al system of linear equations A * X = B, dspsvx dspsvx (3p) - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices dsptrd dsptrd (3p) - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation dsptrf dsptrf (3p) - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method dsptri dsptri (3p) - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF dsptrs dsptrs (3p) - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF dstebz dstebz (3p) - compute the eigenvalues of a symmetric tridiagonal matrix T dstedc dstedc (3p) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method dstein dstein (3p) - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration dsteqr dsteqr (3p) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method dsterf dsterf (3p) - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm dstev dstev (3p) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A dstevd dstevd (3p) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix dstevx dstevx (3p) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A dsvdc dsvdc (3p) - compute the singular value decomposition of a general matrix A. dswap dswap (3p) - Exchange vectors x and y. dsycon dsycon (3p) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF dsyev dsyev (3p) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A dsyevd dsyevd (3p) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A dsyevx dsyevx (3p) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A dsygs2 dsygs2 (3p) - reduce a real symmetric-definite generalized eigenproblem to standard form dsygst dsygst (3p) - reduce a real symmetric-definite generalized eigenproblem to standard form dsygv dsygv (3p) - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x dsymm dsymm (3p) - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C dsymv dsymv (3p) - perform the matrix-vector operation y := alpha*A*x + beta*y dsyr dsyr (3p) - perform the symmetric rank 1 operation A := alpha*x*x' + A dsyr2 dsyr2 (3p) - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A dsyr2k dsyr2k (3p) - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C dsyrfs dsyrfs (3p) - improve 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 dsyrk dsyrk (3p) - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C dsysv dsysv (3p) - compute the solution to a real system of linear equations A * X = B, dsysvx dsysvx (3p) - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B, dsytd2 dsytd2 (3p) - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation dsytf2 dsytf2 (3p) - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method dsytrd dsytrd (3p) - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation dsytrf dsytrf (3p) - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method dsytri dsytri (3p) - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF dsytrs dsytrs (3p) - solve 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 dtbcon dtbcon (3p) - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm dtbmv dtbmv (3p) - perform one of the matrix-vector operations x := A*x or x := A'*x dtbrfs dtbrfs (3p) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix dtbsv dtbsv (3p) - solve one of the systems of equations A*x = b or A'*x = b dtbtrs dtbtrs (3p) - solve a triangular system of the form A * X = B or A**T * X = B, dtgevc dtgevc (3p) - compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) dtgsja dtgsja (3p) - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B dtpcon dtpcon (3p) - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm dtpmv dtpmv (3p) - perform one of the matrix-vector operations x := A*x or x := A'*x dtprfs dtprfs (3p) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix dtpsv dtpsv (3p) - solve one of the systems of equations A*x = b or A'*x = b dtptri dtptri (3p) - compute the inverse of a real upper or lower triangular matrix A stored in packed format dtptrs dtptrs (3p) - solve a triangular system of the form A * X = B or A**T * X = B, dtrco dtrco (3p) - estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. dtrcon dtrcon (3p) - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm dtrdi dtrdi (3p) - compute the determinant and inverse of a triangular matrix A. dtrevc dtrevc (3p) - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T dtrexc dtrexc (3p) - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST dtrmm dtrmm (3p) - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) dtrmv dtrmv (3p) - perform one of the matrix-vector operations x := A*x or x := A'*x dtrrfs dtrrfs (3p) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix dtrsen dtrsen (3p) - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, dtrsl dtrsl (3p) - solve the linear system Ax = b for a triangular matrix A and vectors b and x. dtrsm dtrsm (3p) - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B dtrsna dtrsna (3p) - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal) dtrsv dtrsv (3p) - solve one of the systems of equations A*x = b or A'*x = b dtrsyl dtrsyl (3p) - solve the real Sylvester matrix equation dtrti2 dtrti2 (3p) - compute the inverse of a real upper or lower triangular matrix dtrtri dtrtri (3p) - compute the inverse of a real upper or lower triangular matrix A dtrtrs dtrtrs (3p) - solve a triangular system of the form A * X = B or A**T * X = B, dtzrqf dtzrqf (3p) - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations dzasum dzasum (3p) - Return the sum of the absolute values of a vector x. dznrm2 dznrm2 (3p) - Return the Euclidian norm of a vector. dzsum1 dzsum1 (3p) - take the sum of the absolute values of a complex vector and returns a double precision result ezfftb ezfftb (3p) - computes a perodic sequence from its Fourier coefficients. EZFFTB is a simplified but slower version of RFFTB. ezfftf ezfftf (3p) - computes the Fourier coefficients of a perodic sequence. EZFFTF is a simplified but slower version of RFFTF. ezffti ezffti (3p) - initializes the array WSAVE, which is used in both EZFFTF and EZFFTB. icamax icamax (3p) - Return the index of the element with largest absolute value. icmax1 icmax1 (3p) - find the index of the element whose real part has maximum absolute value idamax idamax (3p) - Return the index of the element with largest absolute value. ilaenv ilaenv (3p) - choose problem-dependent parameters isamax isamax (3p) - Return the index of the element with largest absolute value. izamax izamax (3p) - Return the index of the element with largest absolute value. izmax1 izmax1 (3p) - find the index of the element whose real part has maximum absolute value lapack lapack (3p) - introduction to LAPACK lsame lsame (3p) - case-insensitive comparison of two characters lsamen lsamen (3p) - test if the first N letters of CA are the same as the first N letters of CB, regardless of case rfftb rfftb (3p) - compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. rfftf rfftf (3p) - compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. rffti rffti (3p) - initialize the array xWSAVE, which is used in both xFFTF and xFFTB. sasum sasum (3p) - Return the sum of the absolute values of a vector x. saxpy saxpy (3p) - Compute y := alpha * x + y sbdsqr sbdsqr (3p) - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B scasum scasum (3p) - Return the sum of the absolute values of a vector x. schdc schdc (3p) - compute the Cholesky decomposition of a symmetric positive definite matrix A. schdd schdd (3p) - downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. schex schex (3p) - compute the Cholesky decomposition of a symmetric positive definite matrix A. schud schud (3p) - update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. scnrm2 scnrm2 (3p) - Return the Euclidian norm of a vector. scopy scopy (3p) - Copy x to y scsum1 scsum1 (3p) - take the sum of the absolute values of a complex vector and returns a single precision result sdisna sdisna (3p) - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix sdot sdot (3p) - Compute the dot product of two vectors x and y. sdsdot sdsdot (3p) - Compute a constant plus the double precision dot product of two single precision vectors x and y. second second (3p) - return the user time for a process in seconds. sgbbrd sgbbrd (3p) - reduce