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complib/CSVDC(3) -- CSVDC is a subroutine to reduce a complex NxP matrix X by unitary transformations U and V to diagonal form. Th
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On Entry X COMPLEX(LDX,P), where LDX .GE. N. X contains the matrix whose singular value decomposition is to be computed. X is destroyed by CSVDC. LDX INTEGER. LDX is the leading dimension of the array X. N INTEGER. N is the number of columns of the matrix X. P INTEGER. P is the number of rows of the matrix X. LDU INTEGER. LDU is the leading dimension of the array U (see below). LDV INTEGER. LDV is the leading dimension of the array V (see below). WORK COMPLEX(N). WORK is a scratch array. JOB INT... |
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complib/csycon(3) -- estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the fact
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CSYCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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complib/csyr(3) -- perform the symmetric rank 1 operation A := alpha*x*( x' ) + A,
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CSYR performs the symmetric rank 1 operation where alpha is a complex scalar, x is an n element vector and A is an n by n symmetric matrix. |
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complib/csyrfs(3) -- improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefin
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CSYRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution. |
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complib/csysv(3) -- X = B,
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CSYSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are Nby-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = 'U', or A = L * D * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of... |
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complib/csysvx(3) -- to a complex system of linear equations A * X = B,
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CSYSVX uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also provided. |
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complib/csytf2(3) -- the Bunch-Kaufman diagonal pivoting method
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CSYTF2 computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method: A = U*D*U' or A = L*D*L' where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U' is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the unblocked version of the algorithm, calling Level 2 BLAS.... |
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complib/csytrf(3) -- the Bunch-Kaufman diagonal pivoting method
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CSYTRF computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is A = U*D*U**T or A = L*D*L**T where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with with 1- by-1 and 2-by-2 diagonal blocks. This is the blocked version of the algorithm, calling Level 3 BLAS.... |
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complib/csytri(3) -- compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D
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CSYTRI computes the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF. |
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complib/csytrs(3) -- solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U
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CSYTRS solves a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF. |
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complib/ctbcon(3) -- band matrix A, in either the 1-norm or the infinity-norm
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CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). |
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complib/ctbrfs(3) -- provide error bounds and backward error estimates for the solution to a system of linear equations with a tria
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CTBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by CTBTRS or some other means before entering this routine. CTBRFS does not do iterative refinement because doing so cannot improve the backward error. |
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complib/ctbtrs(3) -- or A**H * X = B,
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CTBTRS solves a triangular system of the form where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular. |
