/* Subroutine */ int cgetrf_(integer *m, integer *n, complex *a, integer *lda, integer *ipiv, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; complex q__1; /* Local variables */ integer i__, j, jb, nb; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); integer iinfo; extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *), cgetf2_(integer *, integer *, complex *, integer *, integer *, integer *), xerbla_( char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern /* Subroutine */ int claswp_(integer *, complex *, integer *, integer *, integer *, integer *, integer *); /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* March 2008 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CGETRF computes an LU factorization of a general M-by-N matrix A */ /* using partial pivoting with row interchanges. */ /* The factorization has the form */ /* A = P * L * U */ /* where P is a permutation matrix, L is lower triangular with unit */ /* diagonal elements (lower trapezoidal if m > n), and U is upper */ /* triangular (upper trapezoidal if m < n). */ /* This is the Crout Level 3 BLAS version of the algorithm. */ /* 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. */ /* A (input/output) COMPLEX array, dimension (LDA,N) */ /* On entry, the M-by-N matrix to be factored. */ /* On exit, the factors L and U from the factorization */ /* A = P*L*U; the unit diagonal elements of L are not stored. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,M). */ /* IPIV (output) INTEGER array, dimension (min(M,N)) */ /* The pivot indices; for 1 <= i <= min(M,N), row i of the */ /* matrix was interchanged with row IPIV(i). */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ /* has been completed, but the factor U is exactly */ /* singular, and division by zero will occur if it is used */ /* to solve a system of equations. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*m)) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_("CGETRF", &i__1); return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } /* Determine the block size for this environment. */ nb = ilaenv_(&c__1, "CGETRF", " ", m, n, &c_n1, &c_n1); if (nb <= 1 || nb >= min(*m,*n)) { /* Use unblocked code. */ cgetf2_(m, n, &a[a_offset], lda, &ipiv[1], info); } else { /* Use blocked code. */ i__1 = min(*m,*n); i__2 = nb; for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Computing MIN */ i__3 = min(*m,*n) - j + 1; jb = min(i__3,nb); /* Update current block. */ i__3 = *m - j + 1; i__4 = j - 1; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "No transpose", &i__3, &jb, &i__4, &q__1, & a[j + a_dim1], lda, &a[j * a_dim1 + 1], lda, &c_b1, &a[j + j * a_dim1], lda); /* Factor diagonal and subdiagonal blocks and test for exact */ /* singularity. */ i__3 = *m - j + 1; cgetf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo); /* Adjust INFO and the pivot indices. */ if (*info == 0 && iinfo > 0) { *info = iinfo + j - 1; } /* Computing MIN */ i__4 = *m, i__5 = j + jb - 1; i__3 = min(i__4,i__5); for (i__ = j; i__ <= i__3; ++i__) { ipiv[i__] = j - 1 + ipiv[i__]; /* L10: */ } /* Apply interchanges to column 1:J-1 */ i__3 = j - 1; i__4 = j + jb - 1; claswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1); if (j + jb <= *n) { /* Apply interchanges to column J+JB:N */ i__3 = *n - j - jb + 1; i__4 = j + jb - 1; claswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, & ipiv[1], &c__1); i__3 = *n - j - jb + 1; i__4 = j - 1; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "No transpose", &jb, &i__3, &i__4, & q__1, &a[j + a_dim1], lda, &a[(j + jb) * a_dim1 + 1], lda, &c_b1, &a[j + (j + jb) * a_dim1], lda); /* Compute block row of U. */ i__3 = *n - j - jb + 1; ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &i__3, & c_b1, &a[j + j * a_dim1], lda, &a[j + (j + jb) * a_dim1], lda); } /* L20: */ } } return 0; /* End of CGETRF */ } /* cgetrf_ */
/* Subroutine */ int cgesc2_(integer *n, complex *a, integer *lda, complex * rhs, integer *ipiv, integer *jpiv, real *scale) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; real r__1; complex q__1, q__2, q__3; /* Local variables */ integer i__, j; real eps; complex temp; real bignum; real smlnum; /* -- LAPACK auxiliary routine (version 3.2) -- */ /* November 2006 */ /* Purpose */ /* ======= */ /* CGESC2 solves a system of linear equations */ /* A * X = scale* RHS */ /* with a general N-by-N matrix A using the LU factorization with */ /* complete pivoting computed by CGETC2. */ /* Arguments */ /* ========= */ /* N (input) INTEGER */ /* The number of columns of the matrix A. */ /* A (input) COMPLEX array, dimension (LDA, N) */ /* On entry, the LU part of the factorization of the n-by-n */ /* matrix A computed by CGETC2: A = P * L * U * Q */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1, N). */ /* RHS (input/output) COMPLEX array, dimension N. */ /* On entry, the right hand side vector b. */ /* On exit, the solution vector X. */ /* IPIV (input) INTEGER array, dimension (N). */ /* The pivot indices; for 1 <= i <= N, row i of the */ /* matrix has been interchanged with row IPIV(i). */ /* JPIV (input) INTEGER array, dimension (N). */ /* The pivot indices; for 1 <= j <= N, column j of the */ /* matrix has been interchanged with column JPIV(j). */ /* SCALE (output) REAL */ /* On exit, SCALE contains the scale factor. SCALE is chosen */ /* 0 <= SCALE <= 1 to prevent owerflow in the solution. */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */ /* Umea University, S-901 87 Umea, Sweden. */ /* ===================================================================== */ /* Set constant to control overflow */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --rhs; --ipiv; --jpiv; /* Function Body */ eps = slamch_("P"); smlnum = slamch_("S") / eps; bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); /* Apply permutations IPIV to RHS */ i__1 = *n - 1; claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &ipiv[1], &c__1); /* Solve for L part */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { i__3 = j; i__4 = j; i__5 = j + i__ * a_dim1; i__6 = i__; q__2.r = a[i__5].r * rhs[i__6].r - a[i__5].i * rhs[i__6].i, q__2.i = a[i__5].r * rhs[i__6].i + a[i__5].i * rhs[i__6] .r; q__1.r = rhs[i__4].r - q__2.r, q__1.i = rhs[i__4].i - q__2.i; rhs[i__3].r = q__1.r, rhs[i__3].i = q__1.i; } } /* Solve for U part */ *scale = 1.f; /* Check for scaling */ i__ = icamax_(n, &rhs[1], &c__1); if (smlnum * 2.f * c_abs(&rhs[i__]) > c_abs(&a[*n + *n * a_dim1])) { r__1 = c_abs(&rhs[i__]); q__1.r = .5f / r__1, q__1.i = 0.f / r__1; temp.r = q__1.r, temp.i = q__1.i; cscal_(n, &temp, &rhs[1], &c__1); *scale *= temp.r; } for (i__ = *n; i__ >= 1; --i__) { c_div(&q__1, &c_b13, &a[i__ + i__ * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; i__1 = i__; i__2 = i__; q__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, q__1.i = rhs[ i__2].r * temp.i + rhs[i__2].i * temp.r; rhs[i__1].r = q__1.r, rhs[i__1].i = q__1.i; i__1 = *n; for (j = i__ + 1; j <= i__1; ++j) { i__2 = i__; i__3 = i__; i__4 = j; i__5 = i__ + j * a_dim1; q__3.r = a[i__5].r * temp.r - a[i__5].i * temp.i, q__3.i = a[i__5] .r * temp.i + a[i__5].i * temp.r; q__2.r = rhs[i__4].r * q__3.r - rhs[i__4].i * q__3.i, q__2.i = rhs[i__4].r * q__3.i + rhs[i__4].i * q__3.r; q__1.r = rhs[i__3].r - q__2.r, q__1.i = rhs[i__3].i - q__2.i; rhs[i__2].r = q__1.r, rhs[i__2].i = q__1.i; } } /* Apply permutations JPIV to the solution (RHS) */ i__1 = *n - 1; claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &jpiv[1], &c_n1); return 0; /* End of CGESC2 */ } /* cgesc2_ */
/* Subroutine */ int cgetrs_(char *trans, integer *n, integer *nrhs, complex * a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer * info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; /* Local variables */ logical notran; /* -- LAPACK routine (version 3.2) -- */ /* November 2006 */ /* Purpose */ /* ======= */ /* CGETRS solves a system of linear equations */ /* A * X = B, A**T * X = B, or A**H * X = B */ /* with a general N-by-N matrix A using the LU factorization computed */ /* by CGETRF. */ /* Arguments */ /* ========= */ /* TRANS (input) CHARACTER*1 */ /* Specifies the form of the system of equations: */ /* = 'N': A * X = B (No transpose) */ /* = 'T': A**T * X = B (Transpose) */ /* = 'C': A**H * X = B (Conjugate transpose) */ /* 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) COMPLEX array, dimension (LDA,N) */ /* The factors L and U from the factorization A = P*L*U */ /* as computed by CGETRF. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* IPIV (input) INTEGER array, dimension (N) */ /* The pivot indices from CGETRF; for 1<=i<=N, row i of the */ /* matrix was interchanged with row IPIV(i). */ /* B (input/output) COMPLEX 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 */ /* ===================================================================== */ /* Test the input parameters. */ /* 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; notran = lsame_(trans, "N"); if (! notran && ! lsame_(trans, "T") && ! lsame_( trans, "C")) { *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_("CGETRS", &i__1); return 0; } /* Quick return if possible */ if (*n == 0 || *nrhs == 0) { return 0; } if (notran) { /* Solve A * X = B. */ /* Apply row interchanges to the right hand sides. */ claswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c__1); /* Solve L*X = B, overwriting B with X. */ ctrsm_("Left", "Lower", "No transpose", "Unit", n, nrhs, &c_b1, &a[ a_offset], lda, &b[b_offset], ldb); /* Solve U*X = B, overwriting B with X. */ ctrsm_("Left", "Upper", "No transpose", "Non-unit", n, nrhs, &c_b1, & a[a_offset], lda, &b[b_offset], ldb); } else { /* Solve A**T * X = B or A**H * X = B. */ /* Solve U'*X = B, overwriting B with X. */ ctrsm_("Left", "Upper", trans, "Non-unit", n, nrhs, &c_b1, &a[ a_offset], lda, &b[b_offset], ldb); /* Solve L'*X = B, overwriting B with X. */ ctrsm_("Left", "Lower", trans, "Unit", n, nrhs, &c_b1, &a[a_offset], lda, &b[b_offset], ldb); /* Apply row interchanges to the solution vectors. */ claswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c_n1); } return 0; /* End of CGETRS */ } /* cgetrs_ */
/* Subroutine */ int cgbtrf_(integer *m, integer *n, integer *kl, integer *ku, complex *ab, integer *ldab, integer *ipiv, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6; complex q__1; /* Builtin functions */ void c_div(complex *, complex *, complex *); /* Local variables */ integer i__, j, i2, i3, j2, j3, k2, jb, nb, ii, jj, jm, ip, jp, km, ju, kv, nw; complex temp; extern /* Subroutine */ int cscal_(integer *, complex *, complex *, integer *), cgemm_(char *, char *, integer *, integer *, integer * , complex *, complex *, integer *, complex *, integer *, complex * , complex *, integer *), cgeru_(integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, integer *), ccopy_(integer *, complex *, integer *, complex *, integer *), cswap_(integer *, complex *, integer *, complex *, integer *); #ifdef LAPACK_DISABLE_MEMORY_HOGS complex work13[1] /* was [65][64] */, work31[1] /* was [65][64] */; /** This function uses too much memory, so we stopped allocating the memory * above and assert false here. */ assert(0 && "cgbtrf_ was called. This function allocates too much" " memory and has been disabled."); #else complex work13[4160] /* was [65][64] */, work31[4160] /* was [65][64] */; #endif extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *), cgbtf2_(integer *, integer *, integer *, integer *, complex *, integer *, integer *, integer *); extern integer icamax_(integer *, complex *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern /* Subroutine */ int claswp_(integer *, complex *, integer *, integer *, integer *, integer *, integer *); /* -- LAPACK routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CGBTRF computes an LU factorization of a complex m-by-n band matrix A */ /* using partial pivoting with row interchanges. */ /* This is the blocked version of the algorithm, calling Level 3 BLAS. */ /* 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 subdiagonals within the band of A. KL >= 0. */ /* KU (input) INTEGER */ /* The number of superdiagonals within the band of A. KU >= 0. */ /* AB (input/output) COMPLEX array, dimension (LDAB,N) */ /* On entry, the matrix A in band storage, in rows KL+1 to */ /* 2*KL+KU+1; rows 1 to KL of the array need not be set. */ /* The j-th column of A is stored in the j-th column of the */ /* array AB as follows: */ /* AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) */ /* On exit, details of the factorization: U is stored as an */ /* upper triangular band matrix with KL+KU superdiagonals in */ /* rows 1 to KL+KU+1, and the multipliers used during the */ /* factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */ /* See below for further details. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. */ /* IPIV (output) INTEGER array, dimension (min(M,N)) */ /* The pivot indices; for 1 <= i <= min(M,N), row i of the */ /* matrix was interchanged with row IPIV(i). */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = +i, U(i,i) is exactly zero. The factorization */ /* has been completed, but the factor U is exactly */ /* singular, and division by zero will occur if it is used */ /* to solve a system of equations. */ /* Further Details */ /* =============== */ /* The band storage scheme is illustrated by the following example, when */ /* M = N = 6, KL = 2, KU = 1: */ /* On entry: On exit: */ /* * * * + + + * * * u14 u25 u36 */ /* * * + + + + * * u13 u24 u35 u46 */ /* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 */ /* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 */ /* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * */ /* a31 a42 a53 a64 * * m31 m42 m53 m64 * * */ /* Array elements marked * are not used by the routine; elements marked */ /* + need not be set on entry, but are required by the routine to store */ /* elements of U because of fill-in resulting from the row interchanges. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* KV is the number of superdiagonals in the factor U, allowing for */ /* fill-in */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --ipiv; /* Function Body */ kv = *ku + *kl; /* Test the input parameters. */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*kl < 0) { *info = -3; } else if (*ku < 0) { *info = -4; } else if (*ldab < *kl + kv + 1) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("CGBTRF", &i__1); return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } /* Determine the block size for this environment */ nb = ilaenv_(&c__1, "CGBTRF", " ", m, n, kl, ku); /* The block size must not exceed the limit set by the size of the */ /* local arrays WORK13 and WORK31. */ nb = min(nb,64); if (nb <= 1 || nb > *kl) { /* Use unblocked code */ cgbtf2_(m, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info); } else { /* Use blocked code */ /* Zero the superdiagonal elements of the work array WORK13 */ i__1 = nb; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * 65 - 66; work13[i__3].r = 0.f, work13[i__3].i = 0.f; /* L10: */ } /* L20: */ } /* Zero the subdiagonal elements of the work array WORK31 */ i__1 = nb; for (j = 1; j <= i__1; ++j) { i__2 = nb; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * 65 - 66; work31[i__3].r = 0.f, work31[i__3].i = 0.f; /* L30: */ } /* L40: */ } /* Gaussian elimination with partial pivoting */ /* Set fill-in elements in columns KU+2 to KV to zero */ i__1 = min(kv,*n); for (j = *ku + 2; j <= i__1; ++j) { i__2 = *kl; for (i__ = kv - j + 2; i__ <= i__2; ++i__) { i__3 = i__ + j * ab_dim1; ab[i__3].r = 0.f, ab[i__3].i = 0.f; /* L50: */ } /* L60: */ } /* JU is the index of the last column affected by the current */ /* stage of the factorization */ ju = 1; i__1 = min(*m,*n); i__2 = nb; for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Computing MIN */ i__3 = nb, i__4 = min(*m,*n) - j + 1; jb = min(i__3,i__4); /* The active part of the matrix is partitioned */ /* A11 A12 A13 */ /* A21 A22 A23 */ /* A31 A32 A33 */ /* Here A11, A21 and A31 denote the current block of JB columns */ /* which is about to be factorized. The number of rows in the */ /* partitioning are JB, I2, I3 respectively, and the numbers */ /* of columns are JB, J2, J3. The superdiagonal elements of A13 */ /* and the subdiagonal elements of A31 lie outside the band. */ /* Computing MIN */ i__3 = *kl - jb, i__4 = *m - j - jb + 1; i2 = min(i__3,i__4); /* Computing MIN */ i__3 = jb, i__4 = *m - j - *kl + 1; i3 = min(i__3,i__4); /* J2 and J3 are computed after JU has been updated. */ /* Factorize the current block of JB columns */ i__3 = j + jb - 1; for (jj = j; jj <= i__3; ++jj) { /* Set fill-in elements in column JJ+KV to zero */ if (jj + kv <= *n) { i__4 = *kl; for (i__ = 1; i__ <= i__4; ++i__) { i__5 = i__ + (jj + kv) * ab_dim1; ab[i__5].r = 0.f, ab[i__5].i = 0.f; /* L70: */ } } /* Find pivot and test for singularity. KM is the number of */ /* subdiagonal elements in the current column. */ /* Computing MIN */ i__4 = *kl, i__5 = *m - jj; km = min(i__4,i__5); i__4 = km + 1; jp = icamax_(&i__4, &ab[kv + 1 + jj * ab_dim1], &c__1); ipiv[jj] = jp + jj - j; i__4 = kv + jp + jj * ab_dim1; if (ab[i__4].r != 0.f || ab[i__4].i != 0.f) { /* Computing MAX */ /* Computing MIN */ i__6 = jj + *ku + jp - 1; i__4 = ju, i__5 = min(i__6,*n); ju = max(i__4,i__5); if (jp != 1) { /* Apply interchange to columns J to J+JB-1 */ if (jp + jj - 1 < j + *kl) { i__4 = *ldab - 1; i__5 = *ldab - 1; cswap_(&jb, &ab[kv + 1 + jj - j + j * ab_dim1], & i__4, &ab[kv + jp + jj - j + j * ab_dim1], &i__5); } else { /* The interchange affects columns J to JJ-1 of A31 */ /* which are stored in the work array WORK31 */ i__4 = jj - j; i__5 = *ldab - 1; cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], &i__5, &work31[jp + jj - j - *kl - 1], & c__65); i__4 = j + jb - jj; i__5 = *ldab - 1; i__6 = *ldab - 1; cswap_(&i__4, &ab[kv + 1 + jj * ab_dim1], &i__5, & ab[kv + jp + jj * ab_dim1], &i__6); } } /* Compute multipliers */ c_div(&q__1, &c_b1, &ab[kv + 1 + jj * ab_dim1]); cscal_(&km, &q__1, &ab[kv + 2 + jj * ab_dim1], &c__1); /* Update trailing submatrix within the band and within */ /* the current block. JM is the index of the last column */ /* which needs to be updated. */ /* Computing MIN */ i__4 = ju, i__5 = j + jb - 1; jm = min(i__4,i__5); if (jm > jj) { i__4 = jm - jj; q__1.r = -1.f, q__1.i = -0.f; i__5 = *ldab - 1; i__6 = *ldab - 1; cgeru_(&km, &i__4, &q__1, &ab[kv + 2 + jj * ab_dim1], &c__1, &ab[kv + (jj + 1) * ab_dim1], &i__5, & ab[kv + 1 + (jj + 1) * ab_dim1], &i__6); } } else { /* If pivot is zero, set INFO to the index of the pivot */ /* unless a zero pivot has already been found. */ if (*info == 0) { *info = jj; } } /* Copy current column of A31 into the work array WORK31 */ /* Computing MIN */ i__4 = jj - j + 1; nw = min(i__4,i3); if (nw > 0) { ccopy_(&nw, &ab[kv + *kl + 1 - jj + j + jj * ab_dim1], & c__1, &work31[(jj - j + 1) * 65 - 65], &c__1); } /* L80: */ } if (j + jb <= *n) { /* Apply the row interchanges to the other blocks. */ /* Computing MIN */ i__3 = ju - j + 1; j2 = min(i__3,kv) - jb; /* Computing MAX */ i__3 = 0, i__4 = ju - j - kv + 1; j3 = max(i__3,i__4); /* Use CLASWP to apply the row interchanges to A12, A22, and */ /* A32. */ i__3 = *ldab - 1; claswp_(&j2, &ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__3, & c__1, &jb, &ipiv[j], &c__1); /* Adjust the pivot indices. */ i__3 = j + jb - 1; for (i__ = j; i__ <= i__3; ++i__) { ipiv[i__] = ipiv[i__] + j - 1; /* L90: */ } /* Apply the row interchanges to A13, A23, and A33 */ /* columnwise. */ k2 = j - 1 + jb + j2; i__3 = j3; for (i__ = 1; i__ <= i__3; ++i__) { jj = k2 + i__; i__4 = j + jb - 1; for (ii = j + i__ - 1; ii <= i__4; ++ii) { ip = ipiv[ii]; if (ip != ii) { i__5 = kv + 1 + ii - jj + jj * ab_dim1; temp.r = ab[i__5].r, temp.i = ab[i__5].i; i__5 = kv + 1 + ii - jj + jj * ab_dim1; i__6 = kv + 1 + ip - jj + jj * ab_dim1; ab[i__5].r = ab[i__6].r, ab[i__5].i = ab[i__6].i; i__5 = kv + 1 + ip - jj + jj * ab_dim1; ab[i__5].r = temp.r, ab[i__5].i = temp.i; } /* L100: */ } /* L110: */ } /* Update the relevant part of the trailing submatrix */ if (j2 > 0) { /* Update A12 */ i__3 = *ldab - 1; i__4 = *ldab - 1; ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &j2, &c_b1, &ab[kv + 1 + j * ab_dim1], &i__3, &ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__4); if (i2 > 0) { /* Update A22 */ q__1.r = -1.f, q__1.i = -0.f; i__3 = *ldab - 1; i__4 = *ldab - 1; i__5 = *ldab - 1; cgemm_("No transpose", "No transpose", &i2, &j2, &jb, &q__1, &ab[kv + 1 + jb + j * ab_dim1], &i__3, &ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__4, &c_b1, &ab[kv + 1 + (j + jb) * ab_dim1], & i__5); } if (i3 > 0) { /* Update A32 */ q__1.r = -1.f, q__1.i = -0.f; i__3 = *ldab - 1; i__4 = *ldab - 1; cgemm_("No transpose", "No transpose", &i3, &j2, &jb, &q__1, work31, &c__65, &ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__3, &c_b1, &ab[kv + *kl + 1 - jb + (j + jb) * ab_dim1], &i__4); } } if (j3 > 0) { /* Copy the lower triangle of A13 into the work array */ /* WORK13 */ i__3 = j3; for (jj = 1; jj <= i__3; ++jj) { i__4 = jb; for (ii = jj; ii <= i__4; ++ii) { i__5 = ii + jj * 65 - 66; i__6 = ii - jj + 1 + (jj + j + kv - 1) * ab_dim1; work13[i__5].r = ab[i__6].r, work13[i__5].i = ab[ i__6].i; /* L120: */ } /* L130: */ } /* Update A13 in the work array */ i__3 = *ldab - 1; ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &j3, &c_b1, &ab[kv + 1 + j * ab_dim1], &i__3, work13, & c__65); if (i2 > 0) { /* Update A23 */ q__1.r = -1.f, q__1.i = -0.f; i__3 = *ldab - 1; i__4 = *ldab - 1; cgemm_("No transpose", "No transpose", &i2, &j3, &jb, &q__1, &ab[kv + 1 + jb + j * ab_dim1], &i__3, work13, &c__65, &c_b1, &ab[jb + 1 + (j + kv) * ab_dim1], &i__4); } if (i3 > 0) { /* Update A33 */ q__1.r = -1.f, q__1.i = -0.f; i__3 = *ldab - 1; cgemm_("No transpose", "No transpose", &i3, &j3, &jb, &q__1, work31, &c__65, work13, &c__65, &c_b1, &ab[*kl + 1 + (j + kv) * ab_dim1], &i__3); } /* Copy the lower triangle of A13 back into place */ i__3 = j3; for (jj = 1; jj <= i__3; ++jj) { i__4 = jb; for (ii = jj; ii <= i__4; ++ii) { i__5 = ii - jj + 1 + (jj + j + kv - 1) * ab_dim1; i__6 = ii + jj * 65 - 66; ab[i__5].r = work13[i__6].r, ab[i__5].i = work13[ i__6].i; /* L140: */ } /* L150: */ } } } else { /* Adjust the pivot indices. */ i__3 = j + jb - 1; for (i__ = j; i__ <= i__3; ++i__) { ipiv[i__] = ipiv[i__] + j - 1; /* L160: */ } } /* Partially undo the interchanges in the current block to */ /* restore the upper triangular form of A31 and copy the upper */ /* triangle of A31 back into place */ i__3 = j; for (jj = j + jb - 1; jj >= i__3; --jj) { jp = ipiv[jj] - jj + 1; if (jp != 1) { /* Apply interchange to columns J to JJ-1 */ if (jp + jj - 1 < j + *kl) { /* The interchange does not affect A31 */ i__4 = jj - j; i__5 = *ldab - 1; i__6 = *ldab - 1; cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], & i__5, &ab[kv + jp + jj - j + j * ab_dim1], & i__6); } else { /* The interchange does affect A31 */ i__4 = jj - j; i__5 = *ldab - 1; cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], & i__5, &work31[jp + jj - j - *kl - 1], &c__65); } } /* Copy the current column of A31 back into place */ /* Computing MIN */ i__4 = i3, i__5 = jj - j + 1; nw = min(i__4,i__5); if (nw > 0) { ccopy_(&nw, &work31[(jj - j + 1) * 65 - 65], &c__1, &ab[ kv + *kl + 1 - jj + j + jj * ab_dim1], &c__1); } /* L170: */ } /* L180: */ } } return 0; /* End of CGBTRF */ } /* cgbtrf_ */
/* Subroutine */ int cgesc2_(integer *n, complex *a, integer *lda, complex * rhs, integer *ipiv, integer *jpiv, real *scale) { /* -- LAPACK auxiliary routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CGESC2 solves a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by CGETC2. Arguments ========= N (input) INTEGER The number of columns of the matrix A. A (input) COMPLEX array, dimension (LDA, N) On entry, the LU part of the factorization of the n-by-n matrix A computed by CGETC2: A = P * L * U * Q LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1, N). RHS (input/output) COMPLEX array, dimension N. On entry, the right hand side vector b. On exit, the solution vector X. IPIV (iput) INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i). JPIV (iput) INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j). SCALE (output) REAL On exit, SCALE contains the scale factor. SCALE is chosen 0 <= SCALE <= 1 to prevent owerflow in the solution. Further Details =============== Based on contributions by Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden. ===================================================================== Set constant to control overflow Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static complex c_b13 = {1.f,0.f}; static integer c_n1 = -1; /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; real r__1; complex q__1, q__2, q__3; /* Builtin functions */ double c_abs(complex *); void c_div(complex *, complex *, complex *); /* Local variables */ static complex temp; static integer i__, j; extern /* Subroutine */ int cscal_(integer *, complex *, complex *, integer *), slabad_(real *, real *); extern integer icamax_(integer *, complex *, integer *); extern doublereal slamch_(char *); static real bignum; extern /* Subroutine */ int claswp_(integer *, complex *, integer *, integer *, integer *, integer *, integer *); static real smlnum, eps; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --rhs; --ipiv; --jpiv; /* Function Body */ eps = slamch_("P"); smlnum = slamch_("S") / eps; bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); /* Apply permutations IPIV to RHS */ i__1 = *n - 1; claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &ipiv[1], &c__1); /* Solve for L part */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { i__3 = j; i__4 = j; i__5 = a_subscr(j, i__); i__6 = i__; q__2.r = a[i__5].r * rhs[i__6].r - a[i__5].i * rhs[i__6].i, q__2.i = a[i__5].r * rhs[i__6].i + a[i__5].i * rhs[i__6] .r; q__1.r = rhs[i__4].r - q__2.r, q__1.i = rhs[i__4].i - q__2.i; rhs[i__3].r = q__1.r, rhs[i__3].i = q__1.i; /* L10: */ } /* L20: */ } /* Solve for U part */ *scale = 1.f; /* Check for scaling */ i__ = icamax_(n, &rhs[1], &c__1); if (smlnum * 2.f * c_abs(&rhs[i__]) > c_abs(&a_ref(*n, *n))) { r__1 = c_abs(&rhs[i__]); q__1.r = .5f / r__1, q__1.i = 0.f / r__1; temp.r = q__1.r, temp.i = q__1.i; cscal_(n, &temp, &rhs[1], &c__1); *scale *= temp.r; } for (i__ = *n; i__ >= 1; --i__) { c_div(&q__1, &c_b13, &a_ref(i__, i__)); temp.r = q__1.r, temp.i = q__1.i; i__1 = i__; i__2 = i__; q__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, q__1.i = rhs[ i__2].r * temp.i + rhs[i__2].i * temp.r; rhs[i__1].r = q__1.r, rhs[i__1].i = q__1.i; i__1 = *n; for (j = i__ + 1; j <= i__1; ++j) { i__2 = i__; i__3 = i__; i__4 = j; i__5 = a_subscr(i__, j); q__3.r = a[i__5].r * temp.r - a[i__5].i * temp.i, q__3.i = a[i__5] .r * temp.i + a[i__5].i * temp.r; q__2.r = rhs[i__4].r * q__3.r - rhs[i__4].i * q__3.i, q__2.i = rhs[i__4].r * q__3.i + rhs[i__4].i * q__3.r; q__1.r = rhs[i__3].r - q__2.r, q__1.i = rhs[i__3].i - q__2.i; rhs[i__2].r = q__1.r, rhs[i__2].i = q__1.i; /* L30: */ } /* L40: */ } /* Apply permutations JPIV to the solution (RHS) */ i__1 = *n - 1; claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &jpiv[1], &c_n1); return 0; /* End of CGESC2 */ } /* cgesc2_ */