/* -- translated by f2c (version 19940927). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include #include "f2c.h" /* Table of constant values */ static real c_b9 = 0.f; static real c_b10 = 1.f; static integer c__3 = 3; static integer c__1 = 1; /* Subroutine */ int slaror_slu(char *side, char *init, integer *m, integer *n, real *a, integer *lda, integer *iseed, real *x, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; real r__1; /* Builtin functions */ double r_sign(real *, real *); /* Local variables */ static integer kbeg, jcol; extern /* Subroutine */ int sger_(integer *, integer *, real *, real *, integer *, real *, integer *, real *, integer *); static integer irow; extern real snrm2_(integer *, real *, integer *); static integer j; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static integer ixfrm, itype, nxfrm; static real xnorm; extern int input_error(char *, int *); static real factor; extern doublereal slarnd_slu(integer *, integer *); extern /* Subroutine */ int slaset_slu(char *, integer *, integer *, real *, real *, real *, integer *); static real xnorms; /* -- LAPACK auxiliary 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 ======= SLAROR pre- or post-multiplies an M by N matrix A by a random orthogonal matrix U, overwriting A. A may optionally be initialized to the identity matrix before multiplying by U. U is generated using the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409). Arguments ========= SIDE (input) CHARACTER*1 Specifies whether A is multiplied on the left or right by U. = 'L': Multiply A on the left (premultiply) by U = 'R': Multiply A on the right (postmultiply) by U' = 'C' or 'T': Multiply A on the left by U and the right by U' (Here, U' means U-transpose.) INIT (input) CHARACTER*1 Specifies whether or not A should be initialized to the identity matrix. = 'I': Initialize A to (a section of) the identity matrix before applying U. = 'N': No initialization. Apply U to the input matrix A. INIT = 'I' may be used to generate square or rectangular orthogonal matrices: For M = N and SIDE = 'L' or 'R', the rows will be orthogonal to each other, as will the columns. If M < N, SIDE = 'R' produces a dense matrix whose rows are orthogonal and whose columns are not, while SIDE = 'L' produces a matrix whose rows are orthogonal, and whose first M columns are orthogonal, and whose remaining columns are zero. If M > N, SIDE = 'L' produces a dense matrix whose columns are orthogonal and whose rows are not, while SIDE = 'R' produces a matrix whose columns are orthogonal, and whose first M rows are orthogonal, and whose remaining rows are zero. M (input) INTEGER The number of rows of A. N (input) INTEGER The number of columns of A. A (input/output) REAL array, dimension (LDA, N) On entry, the array A. On exit, overwritten by U A ( if SIDE = 'L' ), or by A U ( if SIDE = 'R' ), or by U A U' ( if SIDE = 'C' or 'T'). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). ISEED (input/output) INTEGER array, dimension (4) On entry ISEED specifies the seed of the random number generator. The array elements should be between 0 and 4095; if not they will be reduced mod 4096. Also, ISEED(4) must 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 SLAROR to continue the same random number sequence. X (workspace) REAL array, dimension (3*MAX( M, N )) Workspace of length 2*M + N if SIDE = 'L', 2*N + M if SIDE = 'R', 3*N if SIDE = 'C' or 'T'. INFO (output) INTEGER An error flag. It is set to: = 0: normal return < 0: if INFO = -k, the k-th argument had an illegal value = 1: if the random numbers generated by SLARND are bad. ===================================================================== Parameter adjustments */ a_dim1 = *lda; a_offset = a_dim1 + 1; a -= a_offset; --iseed; --x; /* Function Body */ if (*n == 0 || *m == 0) { return 0; } itype = 0; if (strncmp(side, "L", 1)==0) { itype = 1; } else if (strncmp(side, "R", 1)==0) { itype = 2; } else if (strncmp(side, "C", 1)==0 || strncmp(side, "T", 1)==0) { itype = 3; } /* Check for argument errors. */ *info = 0; if (itype == 0) { *info = -1; } else if (*m < 0) { *info = -3; } else if (*n < 0 || itype == 3 && *n != *m) { *info = -4; } else if (*lda < *m) { *info = -6; } if (*info != 0) { i__1 = -(*info); input_error("SLAROR", &i__1); return 0; } if (itype == 1) { nxfrm = *m; } else { nxfrm = *n; } /* Initialize A to the identity matrix if desired */ if (strncmp(init, "I", 1)==0) { slaset_slu("Full", m, n, &c_b9, &c_b10, &a[a_offset], lda); } /* If no rotation possible, multiply by random +/-1 Compute rotation by computing Householder transformations H(2), H(3), ..., H(nhouse) */ i__1 = nxfrm; for (j = 1; j <= i__1; ++j) { x[j] = 0.f; /* L10: */ } i__1 = nxfrm; for (ixfrm = 2; ixfrm <= i__1; ++ixfrm) { kbeg = nxfrm - ixfrm + 1; /* Generate independent normal( 0, 1 ) random numbers */ i__2 = nxfrm; for (j = kbeg; j <= i__2; ++j) { x[j] = slarnd_slu(&c__3, &iseed[1]); /* L20: */ } /* Generate a Householder transformation from the random vector X */ xnorm = snrm2_(&ixfrm, &x[kbeg], &c__1); xnorms = r_sign(&xnorm, &x[kbeg]); r__1 = -(doublereal)x[kbeg]; x[kbeg + nxfrm] = r_sign(&c_b10, &r__1); factor = xnorms * (xnorms + x[kbeg]); if (dabs(factor) < 1e-20f) { *info = 1; input_error("SLAROR", info); return 0; } else { factor = 1.f / factor; } x[kbeg] += xnorms; /* Apply Householder transformation to A */ if (itype == 1 || itype == 3) { /* Apply H(k) from the left. */ sgemv_("T", &ixfrm, n, &c_b10, &a[kbeg + a_dim1], lda, &x[kbeg], & c__1, &c_b9, &x[(nxfrm << 1) + 1], &c__1); r__1 = -(doublereal)factor; sger_(&ixfrm, n, &r__1, &x[kbeg], &c__1, &x[(nxfrm << 1) + 1], & c__1, &a[kbeg + a_dim1], lda); } if (itype == 2 || itype == 3) { /* Apply H(k) from the right. */ sgemv_("N", m, &ixfrm, &c_b10, &a[kbeg * a_dim1 + 1], lda, &x[ kbeg], &c__1, &c_b9, &x[(nxfrm << 1) + 1], &c__1); r__1 = -(doublereal)factor; sger_(m, &ixfrm, &r__1, &x[(nxfrm << 1) + 1], &c__1, &x[kbeg], & c__1, &a[kbeg * a_dim1 + 1], lda); } /* L30: */ } r__1 = slarnd_slu(&c__3, &iseed[1]); x[nxfrm * 2] = r_sign(&c_b10, &r__1); /* Scale the matrix A by D. */ if (itype == 1 || itype == 3) { i__1 = *m; for (irow = 1; irow <= i__1; ++irow) { sscal_(n, &x[nxfrm + irow], &a[irow + a_dim1], lda); /* L40: */ } } if (itype == 2 || itype == 3) { i__1 = *n; for (jcol = 1; jcol <= i__1; ++jcol) { sscal_(m, &x[nxfrm + jcol], &a[jcol * a_dim1 + 1], &c__1); /* L50: */ } } return 0; /* End of SLAROR */ } /* slaror_slu */