#include "blaswrap.h" /* zlatm3.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" /* Double Complex */ VOID zlatm3_(doublecomplex * ret_val, integer *m, integer *n, integer *i__, integer *j, integer *isub, integer *jsub, integer *kl, integer *ku, integer *idist, integer *iseed, doublecomplex *d__, integer *igrade, doublecomplex *dl, doublecomplex *dr, integer *ipvtng, integer *iwork, doublereal *sparse) { /* System generated locals */ integer i__1, i__2; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg( doublecomplex *, doublecomplex *); /* Local variables */ static doublecomplex ctemp; extern doublereal dlaran_(integer *); extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *, integer *); /* -- LAPACK auxiliary test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of dimension (M, N) described by the other paramters. (ISUB,JSUB) is the final position of the (I,J) entry after pivoting according to IPVTNG and IWORK. ZLATM3 is called by the ZLATMR routine in order to build random test matrices. No error checking on parameters is done, because this routine is called in a tight loop by ZLATMR which has already checked the parameters. Use of ZLATM3 differs from CLATM2 in the order in which the random number generator is called to fill in random matrix entries. With ZLATM2, the generator is called to fill in the pivoted matrix columnwise. With ZLATM3, the generator is called to fill in the matrix columnwise, after which it is pivoted. Thus, ZLATM3 can be used to construct random matrices which differ only in their order of rows and/or columns. ZLATM2 is used to construct band matrices while avoiding calling the random number generator for entries outside the band (and therefore generating random numbers in different orders for different pivot orders). The matrix whose (ISUB,JSUB) entry is returned is constructed as follows (this routine only computes one entry): If ISUB is outside (1..M) or JSUB is outside (1..N), return zero (this is convenient for generating matrices in band format). Generate a matrix A with random entries of distribution IDIST. Set the diagonal to D. Grade the matrix, if desired, from the left (by DL) and/or from the right (by DR or DL) as specified by IGRADE. Permute, if desired, the rows and/or columns as specified by IPVTNG and IWORK. Band the matrix to have lower bandwidth KL and upper bandwidth KU. Set random entries to zero as specified by SPARSE. Arguments ========= M - INTEGER Number of rows of matrix. Not modified. N - INTEGER Number of columns of matrix. Not modified. I - INTEGER Row of unpivoted entry to be returned. Not modified. J - INTEGER Column of unpivoted entry to be returned. Not modified. ISUB - INTEGER Row of pivoted entry to be returned. Changed on exit. JSUB - INTEGER Column of pivoted entry to be returned. Changed on exit. KL - INTEGER Lower bandwidth. Not modified. KU - INTEGER Upper bandwidth. Not modified. IDIST - INTEGER On entry, IDIST specifies the type of distribution to be used to generate a random matrix . 1 => real and imaginary parts each UNIFORM( 0, 1 ) 2 => real and imaginary parts each UNIFORM( -1, 1 ) 3 => real and imaginary parts each NORMAL( 0, 1 ) 4 => complex number uniform in DISK( 0 , 1 ) Not modified. ISEED - INTEGER array of dimension ( 4 ) Seed for random number generator. Changed on exit. D - COMPLEX*16 array of dimension ( MIN( I , J ) ) Diagonal entries of matrix. Not modified. IGRADE - INTEGER Specifies grading of matrix as follows: 0 => no grading 1 => matrix premultiplied by diag( DL ) 2 => matrix postmultiplied by diag( DR ) 3 => matrix premultiplied by diag( DL ) and postmultiplied by diag( DR ) 4 => matrix premultiplied by diag( DL ) and postmultiplied by inv( diag( DL ) ) 5 => matrix premultiplied by diag( DL ) and postmultiplied by diag( CONJG(DL) ) 6 => matrix premultiplied by diag( DL ) and postmultiplied by diag( DL ) Not modified. DL - COMPLEX*16 array ( I or J, as appropriate ) Left scale factors for grading matrix. Not modified. DR - COMPLEX*16 array ( I or J, as appropriate ) Right scale factors for grading matrix. Not modified. IPVTNG - INTEGER On entry specifies pivoting permutations as follows: 0 => none. 1 => row pivoting. 2 => column pivoting. 3 => full pivoting, i.e., on both sides. Not modified. IWORK - INTEGER array ( I or J, as appropriate ) This array specifies the permutation used. The row (or column) originally in position K is in position IWORK( K ) after pivoting. This differs from IWORK for ZLATM2. Not modified. SPARSE - DOUBLE PRECISION between 0. and 1. On entry specifies the sparsity of the matrix if sparse matix is to be generated. SPARSE should lie between 0 and 1. A uniform ( 0, 1 ) random number x is generated and compared to SPARSE; if x is larger the matrix entry is unchanged and if x is smaller the entry is set to zero. Thus on the average a fraction SPARSE of the entries will be set to zero. Not modified. ===================================================================== ----------------------------------------------------------------------- Check for I and J in range Parameter adjustments */ --iwork; --dr; --dl; --d__; --iseed; /* Function Body */ if (*i__ < 1 || *i__ > *m || *j < 1 || *j > *n) { *isub = *i__; *jsub = *j; ret_val->r = 0., ret_val->i = 0.; return ; } /* Compute subscripts depending on IPVTNG */ if (*ipvtng == 0) { *isub = *i__; *jsub = *j; } else if (*ipvtng == 1) { *isub = iwork[*i__]; *jsub = *j; } else if (*ipvtng == 2) { *isub = *i__; *jsub = iwork[*j]; } else if (*ipvtng == 3) { *isub = iwork[*i__]; *jsub = iwork[*j]; } /* Check for banding */ if (*jsub > *isub + *ku || *jsub < *isub - *kl) { ret_val->r = 0., ret_val->i = 0.; return ; } /* Check for sparsity */ if (*sparse > 0.) { if (dlaran_(&iseed[1]) < *sparse) { ret_val->r = 0., ret_val->i = 0.; return ; } } /* Compute entry and grade it according to IGRADE */ if (*i__ == *j) { i__1 = *i__; ctemp.r = d__[i__1].r, ctemp.i = d__[i__1].i; } else { zlarnd_(&z__1, idist, &iseed[1]); ctemp.r = z__1.r, ctemp.i = z__1.i; } if (*igrade == 1) { i__1 = *i__; z__1.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__1.i = ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r; ctemp.r = z__1.r, ctemp.i = z__1.i; } else if (*igrade == 2) { i__1 = *j; z__1.r = ctemp.r * dr[i__1].r - ctemp.i * dr[i__1].i, z__1.i = ctemp.r * dr[i__1].i + ctemp.i * dr[i__1].r; ctemp.r = z__1.r, ctemp.i = z__1.i; } else if (*igrade == 3) { i__1 = *i__; z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i = ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r; i__2 = *j; z__1.r = z__2.r * dr[i__2].r - z__2.i * dr[i__2].i, z__1.i = z__2.r * dr[i__2].i + z__2.i * dr[i__2].r; ctemp.r = z__1.r, ctemp.i = z__1.i; } else if (*igrade == 4 && *i__ != *j) { i__1 = *i__; z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i = ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r; z_div(&z__1, &z__2, &dl[*j]); ctemp.r = z__1.r, ctemp.i = z__1.i; } else if (*igrade == 5) { i__1 = *i__; z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i = ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r; d_cnjg(&z__3, &dl[*j]); z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; ctemp.r = z__1.r, ctemp.i = z__1.i; } else if (*igrade == 6) { i__1 = *i__; z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i = ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r; i__2 = *j; z__1.r = z__2.r * dl[i__2].r - z__2.i * dl[i__2].i, z__1.i = z__2.r * dl[i__2].i + z__2.i * dl[i__2].r; ctemp.r = z__1.r, ctemp.i = z__1.i; } ret_val->r = ctemp.r, ret_val->i = ctemp.i; return ; /* End of ZLATM3 */ } /* zlatm3_ */