dsytrs.c

/* dsytrs.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 "clapack.h"


/* Table of constant values */

static doublereal c_b7 = -1.;
static integer c__1 = 1;
static doublereal c_b19 = 1.;

/* Subroutine */ int dsytrs_(char *uplo, integer *n, integer *nrhs, 
	doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer *
	ldb, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1;
    doublereal d__1;

    /* Local variables */
    integer j, k;
    doublereal ak, bk;
    integer kp;
    doublereal akm1, bkm1;
    extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    doublereal akm1k;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    extern logical lsame_(char *, char *);
    doublereal denom;
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *), dswap_(integer *, 
	    doublereal *, integer *, doublereal *, integer *);
    logical upper;
    extern /* Subroutine */ int xerbla_(char *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DSYTRS solves a system of linear equations A*X = B with a real */
/*  symmetric matrix A using the factorization A = U*D*U**T or */
/*  A = L*D*L**T computed by DSYTRF. */

/*  Arguments */
/*  ========= */

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the details of the factorization are stored */
/*          as an upper or lower triangular matrix. */
/*          = 'U':  Upper triangular, form is A = U*D*U**T; */
/*          = 'L':  Lower triangular, form is A = L*D*L**T. */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  NRHS    (input) INTEGER */
/*          The number of right hand sides, i.e., the number of columns */
/*          of the matrix B.  NRHS >= 0. */

/*  A       (input) DOUBLE PRECISION array, dimension (LDA,N) */
/*          The block diagonal matrix D and the multipliers used to */
/*          obtain the factor U or L as computed by DSYTRF. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          Details of the interchanges and the block structure of D */
/*          as determined by DSYTRF. */

/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/*          On entry, the right hand side matrix B. */
/*          On exit, the solution matrix X. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B.  LDB >= max(1,N). */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --ipiv;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < max(1,*n)) {
	*info = -5;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DSYTRS", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0 || *nrhs == 0) {
	return 0;
    }

    if (upper) {

/*        Solve A*X = B, where A = U*D*U'. */

/*        First solve U*D*X = B, overwriting B with X. */

/*        K is the main loop index, decreasing from N to 1 in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

	k = *n;
L10:

/*        If K < 1, exit from loop. */

	if (k < 1) {
	    goto L30;
	}

	if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Interchange rows K and IPIV(K). */

	    kp = ipiv[k];
	    if (kp != k) {
		dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
	    }

/*           Multiply by inv(U(K)), where U(K) is the transformation */
/*           stored in column K of A. */

	    i__1 = k - 1;
	    dger_(&i__1, nrhs, &c_b7, &a[k * a_dim1 + 1], &c__1, &b[k + 
		    b_dim1], ldb, &b[b_dim1 + 1], ldb);

/*           Multiply by the inverse of the diagonal block. */

	    d__1 = 1. / a[k + k * a_dim1];
	    dscal_(nrhs, &d__1, &b[k + b_dim1], ldb);
	    --k;
	} else {

/*           2 x 2 diagonal block */

/*           Interchange rows K-1 and -IPIV(K). */

	    kp = -ipiv[k];
	    if (kp != k - 1) {
		dswap_(nrhs, &b[k - 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
	    }

/*           Multiply by inv(U(K)), where U(K) is the transformation */
/*           stored in columns K-1 and K of A. */

	    i__1 = k - 2;
	    dger_(&i__1, nrhs, &c_b7, &a[k * a_dim1 + 1], &c__1, &b[k + 
		    b_dim1], ldb, &b[b_dim1 + 1], ldb);
	    i__1 = k - 2;
	    dger_(&i__1, nrhs, &c_b7, &a[(k - 1) * a_dim1 + 1], &c__1, &b[k - 
		    1 + b_dim1], ldb, &b[b_dim1 + 1], ldb);

/*           Multiply by the inverse of the diagonal block. */

	    akm1k = a[k - 1 + k * a_dim1];
	    akm1 = a[k - 1 + (k - 1) * a_dim1] / akm1k;
	    ak = a[k + k * a_dim1] / akm1k;
	    denom = akm1 * ak - 1.;
	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		bkm1 = b[k - 1 + j * b_dim1] / akm1k;
		bk = b[k + j * b_dim1] / akm1k;
		b[k - 1 + j * b_dim1] = (ak * bkm1 - bk) / denom;
		b[k + j * b_dim1] = (akm1 * bk - bkm1) / denom;
/* L20: */
	    }
	    k += -2;
	}

	goto L10;
L30:

/*        Next solve U'*X = B, overwriting B with X. */

/*        K is the main loop index, increasing from 1 to N in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

	k = 1;
L40:

/*        If K > N, exit from loop. */

	if (k > *n) {
	    goto L50;
	}

	if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Multiply by inv(U'(K)), where U(K) is the transformation */
/*           stored in column K of A. */

	    i__1 = k - 1;
	    dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a[k * 
		    a_dim1 + 1], &c__1, &c_b19, &b[k + b_dim1], ldb);

/*           Interchange rows K and IPIV(K). */

	    kp = ipiv[k];
	    if (kp != k) {
		dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
	    }
	    ++k;
	} else {

/*           2 x 2 diagonal block */

/*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation */
/*           stored in columns K and K+1 of A. */

	    i__1 = k - 1;
	    dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a[k * 
		    a_dim1 + 1], &c__1, &c_b19, &b[k + b_dim1], ldb);
	    i__1 = k - 1;
	    dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a[(k 
		    + 1) * a_dim1 + 1], &c__1, &c_b19, &b[k + 1 + b_dim1], 
		    ldb);

/*           Interchange rows K and -IPIV(K). */

	    kp = -ipiv[k];
	    if (kp != k) {
		dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
	    }
	    k += 2;
	}

	goto L40;
L50:

	;
    } else {

/*        Solve A*X = B, where A = L*D*L'. */

/*        First solve L*D*X = B, overwriting B with X. */

/*        K is the main loop index, increasing from 1 to N in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

	k = 1;
L60:

/*        If K > N, exit from loop. */

	if (k > *n) {
	    goto L80;
	}

	if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Interchange rows K and IPIV(K). */

	    kp = ipiv[k];
	    if (kp != k) {
		dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
	    }

/*           Multiply by inv(L(K)), where L(K) is the transformation */
/*           stored in column K of A. */

	    if (k < *n) {
		i__1 = *n - k;
		dger_(&i__1, nrhs, &c_b7, &a[k + 1 + k * a_dim1], &c__1, &b[k 
			+ b_dim1], ldb, &b[k + 1 + b_dim1], ldb);
	    }

/*           Multiply by the inverse of the diagonal block. */

	    d__1 = 1. / a[k + k * a_dim1];
	    dscal_(nrhs, &d__1, &b[k + b_dim1], ldb);
	    ++k;
	} else {

/*           2 x 2 diagonal block */

/*           Interchange rows K+1 and -IPIV(K). */

	    kp = -ipiv[k];
	    if (kp != k + 1) {
		dswap_(nrhs, &b[k + 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
	    }

/*           Multiply by inv(L(K)), where L(K) is the transformation */
/*           stored in columns K and K+1 of A. */

	    if (k < *n - 1) {
		i__1 = *n - k - 1;
		dger_(&i__1, nrhs, &c_b7, &a[k + 2 + k * a_dim1], &c__1, &b[k 
			+ b_dim1], ldb, &b[k + 2 + b_dim1], ldb);
		i__1 = *n - k - 1;
		dger_(&i__1, nrhs, &c_b7, &a[k + 2 + (k + 1) * a_dim1], &c__1, 
			 &b[k + 1 + b_dim1], ldb, &b[k + 2 + b_dim1], ldb);
	    }

/*           Multiply by the inverse of the diagonal block. */

	    akm1k = a[k + 1 + k * a_dim1];
	    akm1 = a[k + k * a_dim1] / akm1k;
	    ak = a[k + 1 + (k + 1) * a_dim1] / akm1k;
	    denom = akm1 * ak - 1.;
	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		bkm1 = b[k + j * b_dim1] / akm1k;
		bk = b[k + 1 + j * b_dim1] / akm1k;
		b[k + j * b_dim1] = (ak * bkm1 - bk) / denom;
		b[k + 1 + j * b_dim1] = (akm1 * bk - bkm1) / denom;
/* L70: */
	    }
	    k += 2;
	}

	goto L60;
L80:

/*        Next solve L'*X = B, overwriting B with X. */

/*        K is the main loop index, decreasing from N to 1 in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

	k = *n;
L90:

/*        If K < 1, exit from loop. */

	if (k < 1) {
	    goto L100;
	}

	if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Multiply by inv(L'(K)), where L(K) is the transformation */
/*           stored in column K of A. */

	    if (k < *n) {
		i__1 = *n - k;
		dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[k + 1 + b_dim1], 
			ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b19, &b[k + 
			b_dim1], ldb);
	    }

/*           Interchange rows K and IPIV(K). */

	    kp = ipiv[k];
	    if (kp != k) {
		dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
	    }
	    --k;
	} else {

/*           2 x 2 diagonal block */

/*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation */
/*           stored in columns K-1 and K of A. */

	    if (k < *n) {
		i__1 = *n - k;
		dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[k + 1 + b_dim1], 
			ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b19, &b[k + 
			b_dim1], ldb);
		i__1 = *n - k;
		dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[k + 1 + b_dim1], 
			ldb, &a[k + 1 + (k - 1) * a_dim1], &c__1, &c_b19, &b[
			k - 1 + b_dim1], ldb);
	    }

/*           Interchange rows K and -IPIV(K). */

	    kp = -ipiv[k];
	    if (kp != k) {
		dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
	    }
	    k += -2;
	}

	goto L90;
L100:
	;
    }

    return 0;

/*     End of DSYTRS */

} /* dsytrs_ */