triangular */ /* TRANS (input) CHARACTER*1 */ /* Specifies whether the matrix or its transpose will be used. */ /* = 'N': No transpose */ /* = 'T': Transpose */ /* = 'C': Conjugate transpose */ /* DIAG (output) CHARACTER*1 */ /* Specifies whether or not the matrix A is unit triangular. */ /* = 'N': Non-unit triangular */ /* = 'U': Unit triangular */ /* ISEED (input/output) INTEGER array, dimension (4) */ /* The seed vector for the random number generator (used in */ /* ZLATMS). Modified on exit. */ /* N (input) INTEGER */ /* The order of the matrix to be generated. */ /* A (output) COMPLEX*16 array, dimension (LDA,N) */ /* The triangular matrix A. If UPLO = 'U', the leading N x N */ /* upper triangular part of the array A contains the upper */ /* triangular matrix, and the strictly lower triangular part of */ /* A is not referenced. If UPLO = 'L', the leading N x N lower */ /* triangular part of the array A contains the lower triangular */ /* matrix and the strictly upper triangular part of A is not */ /* referenced. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* B (output) COMPLEX*16 array, dimension (N) */ /* The right hand side vector, if IMAT > 10. */ /* WORK (workspace) COMPLEX*16 array, dimension (2*N) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ --iseed; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --b; --work; --rwork; /* Function Body */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); s_copy(path + 1, "TR", (ftnlen)2, (ftnlen)2); unfl = dlamch_("Safe minimum"); ulp = dlamch_("Epsilon") * dlamch_("Base"); smlnum = unfl; bignum = (1. - ulp) / smlnum; dlabad_(&smlnum, &bignum); if (*imat >= 7 && *imat <= 10 || *imat == 18) { *(unsigned char *)diag = 'U'; } else { *(unsigned char *)diag = 'N'; } *info = 0; /* Quick return if N.LE.0. */ if (*n <= 0) { return 0; } /* Call ZLATB4 to set parameters for CLATMS. */ upper = lsame_(uplo, "U"); if (upper) { zlatb4_(path, imat, n, n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); } else { i__1 = -(*imat); zlatb4_(path, &i__1, n, n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); } /* IMAT <= 6: Non-unit triangular matrix */ if (*imat <= 6) { zlatms_(n, n, dist, &iseed[1], type__, &rwork[1], &mode, &cndnum, & anorm, &kl, &ku, "No packing", &a[a_offset], lda, &work[1], info); /* IMAT > 6: Unit triangular matrix */ /* The diagonal is deliberately set to something other than 1. */ /* IMAT = 7: Matrix is the identity */ } else if (*imat == 7) { if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L10: */ } i__2 = j + j * a_dim1; a[i__2].r = (doublereal) j, a[i__2].i = 0.; /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j + j * a_dim1; a[i__2].r = (doublereal) j, a[i__2].i = 0.; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L30: */ } /* L40: */ } } /* IMAT > 7: Non-trivial unit triangular matrix */ /* Generate a unit triangular matrix T with condition CNDNUM by */ /* forming a triangular matrix with known singular values and */ /* filling in the zero entries with Givens rotations. */ } else if (*imat <= 10) { if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L50: */ } i__2 = j + j * a_dim1; a[i__2].r = (doublereal) j, a[i__2].i = 0.; /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j + j * a_dim1; a[i__2].r = (doublereal) j, a[i__2].i = 0.; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L70: */ } /* L80: */ } } /* Since the trace of a unit triangular matrix is 1, the product */ /* of its singular values must be 1. Let s = sqrt(CNDNUM), */ /* x = sqrt(s) - 1/sqrt(s), y = sqrt(2/(n-2))*x, and z = x**2. */ /* The following triangular matrix has singular values s, 1, 1, */ /* ..., 1, 1/s: */ /* 1 y y y ... y y z */ /* 1 0 0 ... 0 0 y */ /* 1 0 ... 0 0 y */ /* . ... . . . */ /* . . . . */ /* 1 0 y */ /* 1 y */ /* 1 */ /* To fill in the zeros, we first multiply by a matrix with small */ /* condition number of the form */ /* 1 0 0 0 0 ... */ /* 1 + * 0 0 ... */ /* 1 + 0 0 0 */ /* 1 + * 0 0 */ /* 1 + 0 0 */ /* ... */ /* 1 + 0 */ /* 1 0 */ /* 1 */ /* Each element marked with a '*' is formed by taking the product */ /* of the adjacent elements marked with '+'. The '*'s can be */ /* chosen freely, and the '+'s are chosen so that the inverse of */ /* T will have elements of the same magnitude as T. If the *'s in */ /* both T and inv(T) have small magnitude, T is well conditioned. */ /* The two offdiagonals of T are stored in WORK. */ /* The product of these two matrices has the form */ /* 1 y y y y y . y y z */ /* 1 + * 0 0 . 0 0 y */ /* 1 + 0 0 . 0 0 y */ /* 1 + * . . . . */ /* 1 + . . . . */ /* . . . . . */ /* . . . . */ /* 1 + y */ /* 1 y */ /* 1 */ /* Now we multiply by Givens rotations, using the fact that */ /* [ c s ] [ 1 w ] [ -c -s ] = [ 1 -w ] */ /* [ -s c ] [ 0 1 ] [ s -c ] [ 0 1 ] */ /* and */ /* [ -c -s ] [ 1 0 ] [ c s ] = [ 1 0 ] */ /* [ s -c ] [ w 1 ] [ -s c ] [ -w 1 ] */ /* where c = w / sqrt(w**2+4) and s = 2 / sqrt(w**2+4). */ zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = z__2.r * .25, z__1.i = z__2.i * .25; star1.r = z__1.r, star1.i = z__1.i; sfac = .5; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = sfac * z__2.r, z__1.i = sfac * z__2.i; plus1.r = z__1.r, plus1.i = z__1.i; i__1 = *n; for (j = 1; j <= i__1; j += 2) { z_div(&z__1, &star1, &plus1); plus2.r = z__1.r, plus2.i = z__1.i; i__2 = j; work[i__2].r = plus1.r, work[i__2].i = plus1.i; i__2 = *n + j; work[i__2].r = star1.r, work[i__2].i = star1.i; if (j + 1 <= *n) { i__2 = j + 1; work[i__2].r = plus2.r, work[i__2].i = plus2.i; i__2 = *n + j + 1; work[i__2].r = 0., work[i__2].i = 0.; z_div(&z__1, &star1, &plus2); plus1.r = z__1.r, plus1.i = z__1.i; rexp = dlarnd_(&c__2, &iseed[1]); if (rexp < 0.) { d__2 = 1. - rexp; d__1 = -pow_dd(&sfac, &d__2); zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = d__1 * z__2.r, z__1.i = d__1 * z__2.i; star1.r = z__1.r, star1.i = z__1.i; } else { d__2 = rexp + 1.; d__1 = pow_dd(&sfac, &d__2); zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = d__1 * z__2.r, z__1.i = d__1 * z__2.i; star1.r = z__1.r, star1.i = z__1.i; } } /* L90: */ } x = sqrt(cndnum) - 1 / sqrt(cndnum); if (*n > 2) { y = sqrt(2. / (*n - 2)) * x; } else { y = 0.; } z__ = x * x; if (upper) { if (*n > 3) { i__1 = *n - 3; i__2 = *lda + 1; zcopy_(&i__1, &work[1], &c__1, &a[a_dim1 * 3 + 2], &i__2); if (*n > 4) { i__1 = *n - 4; i__2 = *lda + 1; zcopy_(&i__1, &work[*n + 1], &c__1, &a[(a_dim1 << 2) + 2], &i__2); } } i__1 = *n - 1; for (j = 2; j <= i__1; ++j) { i__2 = j * a_dim1 + 1; a[i__2].r = y, a[i__2].i = 0.; i__2 = j + *n * a_dim1; a[i__2].r = y, a[i__2].i = 0.; /* L100: */ } i__1 = *n * a_dim1 + 1; a[i__1].r = z__, a[i__1].i = 0.; } else { if (*n > 3) { i__1 = *n - 3; i__2 = *lda + 1; zcopy_(&i__1, &work[1], &c__1, &a[(a_dim1 << 1) + 3], &i__2); if (*n > 4) { i__1 = *n - 4; i__2 = *lda + 1; zcopy_(&i__1, &work[*n + 1], &c__1, &a[(a_dim1 << 1) + 4], &i__2); } } i__1 = *n - 1; for (j = 2; j <= i__1; ++j) { i__2 = j + a_dim1; a[i__2].r = y, a[i__2].i = 0.; i__2 = *n + j * a_dim1; a[i__2].r = y, a[i__2].i = 0.; /* L110: */ } i__1 = *n + a_dim1; a[i__1].r = z__, a[i__1].i = 0.; } /* Fill in the zeros using Givens rotations. */ if (upper) { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = j + (j + 1) * a_dim1; ra.r = a[i__2].r, ra.i = a[i__2].i; rb.r = 2., rb.i = 0.; zrotg_(&ra, &rb, &c__, &s); /* Multiply by [ c s; -conjg(s) c] on the left. */ if (*n > j + 1) { i__2 = *n - j - 1; zrot_(&i__2, &a[j + (j + 2) * a_dim1], lda, &a[j + 1 + (j + 2) * a_dim1], lda, &c__, &s); } /* Multiply by [-c -s; conjg(s) -c] on the right. */ if (j > 1) { i__2 = j - 1; d__1 = -c__; z__1.r = -s.r, z__1.i = -s.i; zrot_(&i__2, &a[(j + 1) * a_dim1 + 1], &c__1, &a[j * a_dim1 + 1], &c__1, &d__1, &z__1); } /* Negate A(J,J+1). */ i__2 = j + (j + 1) * a_dim1; i__3 = j + (j + 1) * a_dim1; z__1.r = -a[i__3].r, z__1.i = -a[i__3].i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L120: */ } } else { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = j + 1 + j * a_dim1; ra.r = a[i__2].r, ra.i = a[i__2].i; rb.r = 2., rb.i = 0.; zrotg_(&ra, &rb, &c__, &s); d_cnjg(&z__1, &s); s.r = z__1.r, s.i = z__1.i; /* Multiply by [ c -s; conjg(s) c] on the right. */ if (*n > j + 1) { i__2 = *n - j - 1; z__1.r = -s.r, z__1.i = -s.i; zrot_(&i__2, &a[j + 2 + (j + 1) * a_dim1], &c__1, &a[j + 2 + j * a_dim1], &c__1, &c__, &z__1); } /* Multiply by [-c s; -conjg(s) -c] on the left. */ if (j > 1) { i__2 = j - 1; d__1 = -c__; zrot_(&i__2, &a[j + a_dim1], lda, &a[j + 1 + a_dim1], lda, &d__1, &s); } /* Negate A(J+1,J). */ i__2 = j + 1 + j * a_dim1; i__3 = j + 1 + j * a_dim1; z__1.r = -a[i__3].r, z__1.i = -a[i__3].i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L130: */ } } /* IMAT > 10: Pathological test cases. These triangular matrices */ /* are badly scaled or badly conditioned, so when used in solving a */ /* triangular system they may cause overflow in the solution vector. */ } else if (*imat == 11) { /* Type 11: Generate a triangular matrix with elements between */ /* -1 and 1. Give the diagonal norm 2 to make it well-conditioned. */ /* Make the right hand side large so that it requires scaling. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]); i__2 = j + j * a_dim1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.; a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L140: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (j < *n) { i__2 = *n - j; zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]); } i__2 = j + j * a_dim1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.; a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L150: */ } } /* Set the right hand side so that the largest value is BIGNUM. */ zlarnv_(&c__2, &iseed[1], n, &b[1]); iy = izamax_(n, &b[1], &c__1); bnorm = z_abs(&b[iy]); bscal = bignum / max(1.,bnorm); zdscal_(n, &bscal, &b[1], &c__1); } else if (*imat == 12) { /* Type 12: Make the first diagonal element in the solve small to */ /* cause immediate overflow when dividing by T(j,j). */ /* In type 12, the offdiagonal elements are small (CNORM(j) < 1). */ zlarnv_(&c__2, &iseed[1], n, &b[1]); /* Computing MAX */ d__1 = 1., d__2 = (doublereal) (*n - 1); tscal = 1. / max(d__1,d__2); if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]); i__2 = j - 1; zdscal_(&i__2, &tscal, &a[j * a_dim1 + 1], &c__1); i__2 = j + j * a_dim1; zlarnd_(&z__1, &c__5, &iseed[1]); a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L160: */ } i__1 = *n + *n * a_dim1; i__2 = *n + *n * a_dim1; z__1.r = smlnum * a[i__2].r, z__1.i = smlnum * a[i__2].i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (j < *n) { i__2 = *n - j; zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]); i__2 = *n - j; zdscal_(&i__2, &tscal, &a[j + 1 + j * a_dim1], &c__1); } i__2 = j + j * a_dim1; zlarnd_(&z__1, &c__5, &iseed[1]); a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L170: */ } i__1 = a_dim1 + 1; i__2 = a_dim1 + 1; z__1.r = smlnum * a[i__2].r, z__1.i = smlnum * a[i__2].i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; } } else if (*imat == 13) { /* Type 13: Make the first diagonal element in the solve small to */ /* cause immediate overflow when dividing by T(j,j). */ /* In type 13, the offdiagonal elements are O(1) (CNORM(j) > 1). */ zlarnv_(&c__2, &iseed[1], n, &b[1]); if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]); i__2 = j + j * a_dim1; zlarnd_(&z__1, &c__5, &iseed[1]); a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L180: */ } i__1 = *n + *n * a_dim1; i__2 = *n + *n * a_dim1; z__1.r = smlnum * a[i__2].r, z__1.i = smlnum * a[i__2].i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (j < *n) { i__2 = *n - j; zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]); } i__2 = j + j * a_dim1; zlarnd_(&z__1, &c__5, &iseed[1]); a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L190: */ } i__1 = a_dim1 + 1; i__2 = a_dim1 + 1; z__1.r = smlnum * a[i__2].r, z__1.i = smlnum * a[i__2].i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; } } else if (*imat == 14) { /* Type 14: T is diagonal with small numbers on the diagonal to */ /* make the growth factor underflow, but a small right hand side */ /* chosen so that the solution does not overflow. */ if (upper) { jcount = 1; for (j = *n; j >= 1; --j) { i__1 = j - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + j * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; /* L200: */ } if (jcount <= 2) { i__1 = j + j * a_dim1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; } else { i__1 = j + j * a_dim1; zlarnd_(&z__1, &c__5, &iseed[1]); a[i__1].r = z__1.r, a[i__1].i = z__1.i; } ++jcount; if (jcount > 4) { jcount = 1; } /* L210: */ } } else { jcount = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L220: */ } if (jcount <= 2) { i__2 = j + j * a_dim1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; } else { i__2 = j + j * a_dim1; zlarnd_(&z__1, &c__5, &iseed[1]); a[i__2].r = z__1.r, a[i__2].i = z__1.i; } ++jcount; if (jcount > 4) { jcount = 1; } /* L230: */ } } /* Set the right hand side alternately zero and small. */ if (upper) { b[1].r = 0., b[1].i = 0.; for (i__ = *n; i__ >= 2; i__ += -2) { i__1 = i__; b[i__1].r = 0., b[i__1].i = 0.; i__1 = i__ - 1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i; b[i__1].r = z__1.r, b[i__1].i = z__1.i; /* L240: */ } } else { i__1 = *n; b[i__1].r = 0., b[i__1].i = 0.; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; i__ += 2) { i__2 = i__; b[i__2].r = 0., b[i__2].i = 0.; i__2 = i__ + 1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i; b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L250: */ } } } else if (*imat == 15) { /* Type 15: Make the diagonal elements small to cause gradual */ /* overflow when dividing by T(j,j). To control the amount of */ /* scaling needed, the matrix is bidiagonal. */ /* Computing MAX */ d__1 = 1., d__2 = (doublereal) (*n - 1); texp = 1. / max(d__1,d__2); tscal = pow_dd(&smlnum, &texp); zlarnv_(&c__4, &iseed[1], n, &b[1]); if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 2; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L260: */ } if (j > 1) { i__2 = j - 1 + j * a_dim1; a[i__2].r = -1., a[i__2].i = -1.; } i__2 = j + j * a_dim1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L270: */ } i__1 = *n; b[i__1].r = 1., b[i__1].i = 1.; } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j + 2; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L280: */ } if (j < *n) { i__2 = j + 1 + j * a_dim1; a[i__2].r = -1., a[i__2].i = -1.; } i__2 = j + j * a_dim1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L290: */ } b[1].r = 1., b[1].i = 1.; } } else if (*imat == 16) { /* Type 16: One zero diagonal element. */ iy = *n / 2 + 1; if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]); if (j != iy) { i__2 = j + j * a_dim1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.; a[i__2].r = z__1.r, a[i__2].i = z__1.i; } else { i__2 = j + j * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; } /* L300: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (j < *n) { i__2 = *n - j; zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]); } if (j != iy) { i__2 = j + j * a_dim1; zlarnd_(&z__2, &c__5, &iseed[1]); z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.; a[i__2].r = z__1.r, a[i__2].i = z__1.i; } else { i__2 = j + j * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; } /* L310: */ } } zlarnv_(&c__2, &iseed[1], n, &b[1]); zdscal_(n, &c_b92, &b[1], &c__1); } else if (*imat == 17) { /* Type 17: Make the offdiagonal elements large to cause overflow */ /* when adding a column of T. In the non-transposed case, the */ /* matrix is constructed to cause overflow when adding a column in */ /* every other step. */ tscal = unfl / ulp; tscal = (1. - ulp) / tscal; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L320: */ } /* L330: */ } texp = 1.; if (upper) { for (j = *n; j >= 2; j += -2) { i__1 = j * a_dim1 + 1; d__1 = -tscal / (doublereal) (*n + 1); a[i__1].r = d__1, a[i__1].i = 0.; i__1 = j + j * a_dim1; a[i__1].r = 1., a[i__1].i = 0.; i__1 = j; d__1 = texp * (1. - ulp); b[i__1].r = d__1, b[i__1].i = 0.; i__1 = (j - 1) * a_dim1 + 1; d__1 = -(tscal / (doublereal) (*n + 1)) / (doublereal) (*n + 2); a[i__1].r = d__1, a[i__1].i = 0.; i__1 = j - 1 + (j - 1) * a_dim1; a[i__1].r = 1., a[i__1].i = 0.; i__1 = j - 1; d__1 = texp * (doublereal) (*n * *n + *n - 1); b[i__1].r = d__1, b[i__1].i = 0.; texp *= 2.; /* L340: */ } d__1 = (doublereal) (*n + 1) / (doublereal) (*n + 2) * tscal; b[1].r = d__1, b[1].i = 0.; } else { i__1 = *n - 1; for (j = 1; j <= i__1; j += 2) { i__2 = *n + j * a_dim1; d__1 = -tscal / (doublereal) (*n + 1); a[i__2].r = d__1, a[i__2].i = 0.; i__2 = j + j * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; i__2 = j; d__1 = texp * (1. - ulp); b[i__2].r = d__1, b[i__2].i = 0.; i__2 = *n + (j + 1) * a_dim1; d__1 = -(tscal / (doublereal) (*n + 1)) / (doublereal) (*n + 2); a[i__2].r = d__1, a[i__2].i = 0.; i__2 = j + 1 + (j + 1) * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; i__2 = j + 1; d__1 = texp * (doublereal) (*n * *n + *n - 1); b[i__2].r = d__1, b[i__2].i = 0.; texp *= 2.; /* L350: */ } i__1 = *n; d__1 = (doublereal) (*n + 1) / (doublereal) (*n + 2) * tscal; b[i__1].r = d__1, b[i__1].i = 0.; } } else if (*imat == 18) { /* Type 18: Generate a unit triangular matrix with elements */ /* between -1 and 1, and make the right hand side large so that it */ /* requires scaling. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]); i__2 = j + j * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; /* L360: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (j < *n) { i__2 = *n - j; zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]); } i__2 = j + j * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; /* L370: */ } } /* Set the right hand side so that the largest value is BIGNUM. */ zlarnv_(&c__2, &iseed[1], n, &b[1]); iy = izamax_(n, &b[1], &c__1); bnorm = z_abs(&b[iy]); bscal = bignum / max(1.,bnorm); zdscal_(n, &bscal, &b[1], &c__1); } else if (*imat == 19) { /* Type 19: Generate a triangular matrix with elements between */ /* BIGNUM/(n-1) and BIGNUM so that at least one of the column */ /* norms will exceed BIGNUM. */ /* 1/3/91: ZLATRS no longer can handle this case */ /* Computing MAX */ d__1 = 1., d__2 = (doublereal) (*n - 1); tleft = bignum / max(d__1,d__2); /* Computing MAX */ d__1 = 1., d__2 = (doublereal) (*n); tscal = bignum * ((doublereal) (*n - 1) / max(d__1,d__2)); if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { zlarnv_(&c__5, &iseed[1], &j, &a[j * a_dim1 + 1]); dlarnv_(&c__1, &iseed[1], &j, &rwork[1]); i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; d__1 = tleft + rwork[i__] * tscal; z__1.r = d__1 * a[i__4].r, z__1.i = d__1 * a[i__4].i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L380: */ } /* L390: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n - j + 1; zlarnv_(&c__5, &iseed[1], &i__2, &a[j + j * a_dim1]); i__2 = *n - j + 1; dlarnv_(&c__1, &iseed[1], &i__2, &rwork[1]); i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; d__1 = tleft + rwork[i__ - j + 1] * tscal; z__1.r = d__1 * a[i__4].r, z__1.i = d__1 * a[i__4].i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L400: */ } /* L410: */ } } zlarnv_(&c__2, &iseed[1], n, &b[1]); zdscal_(n, &c_b92, &b[1], &c__1); } /* Flip the matrix if the transpose will be used. */ if (! lsame_(trans, "N")) { if (upper) { i__1 = *n / 2; for (j = 1; j <= i__1; ++j) { i__2 = *n - (j << 1) + 1; zswap_(&i__2, &a[j + j * a_dim1], lda, &a[j + 1 + (*n - j + 1) * a_dim1], &c_n1); /* L420: */ } } else { i__1 = *n / 2; for (j = 1; j <= i__1; ++j) { i__2 = *n - (j << 1) + 1; i__3 = -(*lda); zswap_(&i__2, &a[j + j * a_dim1], &c__1, &a[*n - j + 1 + (j + 1) * a_dim1], &i__3); /* L430: */ } } } return 0; /* End of ZLATTR */ } /* zlattr_ */