clagge.c

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems

/*  -- 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 complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__3 = 3;
static integer c__1 = 1;

/* Subroutine */ int clagge_(integer *m, integer *n, integer *kl, integer *ku,
	 real *d, complex *a, integer *lda, integer *iseed, complex *work, 
	integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    doublereal d__1;
    complex q__1;

    /* Builtin functions */
    double c_abs(complex *);
    void c_div(complex *, complex *, complex *);

    /* Local variables */
    static integer i, j;
    extern /* Subroutine */ int cgerc_(integer *, integer *, complex *, 
	    complex *, integer *, complex *, integer *, complex *, integer *),
	     cscal_(integer *, complex *, complex *, integer *), cgemv_(char *
	    , integer *, integer *, complex *, complex *, integer *, complex *
	    , integer *, complex *, complex *, integer *);
    extern real scnrm2_(integer *, complex *, integer *);
    static complex wa, wb;
    extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
    static real wn;
    extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_(
	    integer *, integer *, integer *, complex *);
    static complex 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   
       September 30, 1994   


    Purpose   
    =======   

    CLAGGE generates a complex general m by n matrix A, by pre- and post- 
  
    multiplying a real diagonal matrix D with random unitary matrices:   
    A = U*D*V. The lower and upper bandwidths may then be reduced to   
    kl and ku by additional unitary 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) COMPLEX 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) COMPLEX 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);
	xerbla_("CLAGGE", &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) {
	    i__3 = i + j * a_dim1;
	    a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
	}
/* L20: */
    }
    i__1 = min(*m,*n);
    for (i = 1; i <= i__1; ++i) {
	i__2 = i + i * a_dim1;
	i__3 = i;
	a[i__2].r = d[i__3], a[i__2].i = 0.f;
/* L30: */
    }

/*     pre- and post-multiply A by random unitary matrices */

    for (i = min(*m,*n); i >= 1; --i) {
	if (i < *m) {

/*           generate random reflection */

	    i__1 = *m - i + 1;
	    clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
	    i__1 = *m - i + 1;
	    wn = scnrm2_(&i__1, &work[1], &c__1);
	    d__1 = wn / c_abs(&work[1]);
	    q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
	    wa.r = q__1.r, wa.i = q__1.i;
	    if (wn == 0.f) {
		tau.r = 0.f, tau.i = 0.f;
	    } else {
		q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
		wb.r = q__1.r, wb.i = q__1.i;
		i__1 = *m - i;
		c_div(&q__1, &c_b2, &wb);
		cscal_(&i__1, &q__1, &work[2], &c__1);
		work[1].r = 1.f, work[1].i = 0.f;
		c_div(&q__1, &wb, &wa);
		d__1 = q__1.r;
		tau.r = d__1, tau.i = 0.f;
	    }

/*           multiply A(i:m,i:n) by random reflection from the lef
t */

	    i__1 = *m - i + 1;
	    i__2 = *n - i + 1;
	    cgemv_("Conjugate transpose", &i__1, &i__2, &c_b2, &a[i + i * 
		    a_dim1], lda, &work[1], &c__1, &c_b1, &work[*m + 1], &
		    c__1);
	    i__1 = *m - i + 1;
	    i__2 = *n - i + 1;
	    q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
	    cgerc_(&i__1, &i__2, &q__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;
	    clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
	    i__1 = *n - i + 1;
	    wn = scnrm2_(&i__1, &work[1], &c__1);
	    d__1 = wn / c_abs(&work[1]);
	    q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
	    wa.r = q__1.r, wa.i = q__1.i;
	    if (wn == 0.f) {
		tau.r = 0.f, tau.i = 0.f;
	    } else {
		q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
		wb.r = q__1.r, wb.i = q__1.i;
		i__1 = *n - i;
		c_div(&q__1, &c_b2, &wb);
		cscal_(&i__1, &q__1, &work[2], &c__1);
		work[1].r = 1.f, work[1].i = 0.f;
		c_div(&q__1, &wb, &wa);
		d__1 = q__1.r;
		tau.r = d__1, tau.i = 0.f;
	    }

/*           multiply A(i:m,i:n) by random reflection from the rig
ht */

	    i__1 = *m - i + 1;
	    i__2 = *n - i + 1;
	    cgemv_("No transpose", &i__1, &i__2, &c_b2, &a[i + i * a_dim1], 
		    lda, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
	    i__1 = *m - i + 1;
	    i__2 = *n - i + 1;
	    q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
	    cgerc_(&i__1, &i__2, &q__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 = scnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
		d__1 = wn / c_abs(&a[*kl + i + i * a_dim1]);
		i__2 = *kl + i + i * a_dim1;
		q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
		wa.r = q__1.r, wa.i = q__1.i;
		if (wn == 0.f) {
		    tau.r = 0.f, tau.i = 0.f;
		} else {
		    i__2 = *kl + i + i * a_dim1;
		    q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
		    wb.r = q__1.r, wb.i = q__1.i;
		    i__2 = *m - *kl - i;
		    c_div(&q__1, &c_b2, &wb);
		    cscal_(&i__2, &q__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
		    i__2 = *kl + i + i * a_dim1;
		    a[i__2].r = 1.f, a[i__2].i = 0.f;
		    c_div(&q__1, &wb, &wa);
		    d__1 = q__1.r;
		    tau.r = d__1, tau.i = 0.f;
		}

/*              apply reflection to A(kl+i:m,i+1:n) from the l
eft */

		i__2 = *m - *kl - i + 1;
		i__3 = *n - i;
		cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl + i 
			+ (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &
			c__1, &c_b1, &work[1], &c__1);
		i__2 = *m - *kl - i + 1;
		i__3 = *n - i;
		q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
		cgerc_(&i__2, &i__3, &q__1, &a[*kl + i + i * a_dim1], &c__1, &
			work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
		i__2 = *kl + i + i * a_dim1;
		q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
		a[i__2].r = q__1.r, a[i__2].i = q__1.i;
	    }

/* 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 = scnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
		d__1 = wn / c_abs(&a[i + (*ku + i) * a_dim1]);
		i__2 = i + (*ku + i) * a_dim1;
		q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
		wa.r = q__1.r, wa.i = q__1.i;
		if (wn == 0.f) {
		    tau.r = 0.f, tau.i = 0.f;
		} else {
		    i__2 = i + (*ku + i) * a_dim1;
		    q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
		    wb.r = q__1.r, wb.i = q__1.i;
		    i__2 = *n - *ku - i;
		    c_div(&q__1, &c_b2, &wb);
		    cscal_(&i__2, &q__1, &a[i + (*ku + i + 1) * a_dim1], lda);
		    i__2 = i + (*ku + i) * a_dim1;
		    a[i__2].r = 1.f, a[i__2].i = 0.f;
		    c_div(&q__1, &wb, &wa);
		    d__1 = q__1.r;
		    tau.r = d__1, tau.i = 0.f;
		}

/*              apply reflection to A(i+1:m,ku+i:n) from the r
ight */

		i__2 = *n - *ku - i + 1;
		clacgv_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
		i__2 = *m - i;
		i__3 = *n - *ku - i + 1;
		cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i + 1 + (*ku + 
			i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &
			c_b1, &work[1], &c__1);
		i__2 = *m - i;
		i__3 = *n - *ku - i + 1;
		q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
		cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i + (*ku + i) 
			* a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
		i__2 = i + (*ku + i) * a_dim1;
		q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
		a[i__2].r = q__1.r, a[i__2].i = q__1.i;
	    }
	} 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 = scnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
		d__1 = wn / c_abs(&a[i + (*ku + i) * a_dim1]);
		i__2 = i + (*ku + i) * a_dim1;
		q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
		wa.r = q__1.r, wa.i = q__1.i;
		if (wn == 0.f) {
		    tau.r = 0.f, tau.i = 0.f;
		} else {
		    i__2 = i + (*ku + i) * a_dim1;
		    q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
		    wb.r = q__1.r, wb.i = q__1.i;
		    i__2 = *n - *ku - i;
		    c_div(&q__1, &c_b2, &wb);
		    cscal_(&i__2, &q__1, &a[i + (*ku + i + 1) * a_dim1], lda);
		    i__2 = i + (*ku + i) * a_dim1;
		    a[i__2].r = 1.f, a[i__2].i = 0.f;
		    c_div(&q__1, &wb, &wa);
		    d__1 = q__1.r;
		    tau.r = d__1, tau.i = 0.f;
		}

/*              apply reflection to A(i+1:m,ku+i:n) from the r
ight */

		i__2 = *n - *ku - i + 1;
		clacgv_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
		i__2 = *m - i;
		i__3 = *n - *ku - i + 1;
		cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i + 1 + (*ku + 
			i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &
			c_b1, &work[1], &c__1);
		i__2 = *m - i;
		i__3 = *n - *ku - i + 1;
		q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
		cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i + (*ku + i) 
			* a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
		i__2 = i + (*ku + i) * a_dim1;
		q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
		a[i__2].r = q__1.r, a[i__2].i = q__1.i;
	    }

/* 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 = scnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
		d__1 = wn / c_abs(&a[*kl + i + i * a_dim1]);
		i__2 = *kl + i + i * a_dim1;
		q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
		wa.r = q__1.r, wa.i = q__1.i;
		if (wn == 0.f) {
		    tau.r = 0.f, tau.i = 0.f;
		} else {
		    i__2 = *kl + i + i * a_dim1;
		    q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
		    wb.r = q__1.r, wb.i = q__1.i;
		    i__2 = *m - *kl - i;
		    c_div(&q__1, &c_b2, &wb);
		    cscal_(&i__2, &q__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
		    i__2 = *kl + i + i * a_dim1;
		    a[i__2].r = 1.f, a[i__2].i = 0.f;
		    c_div(&q__1, &wb, &wa);
		    d__1 = q__1.r;
		    tau.r = d__1, tau.i = 0.f;
		}

/*              apply reflection to A(kl+i:m,i+1:n) from the l
eft */

		i__2 = *m - *kl - i + 1;
		i__3 = *n - i;
		cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl + i 
			+ (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &
			c__1, &c_b1, &work[1], &c__1);
		i__2 = *m - *kl - i + 1;
		i__3 = *n - i;
		q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
		cgerc_(&i__2, &i__3, &q__1, &a[*kl + i + i * a_dim1], &c__1, &
			work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
		i__2 = *kl + i + i * a_dim1;
		q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
		a[i__2].r = q__1.r, a[i__2].i = q__1.i;
	    }
	}

	i__2 = *m;
	for (j = *kl + i + 1; j <= i__2; ++j) {
	    i__3 = j + i * a_dim1;
	    a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L50: */
	}

	i__2 = *n;
	for (j = *ku + i + 1; j <= i__2; ++j) {
	    i__3 = i + j * a_dim1;
	    a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L60: */
	}
/* L70: */
    }
    return 0;

/*     End of CLAGGE */

} /* clagge_ */