/* -- translated by f2c (version 19940927). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Table of constant values */ static integer c__3 = 3; static integer c__1 = 1; static real c_b11 = 1.f; static real c_b13 = 0.f; /* Subroutine */ int slagge_slu(integer *m, integer *n, integer *kl, integer *ku, real *d, real *a, integer *lda, integer *iseed, real *work, integer * info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; real r__1; /* Builtin functions */ double r_sign(real *, real *); /* Local variables */ extern /* Subroutine */ int sger_(integer *, integer *, real *, real *, integer *, real *, integer *, real *, integer *); extern real snrm2_(integer *, real *, integer *); static integer i, j; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static real wa, wb, wn; extern /* Subroutine */ int slarnv_slu(integer *, integer *, integer *, real *); extern int input_error(char *, int *); static real tau; /* -- LAPACK auxiliary test routine (version 2.0) Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= SLAGGE generates a real general m by n matrix A, by pre- and post- multiplying a real diagonal matrix D with random orthogonal matrices: A = U*D*V. The lower and upper bandwidths may then be reduced to kl and ku by additional orthogonal transformations. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. KL (input) INTEGER The number of nonzero subdiagonals within the band of A. 0 <= KL <= M-1. KU (input) INTEGER The number of nonzero superdiagonals within the band of A. 0 <= KU <= N-1. D (input) REAL array, dimension (min(M,N)) The diagonal elements of the diagonal matrix D. A (output) REAL array, dimension (LDA,N) The generated m by n matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= M. ISEED (input/output) INTEGER array, dimension (4) On entry, the seed of the random number generator; the array elements must be between 0 and 4095, and ISEED(4) must be odd. On exit, the seed is updated. WORK (workspace) REAL array, dimension (M+N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== Test the input arguments Parameter adjustments */ --d; a_dim1 = *lda; a_offset = a_dim1 + 1; a -= a_offset; --iseed; --work; /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*kl < 0 || *kl > *m - 1) { *info = -3; } else if (*ku < 0 || *ku > *n - 1) { *info = -4; } else if (*lda < max(1,*m)) { *info = -7; } if (*info < 0) { i__1 = -(*info); input_error("SLAGGE", &i__1); return 0; } /* initialize A to diagonal matrix */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i = 1; i <= i__2; ++i) { a[i + j * a_dim1] = 0.f; /* L10: */ } /* L20: */ } i__1 = min(*m,*n); for (i = 1; i <= i__1; ++i) { a[i + i * a_dim1] = d[i]; /* L30: */ } /* pre- and post-multiply A by random orthogonal matrices */ for (i = min(*m,*n); i >= 1; --i) { if (i < *m) { /* generate random reflection */ i__1 = *m - i + 1; slarnv_slu(&c__3, &iseed[1], &i__1, &work[1]); i__1 = *m - i + 1; wn = snrm2_(&i__1, &work[1], &c__1); wa = r_sign(&wn, &work[1]); if (wn == 0.f) { tau = 0.f; } else { wb = work[1] + wa; i__1 = *m - i; r__1 = 1.f / wb; sscal_(&i__1, &r__1, &work[2], &c__1); work[1] = 1.f; tau = wb / wa; } /* multiply A(i:m,i:n) by random reflection from the lef t */ i__1 = *m - i + 1; i__2 = *n - i + 1; sgemv_("Transpose", &i__1, &i__2, &c_b11, &a[i + i * a_dim1], lda, &work[1], &c__1, &c_b13, &work[*m + 1], &c__1); i__1 = *m - i + 1; i__2 = *n - i + 1; r__1 = -(doublereal)tau; sger_(&i__1, &i__2, &r__1, &work[1], &c__1, &work[*m + 1], &c__1, &a[i + i * a_dim1], lda); } if (i < *n) { /* generate random reflection */ i__1 = *n - i + 1; slarnv_slu(&c__3, &iseed[1], &i__1, &work[1]); i__1 = *n - i + 1; wn = snrm2_(&i__1, &work[1], &c__1); wa = r_sign(&wn, &work[1]); if (wn == 0.f) { tau = 0.f; } else { wb = work[1] + wa; i__1 = *n - i; r__1 = 1.f / wb; sscal_(&i__1, &r__1, &work[2], &c__1); work[1] = 1.f; tau = wb / wa; } /* multiply A(i:m,i:n) by random reflection from the rig ht */ i__1 = *m - i + 1; i__2 = *n - i + 1; sgemv_("No transpose", &i__1, &i__2, &c_b11, &a[i + i * a_dim1], lda, &work[1], &c__1, &c_b13, &work[*n + 1], &c__1); i__1 = *m - i + 1; i__2 = *n - i + 1; r__1 = -(doublereal)tau; sger_(&i__1, &i__2, &r__1, &work[*n + 1], &c__1, &work[1], &c__1, &a[i + i * a_dim1], lda); } /* L40: */ } /* Reduce number of subdiagonals to KL and number of superdiagonals to KU Computing MAX */ i__2 = *m - 1 - *kl, i__3 = *n - 1 - *ku; i__1 = max(i__2,i__3); for (i = 1; i <= i__1; ++i) { if (*kl <= *ku) { /* annihilate subdiagonal elements first (necessary if K L = 0) Computing MIN */ i__2 = *m - 1 - *kl; if (i <= min(i__2,*n)) { /* generate reflection to annihilate A(kl+i+1:m,i ) */ i__2 = *m - *kl - i + 1; wn = snrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1); wa = r_sign(&wn, &a[*kl + i + i * a_dim1]); if (wn == 0.f) { tau = 0.f; } else { wb = a[*kl + i + i * a_dim1] + wa; i__2 = *m - *kl - i; r__1 = 1.f / wb; sscal_(&i__2, &r__1, &a[*kl + i + 1 + i * a_dim1], &c__1); a[*kl + i + i * a_dim1] = 1.f; tau = wb / wa; } /* apply reflection to A(kl+i:m,i+1:n) from the l eft */ i__2 = *m - *kl - i + 1; i__3 = *n - i; sgemv_("Transpose", &i__2, &i__3, &c_b11, &a[*kl + i + (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &c__1, & c_b13, &work[1], &c__1); i__2 = *m - *kl - i + 1; i__3 = *n - i; r__1 = -(doublereal)tau; sger_(&i__2, &i__3, &r__1, &a[*kl + i + i * a_dim1], &c__1, & work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda); a[*kl + i + i * a_dim1] = -(doublereal)wa; } /* Computing MIN */ i__2 = *n - 1 - *ku; if (i <= min(i__2,*m)) { /* generate reflection to annihilate A(i,ku+i+1:n ) */ i__2 = *n - *ku - i + 1; wn = snrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda); wa = r_sign(&wn, &a[i + (*ku + i) * a_dim1]); if (wn == 0.f) { tau = 0.f; } else { wb = a[i + (*ku + i) * a_dim1] + wa; i__2 = *n - *ku - i; r__1 = 1.f / wb; sscal_(&i__2, &r__1, &a[i + (*ku + i + 1) * a_dim1], lda); a[i + (*ku + i) * a_dim1] = 1.f; tau = wb / wa; } /* apply reflection to A(i+1:m,ku+i:n) from the r ight */ i__2 = *m - i; i__3 = *n - *ku - i + 1; sgemv_("No transpose", &i__2, &i__3, &c_b11, &a[i + 1 + (*ku + i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &c_b13, &work[1], &c__1); i__2 = *m - i; i__3 = *n - *ku - i + 1; r__1 = -(doublereal)tau; sger_(&i__2, &i__3, &r__1, &work[1], &c__1, &a[i + (*ku + i) * a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda); a[i + (*ku + i) * a_dim1] = -(doublereal)wa; } } else { /* annihilate superdiagonal elements first (necessary if KU = 0) Computing MIN */ i__2 = *n - 1 - *ku; if (i <= min(i__2,*m)) { /* generate reflection to annihilate A(i,ku+i+1:n ) */ i__2 = *n - *ku - i + 1; wn = snrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda); wa = r_sign(&wn, &a[i + (*ku + i) * a_dim1]); if (wn == 0.f) { tau = 0.f; } else { wb = a[i + (*ku + i) * a_dim1] + wa; i__2 = *n - *ku - i; r__1 = 1.f / wb; sscal_(&i__2, &r__1, &a[i + (*ku + i + 1) * a_dim1], lda); a[i + (*ku + i) * a_dim1] = 1.f; tau = wb / wa; } /* apply reflection to A(i+1:m,ku+i:n) from the r ight */ i__2 = *m - i; i__3 = *n - *ku - i + 1; sgemv_("No transpose", &i__2, &i__3, &c_b11, &a[i + 1 + (*ku + i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &c_b13, &work[1], &c__1); i__2 = *m - i; i__3 = *n - *ku - i + 1; r__1 = -(doublereal)tau; sger_(&i__2, &i__3, &r__1, &work[1], &c__1, &a[i + (*ku + i) * a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda); a[i + (*ku + i) * a_dim1] = -(doublereal)wa; } /* Computing MIN */ i__2 = *m - 1 - *kl; if (i <= min(i__2,*n)) { /* generate reflection to annihilate A(kl+i+1:m,i ) */ i__2 = *m - *kl - i + 1; wn = snrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1); wa = r_sign(&wn, &a[*kl + i + i * a_dim1]); if (wn == 0.f) { tau = 0.f; } else { wb = a[*kl + i + i * a_dim1] + wa; i__2 = *m - *kl - i; r__1 = 1.f / wb; sscal_(&i__2, &r__1, &a[*kl + i + 1 + i * a_dim1], &c__1); a[*kl + i + i * a_dim1] = 1.f; tau = wb / wa; } /* apply reflection to A(kl+i:m,i+1:n) from the l eft */ i__2 = *m - *kl - i + 1; i__3 = *n - i; sgemv_("Transpose", &i__2, &i__3, &c_b11, &a[*kl + i + (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &c__1, & c_b13, &work[1], &c__1); i__2 = *m - *kl - i + 1; i__3 = *n - i; r__1 = -(doublereal)tau; sger_(&i__2, &i__3, &r__1, &a[*kl + i + i * a_dim1], &c__1, & work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda); a[*kl + i + i * a_dim1] = -(doublereal)wa; } } i__2 = *m; for (j = *kl + i + 1; j <= i__2; ++j) { a[j + i * a_dim1] = 0.f; /* L50: */ } i__2 = *n; for (j = *ku + i + 1; j <= i__2; ++j) { a[i + j * a_dim1] = 0.f; /* L60: */ } /* L70: */ } return 0; /* End of SLAGGE */ } /* slagge_slu */