#include "blaswrap.h" /* slatm6.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" /* Table of constant values */ static integer c__1 = 1; static integer c__4 = 4; static integer c__12 = 12; static integer c__8 = 8; static integer c__40 = 40; static integer c__2 = 2; static integer c__3 = 3; static integer c__60 = 60; /* Subroutine */ int slatm6_(integer *type__, integer *n, real *a, integer * lda, real *b, real *x, integer *ldx, real *y, integer *ldy, real * alpha, real *beta, real *wx, real *wy, real *s, real *dif) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer i__, j; static real z__[144] /* was [12][12] */; static integer info; static real work[100]; extern /* Subroutine */ int slakf2_(integer *, integer *, real *, integer *, real *, real *, real *, real *, integer *), sgesvd_(char *, char *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *); /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SLATM6 generates test matrices for the generalized eigenvalue problem, their corresponding right and left eigenvector matrices, and also reciprocal condition numbers for all eigenvalues and the reciprocal condition numbers of eigenvectors corresponding to the 1th and 5th eigenvalues. Test Matrices ============= Two kinds of test matrix pairs (A, B) = inverse(YH) * (Da, Db) * inverse(X) are used in the tests: Type 1: Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 0 2+a 0 0 0 0 1 0 0 0 0 0 3+a 0 0 0 0 1 0 0 0 0 0 4+a 0 0 0 0 1 0 0 0 0 0 5+a , 0 0 0 0 1 , and Type 2: Da = 1 -1 0 0 0 Db = 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1+a 1+b 0 0 0 1 0 0 0 0 -1-b 1+a , 0 0 0 0 1 . In both cases the same inverse(YH) and inverse(X) are used to compute (A, B), giving the exact eigenvectors to (A,B) as (YH, X): YH: = 1 0 -y y -y X = 1 0 -x -x x 0 1 -y y -y 0 1 x -x -x 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1, 0 0 0 0 1 , where a, b, x and y will have all values independently of each other. Arguments ========= TYPE (input) INTEGER Specifies the problem type (see futher details). N (input) INTEGER Size of the matrices A and B. A (output) REAL array, dimension (LDA, N). On exit A N-by-N is initialized according to TYPE. LDA (input) INTEGER The leading dimension of A and of B. B (output) REAL array, dimension (LDA, N). On exit B N-by-N is initialized according to TYPE. X (output) REAL array, dimension (LDX, N). On exit X is the N-by-N matrix of right eigenvectors. LDX (input) INTEGER The leading dimension of X. Y (output) REAL array, dimension (LDY, N). On exit Y is the N-by-N matrix of left eigenvectors. LDY (input) INTEGER The leading dimension of Y. ALPHA (input) REAL BETA (input) REAL Weighting constants for matrix A. WX (input) REAL Constant for right eigenvector matrix. WY (input) REAL Constant for left eigenvector matrix. S (output) REAL array, dimension (N) S(i) is the reciprocal condition number for eigenvalue i. DIF (output) REAL array, dimension (N) DIF(i) is the reciprocal condition number for eigenvector i. ===================================================================== Generate test problem ... (Da, Db) ... Parameter adjustments */ b_dim1 = *lda; b_offset = 1 + b_dim1; b -= b_offset; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; y_dim1 = *ldy; y_offset = 1 + y_dim1; y -= y_offset; --s; --dif; /* Function Body */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (i__ == j) { a[i__ + i__ * a_dim1] = (real) i__ + *alpha; b[i__ + i__ * b_dim1] = 1.f; } else { a[i__ + j * a_dim1] = 0.f; b[i__ + j * b_dim1] = 0.f; } /* L10: */ } /* L20: */ } /* Form X and Y */ slacpy_("F", n, n, &b[b_offset], lda, &y[y_offset], ldy); y[y_dim1 + 3] = -(*wy); y[y_dim1 + 4] = *wy; y[y_dim1 + 5] = -(*wy); y[(y_dim1 << 1) + 3] = -(*wy); y[(y_dim1 << 1) + 4] = *wy; y[(y_dim1 << 1) + 5] = -(*wy); slacpy_("F", n, n, &b[b_offset], lda, &x[x_offset], ldx); x[x_dim1 * 3 + 1] = -(*wx); x[(x_dim1 << 2) + 1] = -(*wx); x[x_dim1 * 5 + 1] = *wx; x[x_dim1 * 3 + 2] = *wx; x[(x_dim1 << 2) + 2] = -(*wx); x[x_dim1 * 5 + 2] = -(*wx); /* Form (A, B) */ b[b_dim1 * 3 + 1] = *wx + *wy; b[b_dim1 * 3 + 2] = -(*wx) + *wy; b[(b_dim1 << 2) + 1] = *wx - *wy; b[(b_dim1 << 2) + 2] = *wx - *wy; b[b_dim1 * 5 + 1] = -(*wx) + *wy; b[b_dim1 * 5 + 2] = *wx + *wy; if (*type__ == 1) { a[a_dim1 * 3 + 1] = *wx * a[a_dim1 + 1] + *wy * a[a_dim1 * 3 + 3]; a[a_dim1 * 3 + 2] = -(*wx) * a[(a_dim1 << 1) + 2] + *wy * a[a_dim1 * 3 + 3]; a[(a_dim1 << 2) + 1] = *wx * a[a_dim1 + 1] - *wy * a[(a_dim1 << 2) + 4]; a[(a_dim1 << 2) + 2] = *wx * a[(a_dim1 << 1) + 2] - *wy * a[(a_dim1 << 2) + 4]; a[a_dim1 * 5 + 1] = -(*wx) * a[a_dim1 + 1] + *wy * a[a_dim1 * 5 + 5]; a[a_dim1 * 5 + 2] = *wx * a[(a_dim1 << 1) + 2] + *wy * a[a_dim1 * 5 + 5]; } else if (*type__ == 2) { a[a_dim1 * 3 + 1] = *wx * 2.f + *wy; a[a_dim1 * 3 + 2] = *wy; a[(a_dim1 << 2) + 1] = -(*wy) * (*alpha + 2.f + *beta); a[(a_dim1 << 2) + 2] = *wx * 2.f - *wy * (*alpha + 2.f + *beta); a[a_dim1 * 5 + 1] = *wx * -2.f + *wy * (*alpha - *beta); a[a_dim1 * 5 + 2] = *wy * (*alpha - *beta); a[a_dim1 + 1] = 1.f; a[(a_dim1 << 1) + 1] = -1.f; a[a_dim1 + 2] = 1.f; a[(a_dim1 << 1) + 2] = a[a_dim1 + 1]; a[a_dim1 * 3 + 3] = 1.f; a[(a_dim1 << 2) + 4] = *alpha + 1.f; a[a_dim1 * 5 + 4] = *beta + 1.f; a[(a_dim1 << 2) + 5] = -a[a_dim1 * 5 + 4]; a[a_dim1 * 5 + 5] = a[(a_dim1 << 2) + 4]; } /* Compute condition numbers */ if (*type__ == 1) { s[1] = 1.f / sqrt((*wy * 3.f * *wy + 1.f) / (a[a_dim1 + 1] * a[a_dim1 + 1] + 1.f)); s[2] = 1.f / sqrt((*wy * 3.f * *wy + 1.f) / (a[(a_dim1 << 1) + 2] * a[ (a_dim1 << 1) + 2] + 1.f)); s[3] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[a_dim1 * 3 + 3] * a[ a_dim1 * 3 + 3] + 1.f)); s[4] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[(a_dim1 << 2) + 4] * a[ (a_dim1 << 2) + 4] + 1.f)); s[5] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[a_dim1 * 5 + 5] * a[ a_dim1 * 5 + 5] + 1.f)); slakf2_(&c__1, &c__4, &a[a_offset], lda, &a[(a_dim1 << 1) + 2], &b[ b_offset], &b[(b_dim1 << 1) + 2], z__, &c__12); sgesvd_("N", "N", &c__8, &c__8, z__, &c__12, work, &work[8], &c__1, & work[9], &c__1, &work[10], &c__40, &info); dif[1] = work[7]; slakf2_(&c__4, &c__1, &a[a_offset], lda, &a[a_dim1 * 5 + 5], &b[ b_offset], &b[b_dim1 * 5 + 5], z__, &c__12); sgesvd_("N", "N", &c__8, &c__8, z__, &c__12, work, &work[8], &c__1, & work[9], &c__1, &work[10], &c__40, &info); dif[5] = work[7]; } else if (*type__ == 2) { s[1] = 1.f / sqrt(*wy * *wy + .33333333333333331f); s[2] = s[1]; s[3] = 1.f / sqrt(*wx * *wx + .5f); s[4] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / ((*alpha + 1.f) * (*alpha + 1.f) + 1.f + (*beta + 1.f) * (*beta + 1.f))); s[5] = s[4]; slakf2_(&c__2, &c__3, &a[a_offset], lda, &a[a_dim1 * 3 + 3], &b[ b_offset], &b[b_dim1 * 3 + 3], z__, &c__12); sgesvd_("N", "N", &c__12, &c__12, z__, &c__12, work, &work[12], &c__1, &work[13], &c__1, &work[14], &c__60, &info); dif[1] = work[11]; slakf2_(&c__3, &c__2, &a[a_offset], lda, &a[(a_dim1 << 2) + 4], &b[ b_offset], &b[(b_dim1 << 2) + 4], z__, &c__12); sgesvd_("N", "N", &c__12, &c__12, z__, &c__12, work, &work[12], &c__1, &work[13], &c__1, &work[14], &c__60, &info); dif[5] = work[11]; } return 0; /* End of SLATM6 */ } /* slatm6_ */