/* cher2k.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" #include "blaswrap.h" /* Subroutine */ int cher2k_(char *uplo, char *trans, integer *n, integer *k, complex *alpha, complex *a, integer *lda, complex *b, integer *ldb, real *beta, complex *c__, integer *ldc) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7; real r__1; complex q__1, q__2, q__3, q__4, q__5, q__6; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ integer i__, j, l, info; complex temp1, temp2; extern logical lsame_(char *, char *); integer nrowa; logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CHER2K performs one of the hermitian rank 2k operations */ /* C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C, */ /* or */ /* C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C, */ /* where alpha and beta are scalars with beta real, C is an n by n */ /* hermitian matrix and A and B are n by k matrices in the first case */ /* and k by n matrices in the second case. */ /* Arguments */ /* ========== */ /* UPLO - CHARACTER*1. */ /* On entry, UPLO specifies whether the upper or lower */ /* triangular part of the array C is to be referenced as */ /* follows: */ /* UPLO = 'U' or 'u' Only the upper triangular part of C */ /* is to be referenced. */ /* UPLO = 'L' or 'l' Only the lower triangular part of C */ /* is to be referenced. */ /* Unchanged on exit. */ /* TRANS - CHARACTER*1. */ /* On entry, TRANS specifies the operation to be performed as */ /* follows: */ /* TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) + */ /* conjg( alpha )*B*conjg( A' ) + */ /* beta*C. */ /* TRANS = 'C' or 'c' C := alpha*conjg( A' )*B + */ /* conjg( alpha )*conjg( B' )*A + */ /* beta*C. */ /* Unchanged on exit. */ /* N - INTEGER. */ /* On entry, N specifies the order of the matrix C. N must be */ /* at least zero. */ /* Unchanged on exit. */ /* K - INTEGER. */ /* On entry with TRANS = 'N' or 'n', K specifies the number */ /* of columns of the matrices A and B, and on entry with */ /* TRANS = 'C' or 'c', K specifies the number of rows of the */ /* matrices A and B. K must be at least zero. */ /* Unchanged on exit. */ /* ALPHA - COMPLEX . */ /* On entry, ALPHA specifies the scalar alpha. */ /* Unchanged on exit. */ /* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is */ /* k when TRANS = 'N' or 'n', and is n otherwise. */ /* Before entry with TRANS = 'N' or 'n', the leading n by k */ /* part of the array A must contain the matrix A, otherwise */ /* the leading k by n part of the array A must contain the */ /* matrix A. */ /* Unchanged on exit. */ /* LDA - INTEGER. */ /* On entry, LDA specifies the first dimension of A as declared */ /* in the calling (sub) program. When TRANS = 'N' or 'n' */ /* then LDA must be at least max( 1, n ), otherwise LDA must */ /* be at least max( 1, k ). */ /* Unchanged on exit. */ /* B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is */ /* k when TRANS = 'N' or 'n', and is n otherwise. */ /* Before entry with TRANS = 'N' or 'n', the leading n by k */ /* part of the array B must contain the matrix B, otherwise */ /* the leading k by n part of the array B must contain the */ /* matrix B. */ /* Unchanged on exit. */ /* LDB - INTEGER. */ /* On entry, LDB specifies the first dimension of B as declared */ /* in the calling (sub) program. When TRANS = 'N' or 'n' */ /* then LDB must be at least max( 1, n ), otherwise LDB must */ /* be at least max( 1, k ). */ /* Unchanged on exit. */ /* BETA - REAL . */ /* On entry, BETA specifies the scalar beta. */ /* Unchanged on exit. */ /* C - COMPLEX array of DIMENSION ( LDC, n ). */ /* Before entry with UPLO = 'U' or 'u', the leading n by n */ /* upper triangular part of the array C must contain the upper */ /* triangular part of the hermitian matrix and the strictly */ /* lower triangular part of C is not referenced. On exit, the */ /* upper triangular part of the array C is overwritten by the */ /* upper triangular part of the updated matrix. */ /* Before entry with UPLO = 'L' or 'l', the leading n by n */ /* lower triangular part of the array C must contain the lower */ /* triangular part of the hermitian matrix and the strictly */ /* upper triangular part of C is not referenced. On exit, the */ /* lower triangular part of the array C is overwritten by the */ /* lower triangular part of the updated matrix. */ /* Note that the imaginary parts of the diagonal elements need */ /* not be set, they are assumed to be zero, and on exit they */ /* are set to zero. */ /* LDC - INTEGER. */ /* On entry, LDC specifies the first dimension of C as declared */ /* in the calling (sub) program. LDC must be at least */ /* max( 1, n ). */ /* Unchanged on exit. */ /* Level 3 Blas routine. */ /* -- Written on 8-February-1989. */ /* Jack Dongarra, Argonne National Laboratory. */ /* Iain Duff, AERE Harwell. */ /* Jeremy Du Croz, Numerical Algorithms Group Ltd. */ /* Sven Hammarling, Numerical Algorithms Group Ltd. */ /* -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1. */ /* Ed Anderson, Cray Research Inc. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Parameters .. */ /* .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; /* Function Body */ if (lsame_(trans, "N")) { nrowa = *n; } else { nrowa = *k; } upper = lsame_(uplo, "U"); info = 0; if (! upper && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "C")) { info = 2; } else if (*n < 0) { info = 3; } else if (*k < 0) { info = 4; } else if (*lda < max(1,nrowa)) { info = 7; } else if (*ldb < max(1,nrowa)) { info = 9; } else if (*ldc < max(1,*n)) { info = 12; } if (info != 0) { xerbla_("CHER2K", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || (alpha->r == 0.f && alpha->i == 0.f || *k == 0) && *beta == 1.f) { return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0.f && alpha->i == 0.f) { if (upper) { if (*beta == 0.f) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0.f, c__[i__3].i = 0.f; /* L10: */ } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[ i__4].i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L30: */ } i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; r__1 = *beta * c__[i__3].r; c__[i__2].r = r__1, c__[i__2].i = 0.f; /* L40: */ } } } else { if (*beta == 0.f) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0.f, c__[i__3].i = 0.f; /* L50: */ } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; r__1 = *beta * c__[i__3].r; c__[i__2].r = r__1, c__[i__2].i = 0.f; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[ i__4].i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L70: */ } /* L80: */ } } } return 0; } /* Start the operations. */ if (lsame_(trans, "N")) { /* Form C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + */ /* C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.f) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0.f, c__[i__3].i = 0.f; /* L90: */ } } else if (*beta != 1.f) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[ i__4].i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L100: */ } i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; r__1 = *beta * c__[i__3].r; c__[i__2].r = r__1, c__[i__2].i = 0.f; } else { i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; r__1 = c__[i__3].r; c__[i__2].r = r__1, c__[i__2].i = 0.f; } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = j + l * a_dim1; i__4 = j + l * b_dim1; if (a[i__3].r != 0.f || a[i__3].i != 0.f || (b[i__4].r != 0.f || b[i__4].i != 0.f)) { r_cnjg(&q__2, &b[j + l * b_dim1]); q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i = alpha->r * q__2.i + alpha->i * q__2.r; temp1.r = q__1.r, temp1.i = q__1.i; i__3 = j + l * a_dim1; q__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, q__2.i = alpha->r * a[i__3].i + alpha->i * a[ i__3].r; r_cnjg(&q__1, &q__2); temp2.r = q__1.r, temp2.i = q__1.i; i__3 = j - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__ + j * c_dim1; i__5 = i__ + j * c_dim1; i__6 = i__ + l * a_dim1; q__3.r = a[i__6].r * temp1.r - a[i__6].i * temp1.i, q__3.i = a[i__6].r * temp1.i + a[ i__6].i * temp1.r; q__2.r = c__[i__5].r + q__3.r, q__2.i = c__[i__5] .i + q__3.i; i__7 = i__ + l * b_dim1; q__4.r = b[i__7].r * temp2.r - b[i__7].i * temp2.i, q__4.i = b[i__7].r * temp2.i + b[ i__7].i * temp2.r; q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i; c__[i__4].r = q__1.r, c__[i__4].i = q__1.i; /* L110: */ } i__3 = j + j * c_dim1; i__4 = j + j * c_dim1; i__5 = j + l * a_dim1; q__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, q__2.i = a[i__5].r * temp1.i + a[i__5].i * temp1.r; i__6 = j + l * b_dim1; q__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, q__3.i = b[i__6].r * temp2.i + b[i__6].i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = c__[i__4].r + q__1.r; c__[i__3].r = r__1, c__[i__3].i = 0.f; } /* L120: */ } /* L130: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.f) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0.f, c__[i__3].i = 0.f; /* L140: */ } } else if (*beta != 1.f) { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[ i__4].i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L150: */ } i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; r__1 = *beta * c__[i__3].r; c__[i__2].r = r__1, c__[i__2].i = 0.f; } else { i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; r__1 = c__[i__3].r; c__[i__2].r = r__1, c__[i__2].i = 0.f; } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = j + l * a_dim1; i__4 = j + l * b_dim1; if (a[i__3].r != 0.f || a[i__3].i != 0.f || (b[i__4].r != 0.f || b[i__4].i != 0.f)) { r_cnjg(&q__2, &b[j + l * b_dim1]); q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i = alpha->r * q__2.i + alpha->i * q__2.r; temp1.r = q__1.r, temp1.i = q__1.i; i__3 = j + l * a_dim1; q__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, q__2.i = alpha->r * a[i__3].i + alpha->i * a[ i__3].r; r_cnjg(&q__1, &q__2); temp2.r = q__1.r, temp2.i = q__1.i; i__3 = *n; for (i__ = j + 1; i__ <= i__3; ++i__) { i__4 = i__ + j * c_dim1; i__5 = i__ + j * c_dim1; i__6 = i__ + l * a_dim1; q__3.r = a[i__6].r * temp1.r - a[i__6].i * temp1.i, q__3.i = a[i__6].r * temp1.i + a[ i__6].i * temp1.r; q__2.r = c__[i__5].r + q__3.r, q__2.i = c__[i__5] .i + q__3.i; i__7 = i__ + l * b_dim1; q__4.r = b[i__7].r * temp2.r - b[i__7].i * temp2.i, q__4.i = b[i__7].r * temp2.i + b[ i__7].i * temp2.r; q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i; c__[i__4].r = q__1.r, c__[i__4].i = q__1.i; /* L160: */ } i__3 = j + j * c_dim1; i__4 = j + j * c_dim1; i__5 = j + l * a_dim1; q__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, q__2.i = a[i__5].r * temp1.i + a[i__5].i * temp1.r; i__6 = j + l * b_dim1; q__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, q__3.i = b[i__6].r * temp2.i + b[i__6].i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = c__[i__4].r + q__1.r; c__[i__3].r = r__1, c__[i__3].i = 0.f; } /* L170: */ } /* L180: */ } } } else { /* Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + */ /* C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp1.r = 0.f, temp1.i = 0.f; temp2.r = 0.f, temp2.i = 0.f; i__3 = *k; for (l = 1; l <= i__3; ++l) { r_cnjg(&q__3, &a[l + i__ * a_dim1]); i__4 = l + j * b_dim1; q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i, q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4] .r; q__1.r = temp1.r + q__2.r, q__1.i = temp1.i + q__2.i; temp1.r = q__1.r, temp1.i = q__1.i; r_cnjg(&q__3, &b[l + i__ * b_dim1]); i__4 = l + j * a_dim1; q__2.r = q__3.r * a[i__4].r - q__3.i * a[i__4].i, q__2.i = q__3.r * a[i__4].i + q__3.i * a[i__4] .r; q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i; temp2.r = q__1.r, temp2.i = q__1.i; /* L190: */ } if (i__ == j) { if (*beta == 0.f) { i__3 = j + j * c_dim1; q__2.r = alpha->r * temp1.r - alpha->i * temp1.i, q__2.i = alpha->r * temp1.i + alpha->i * temp1.r; r_cnjg(&q__4, alpha); q__3.r = q__4.r * temp2.r - q__4.i * temp2.i, q__3.i = q__4.r * temp2.i + q__4.i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = q__1.r; c__[i__3].r = r__1, c__[i__3].i = 0.f; } else { i__3 = j + j * c_dim1; i__4 = j + j * c_dim1; q__2.r = alpha->r * temp1.r - alpha->i * temp1.i, q__2.i = alpha->r * temp1.i + alpha->i * temp1.r; r_cnjg(&q__4, alpha); q__3.r = q__4.r * temp2.r - q__4.i * temp2.i, q__3.i = q__4.r * temp2.i + q__4.i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = *beta * c__[i__4].r + q__1.r; c__[i__3].r = r__1, c__[i__3].i = 0.f; } } else { if (*beta == 0.f) { i__3 = i__ + j * c_dim1; q__2.r = alpha->r * temp1.r - alpha->i * temp1.i, q__2.i = alpha->r * temp1.i + alpha->i * temp1.r; r_cnjg(&q__4, alpha); q__3.r = q__4.r * temp2.r - q__4.i * temp2.i, q__3.i = q__4.r * temp2.i + q__4.i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; } else { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; q__3.r = *beta * c__[i__4].r, q__3.i = *beta * c__[i__4].i; q__4.r = alpha->r * temp1.r - alpha->i * temp1.i, q__4.i = alpha->r * temp1.i + alpha->i * temp1.r; q__2.r = q__3.r + q__4.r, q__2.i = q__3.i + q__4.i; r_cnjg(&q__6, alpha); q__5.r = q__6.r * temp2.r - q__6.i * temp2.i, q__5.i = q__6.r * temp2.i + q__6.i * temp2.r; q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; } } /* L200: */ } /* L210: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { temp1.r = 0.f, temp1.i = 0.f; temp2.r = 0.f, temp2.i = 0.f; i__3 = *k; for (l = 1; l <= i__3; ++l) { r_cnjg(&q__3, &a[l + i__ * a_dim1]); i__4 = l + j * b_dim1; q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i, q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4] .r; q__1.r = temp1.r + q__2.r, q__1.i = temp1.i + q__2.i; temp1.r = q__1.r, temp1.i = q__1.i; r_cnjg(&q__3, &b[l + i__ * b_dim1]); i__4 = l + j * a_dim1; q__2.r = q__3.r * a[i__4].r - q__3.i * a[i__4].i, q__2.i = q__3.r * a[i__4].i + q__3.i * a[i__4] .r; q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i; temp2.r = q__1.r, temp2.i = q__1.i; /* L220: */ } if (i__ == j) { if (*beta == 0.f) { i__3 = j + j * c_dim1; q__2.r = alpha->r * temp1.r - alpha->i * temp1.i, q__2.i = alpha->r * temp1.i + alpha->i * temp1.r; r_cnjg(&q__4, alpha); q__3.r = q__4.r * temp2.r - q__4.i * temp2.i, q__3.i = q__4.r * temp2.i + q__4.i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = q__1.r; c__[i__3].r = r__1, c__[i__3].i = 0.f; } else { i__3 = j + j * c_dim1; i__4 = j + j * c_dim1; q__2.r = alpha->r * temp1.r - alpha->i * temp1.i, q__2.i = alpha->r * temp1.i + alpha->i * temp1.r; r_cnjg(&q__4, alpha); q__3.r = q__4.r * temp2.r - q__4.i * temp2.i, q__3.i = q__4.r * temp2.i + q__4.i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; r__1 = *beta * c__[i__4].r + q__1.r; c__[i__3].r = r__1, c__[i__3].i = 0.f; } } else { if (*beta == 0.f) { i__3 = i__ + j * c_dim1; q__2.r = alpha->r * temp1.r - alpha->i * temp1.i, q__2.i = alpha->r * temp1.i + alpha->i * temp1.r; r_cnjg(&q__4, alpha); q__3.r = q__4.r * temp2.r - q__4.i * temp2.i, q__3.i = q__4.r * temp2.i + q__4.i * temp2.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; } else { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; q__3.r = *beta * c__[i__4].r, q__3.i = *beta * c__[i__4].i; q__4.r = alpha->r * temp1.r - alpha->i * temp1.i, q__4.i = alpha->r * temp1.i + alpha->i * temp1.r; q__2.r = q__3.r + q__4.r, q__2.i = q__3.i + q__4.i; r_cnjg(&q__6, alpha); q__5.r = q__6.r * temp2.r - q__6.i * temp2.i, q__5.i = q__6.r * temp2.i + q__6.i * temp2.r; q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; } } /* L230: */ } /* L240: */ } } } return 0; /* End of CHER2K. */ } /* cher2k_ */