/* dlattp.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static integer c__2 = 2; static integer c__1 = 1; static doublereal c_b36 = 2.; static doublereal c_b48 = 1.; /* Subroutine */ int dlattp_(integer *imat, char *uplo, char *trans, char * diag, integer *iseed, integer *n, doublereal *a, doublereal *b, doublereal *work, integer *info) { /* System generated locals */ integer i__1, i__2; doublereal d__1, d__2; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); double pow_dd(doublereal *, doublereal *), sqrt(doublereal), d_sign( doublereal *, doublereal *); /* Local variables */ doublereal c__; integer i__, j; doublereal s, t, x, y, z__; integer jc; doublereal ra; integer jj; doublereal rb; integer jl, kl, jr, ku, iy, jx; doublereal ulp, sfac; integer mode; char path[3], dist[1]; doublereal unfl; extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); doublereal rexp; char type__[1]; doublereal texp, star1, plus1, plus2, bscal; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); doublereal tscal, anorm, bnorm, tleft; extern /* Subroutine */ int drotg_(doublereal *, doublereal *, doublereal *, doublereal *); doublereal stemp; logical upper; extern /* Subroutine */ int dlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *), dlabad_(doublereal *, doublereal *); extern doublereal dlamch_(char *); extern integer idamax_(integer *, doublereal *, integer *); extern doublereal dlarnd_(integer *, integer *); char packit[1]; doublereal bignum, cndnum; extern /* Subroutine */ int dlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublereal *, integer *, doublereal *, integer *), dlarnv_(integer *, integer *, integer *, doublereal *); integer jcnext, jcount; doublereal smlnum; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DLATTP generates a triangular test matrix in packed storage. */ /* IMAT and UPLO uniquely specify the properties of the test */ /* matrix, which is returned in the array AP. */ /* 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 (= 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 */ /* DLATMS). Modified on exit. */ /* N (input) INTEGER */ /* The order of the matrix to be generated. */ /* A (output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */ /* The upper or lower triangular matrix A, packed columnwise in */ /* a linear array. The j-th column of A is stored in the array */ /* AP as follows: */ /* if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; */ /* if UPLO = 'L', */ /* AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. */ /* B (output) DOUBLE PRECISION array, dimension (N) */ /* The right hand side vector, if IMAT > 10. */ /* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -k, the k-th argument had an illegal value */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ --work; --b; --a; --iseed; /* Function Body */ s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "TP", (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 DLATB4 to set parameters for SLATMS. */ upper = lsame_(uplo, "U"); if (upper) { dlatb4_(path, imat, n, n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); *(unsigned char *)packit = 'C'; } else { i__1 = -(*imat); dlatb4_(path, &i__1, n, n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); *(unsigned char *)packit = 'R'; } /* IMAT <= 6: Non-unit triangular matrix */ if (*imat <= 6) { dlatms_(n, n, dist, &iseed[1], type__, &b[1], &mode, &cndnum, &anorm, &kl, &ku, packit, &a[1], n, &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) { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { a[jc + i__ - 1] = 0.; /* L10: */ } a[jc + j - 1] = (doublereal) j; jc += j; /* L20: */ } } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { a[jc] = (doublereal) j; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { a[jc + i__ - j] = 0.; /* L30: */ } jc = jc + *n - j + 1; /* 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) { jc = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { a[jc + i__] = 0.; /* L50: */ } a[jc + j] = (doublereal) j; jc += j; /* L60: */ } } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { a[jc] = (doublereal) j; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { a[jc + i__ - j] = 0.; /* L70: */ } jc = jc + *n - j + 1; /* 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). */ star1 = .25; sfac = .5; plus1 = sfac; i__1 = *n; for (j = 1; j <= i__1; j += 2) { plus2 = star1 / plus1; work[j] = plus1; work[*n + j] = star1; if (j + 1 <= *n) { work[j + 1] = plus2; work[*n + j + 1] = 0.; plus1 = star1 / plus2; rexp = dlarnd_(&c__2, &iseed[1]); star1 *= pow_dd(&sfac, &rexp); if (rexp < 0.) { d__1 = 1. - rexp; star1 = -pow_dd(&sfac, &d__1); } else { d__1 = rexp + 1.; star1 = pow_dd(&sfac, &d__1); } } /* L90: */ } x = sqrt(cndnum) - 1. / sqrt(cndnum); if (*n > 2) { y = sqrt(2. / (doublereal) (*n - 2)) * x; } else { y = 0.; } z__ = x * x; if (upper) { /* Set the upper triangle of A with a unit triangular matrix */ /* of known condition number. */ jc = 1; i__1 = *n; for (j = 2; j <= i__1; ++j) { a[jc + 1] = y; if (j > 2) { a[jc + j - 1] = work[j - 2]; } if (j > 3) { a[jc + j - 2] = work[*n + j - 3]; } jc += j; /* L100: */ } jc -= *n; a[jc + 1] = z__; i__1 = *n - 1; for (j = 2; j <= i__1; ++j) { a[jc + j] = y; /* L110: */ } } else { /* Set the lower triangle of A with a unit triangular matrix */ /* of known condition number. */ i__1 = *n - 1; for (i__ = 2; i__ <= i__1; ++i__) { a[i__] = y; /* L120: */ } a[*n] = z__; jc = *n + 1; i__1 = *n - 1; for (j = 2; j <= i__1; ++j) { a[jc + 1] = work[j - 1]; if (j < *n - 1) { a[jc + 2] = work[*n + j - 1]; } a[jc + *n - j] = y; jc = jc + *n - j + 1; /* L130: */ } } /* Fill in the zeros using Givens rotations */ if (upper) { jc = 1; i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { jcnext = jc + j; ra = a[jcnext + j - 1]; rb = 2.; drotg_(&ra, &rb, &c__, &s); /* Multiply by [ c s; -s c] on the left. */ if (*n > j + 1) { jx = jcnext + j; i__2 = *n; for (i__ = j + 2; i__ <= i__2; ++i__) { stemp = c__ * a[jx + j] + s * a[jx + j + 1]; a[jx + j + 1] = -s * a[jx + j] + c__ * a[jx + j + 1]; a[jx + j] = stemp; jx += i__; /* L140: */ } } /* Multiply by [-c -s; s -c] on the right. */ if (j > 1) { i__2 = j - 1; d__1 = -c__; d__2 = -s; drot_(&i__2, &a[jcnext], &c__1, &a[jc], &c__1, &d__1, & d__2); } /* Negate A(J,J+1). */ a[jcnext + j - 1] = -a[jcnext + j - 1]; jc = jcnext; /* L150: */ } } else { jc = 1; i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { jcnext = jc + *n - j + 1; ra = a[jc + 1]; rb = 2.; drotg_(&ra, &rb, &c__, &s); /* Multiply by [ c -s; s c] on the right. */ if (*n > j + 1) { i__2 = *n - j - 1; d__1 = -s; drot_(&i__2, &a[jcnext + 1], &c__1, &a[jc + 2], &c__1, & c__, &d__1); } /* Multiply by [-c s; -s -c] on the left. */ if (j > 1) { jx = 1; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { stemp = -c__ * a[jx + j - i__] + s * a[jx + j - i__ + 1]; a[jx + j - i__ + 1] = -s * a[jx + j - i__] - c__ * a[ jx + j - i__ + 1]; a[jx + j - i__] = stemp; jx = jx + *n - i__ + 1; /* L160: */ } } /* Negate A(J+1,J). */ a[jc + 1] = -a[jc + 1]; jc = jcnext; /* L170: */ } } /* 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) { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { dlarnv_(&c__2, &iseed[1], &j, &a[jc]); a[jc + j - 1] = d_sign(&c_b36, &a[jc + j - 1]); jc += j; /* L180: */ } } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n - j + 1; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc]); a[jc] = d_sign(&c_b36, &a[jc]); jc = jc + *n - j + 1; /* L190: */ } } /* Set the right hand side so that the largest value is BIGNUM. */ dlarnv_(&c__2, &iseed[1], n, &b[1]); iy = idamax_(n, &b[1], &c__1); bnorm = (d__1 = b[iy], abs(d__1)); bscal = bignum / max(1.,bnorm); dscal_(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). */ dlarnv_(&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) { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc]); i__2 = j - 1; dscal_(&i__2, &tscal, &a[jc], &c__1); d__1 = dlarnd_(&c__2, &iseed[1]); a[jc + j - 1] = d_sign(&c_b48, &d__1); jc += j; /* L200: */ } a[*n * (*n + 1) / 2] = smlnum; } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n - j; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc + 1]); i__2 = *n - j; dscal_(&i__2, &tscal, &a[jc + 1], &c__1); d__1 = dlarnd_(&c__2, &iseed[1]); a[jc] = d_sign(&c_b48, &d__1); jc = jc + *n - j + 1; /* L210: */ } a[1] = smlnum; } } 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). */ dlarnv_(&c__2, &iseed[1], n, &b[1]); if (upper) { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc]); d__1 = dlarnd_(&c__2, &iseed[1]); a[jc + j - 1] = d_sign(&c_b48, &d__1); jc += j; /* L220: */ } a[*n * (*n + 1) / 2] = smlnum; } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n - j; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc + 1]); d__1 = dlarnd_(&c__2, &iseed[1]); a[jc] = d_sign(&c_b48, &d__1); jc = jc + *n - j + 1; /* L230: */ } a[1] = smlnum; } } 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; jc = (*n - 1) * *n / 2 + 1; for (j = *n; j >= 1; --j) { i__1 = j - 1; for (i__ = 1; i__ <= i__1; ++i__) { a[jc + i__ - 1] = 0.; /* L240: */ } if (jcount <= 2) { a[jc + j - 1] = smlnum; } else { a[jc + j - 1] = 1.; } ++jcount; if (jcount > 4) { jcount = 1; } jc = jc - j + 1; /* L250: */ } } else { jcount = 1; jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { a[jc + i__ - j] = 0.; /* L260: */ } if (jcount <= 2) { a[jc] = smlnum; } else { a[jc] = 1.; } ++jcount; if (jcount > 4) { jcount = 1; } jc = jc + *n - j + 1; /* L270: */ } } /* Set the right hand side alternately zero and small. */ if (upper) { b[1] = 0.; for (i__ = *n; i__ >= 2; i__ += -2) { b[i__] = 0.; b[i__ - 1] = smlnum; /* L280: */ } } else { b[*n] = 0.; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; i__ += 2) { b[i__] = 0.; b[i__ + 1] = smlnum; /* L290: */ } } } 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); dlarnv_(&c__2, &iseed[1], n, &b[1]); if (upper) { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 2; for (i__ = 1; i__ <= i__2; ++i__) { a[jc + i__ - 1] = 0.; /* L300: */ } if (j > 1) { a[jc + j - 2] = -1.; } a[jc + j - 1] = tscal; jc += j; /* L310: */ } b[*n] = 1.; } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j + 2; i__ <= i__2; ++i__) { a[jc + i__ - j] = 0.; /* L320: */ } if (j < *n) { a[jc + 1] = -1.; } a[jc] = tscal; jc = jc + *n - j + 1; /* L330: */ } b[1] = 1.; } } else if (*imat == 16) { /* Type 16: One zero diagonal element. */ iy = *n / 2 + 1; if (upper) { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { dlarnv_(&c__2, &iseed[1], &j, &a[jc]); if (j != iy) { a[jc + j - 1] = d_sign(&c_b36, &a[jc + j - 1]); } else { a[jc + j - 1] = 0.; } jc += j; /* L340: */ } } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n - j + 1; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc]); if (j != iy) { a[jc] = d_sign(&c_b36, &a[jc]); } else { a[jc] = 0.; } jc = jc + *n - j + 1; /* L350: */ } } dlarnv_(&c__2, &iseed[1], n, &b[1]); dscal_(n, &c_b36, &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 * (*n + 1) / 2; for (j = 1; j <= i__1; ++j) { a[j] = 0.; /* L360: */ } texp = 1.; if (upper) { jc = (*n - 1) * *n / 2 + 1; for (j = *n; j >= 2; j += -2) { a[jc] = -tscal / (doublereal) (*n + 1); a[jc + j - 1] = 1.; b[j] = texp * (1. - ulp); jc = jc - j + 1; a[jc] = -(tscal / (doublereal) (*n + 1)) / (doublereal) (*n + 2); a[jc + j - 2] = 1.; b[j - 1] = texp * (doublereal) (*n * *n + *n - 1); texp *= 2.; jc = jc - j + 2; /* L370: */ } b[1] = (doublereal) (*n + 1) / (doublereal) (*n + 2) * tscal; } else { jc = 1; i__1 = *n - 1; for (j = 1; j <= i__1; j += 2) { a[jc + *n - j] = -tscal / (doublereal) (*n + 1); a[jc] = 1.; b[j] = texp * (1. - ulp); jc = jc + *n - j + 1; a[jc + *n - j - 1] = -(tscal / (doublereal) (*n + 1)) / ( doublereal) (*n + 2); a[jc] = 1.; b[j + 1] = texp * (doublereal) (*n * *n + *n - 1); texp *= 2.; jc = jc + *n - j; /* L380: */ } b[*n] = (doublereal) (*n + 1) / (doublereal) (*n + 2) * tscal; } } 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) { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc]); a[jc + j - 1] = 0.; jc += j; /* L390: */ } } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (j < *n) { i__2 = *n - j; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc + 1]); } a[jc] = 0.; jc = jc + *n - j + 1; /* L400: */ } } /* Set the right hand side so that the largest value is BIGNUM. */ dlarnv_(&c__2, &iseed[1], n, &b[1]); iy = idamax_(n, &b[1], &c__1); bnorm = (d__1 = b[iy], abs(d__1)); bscal = bignum / max(1.,bnorm); dscal_(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. */ /* 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) { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { dlarnv_(&c__2, &iseed[1], &j, &a[jc]); i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { a[jc + i__ - 1] = d_sign(&tleft, &a[jc + i__ - 1]) + tscal * a[jc + i__ - 1]; /* L410: */ } jc += j; /* L420: */ } } else { jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n - j + 1; dlarnv_(&c__2, &iseed[1], &i__2, &a[jc]); i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { a[jc + i__ - j] = d_sign(&tleft, &a[jc + i__ - j]) + tscal * a[jc + i__ - j]; /* L430: */ } jc = jc + *n - j + 1; /* L440: */ } } dlarnv_(&c__2, &iseed[1], n, &b[1]); dscal_(n, &c_b36, &b[1], &c__1); } /* Flip the matrix across its counter-diagonal if the transpose will */ /* be used. */ if (! lsame_(trans, "N")) { if (upper) { jj = 1; jr = *n * (*n + 1) / 2; i__1 = *n / 2; for (j = 1; j <= i__1; ++j) { jl = jj; i__2 = *n - j; for (i__ = j; i__ <= i__2; ++i__) { t = a[jr - i__ + j]; a[jr - i__ + j] = a[jl]; a[jl] = t; jl += i__; /* L450: */ } jj = jj + j + 1; jr -= *n - j + 1; /* L460: */ } } else { jl = 1; jj = *n * (*n + 1) / 2; i__1 = *n / 2; for (j = 1; j <= i__1; ++j) { jr = jj; i__2 = *n - j; for (i__ = j; i__ <= i__2; ++i__) { t = a[jl + i__ - j]; a[jl + i__ - j] = a[jr]; a[jr] = t; jr -= i__; /* L470: */ } jl = jl + *n - j + 1; jj = jj - j - 1; /* L480: */ } } } return 0; /* End of DLATTP */ } /* dlattp_ */