asi-triangular matrix T strexc strexc (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 strmm strmm (3p) - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) strmv strmv (3p) - perform one of the matrix-vector operations x := A*x, or x := A'*x strrfs strrfs (3p) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix strsen strsen (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, strsl strsl (3p) - solve the linear system Ax = b for a triangular matrix A and vectors b and x. strsm strsm (3p) - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B strsna strsna (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) strsv strsv (3p) - solve one of the systems of equations A*x = b, or A'*x = b strsyl strsyl (3p) - solve the real Sylvester matrix equation strti2 strti2 (3p) - compute the inverse of a real upper or lower triangular matrix strtri strtri (3p) - compute the inverse of a real upper or lower triangular matrix A strtrs strtrs (3p) - solve a triangular system of the form A * X = B or A**T * X = B, stzrqf stzrqf (3p) - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations vcosqb vcosqb (3p) - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 * N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. vcosqf vcosqf (3p) - compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 * N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. vcosqi vcosqi (3p) - initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. vcosti vcosti (3p) - initialize the array xWSAVE, which is used in xCOST. vdcosqb vdcosqb (3p) - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 * N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. vdcosqf vdcosqf (3p) - compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 * N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. vdcosqi vdcosqi (3p) - initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. vdcosti vdcosti (3p) - initialize the array xWSAVE, which is used in xCOST. vdfftb vdfftb (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. vdfftf vdfftf (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. vdffti vdffti (3p) - initialize the array xWSAVE, which is used in both xFFTF and xFFTB. vdsinqb vdsinqb (3p) - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 * N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. vdsinqf vdsinqf (3p) - compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 * N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. vdsinqi vdsinqi (3p) - initialize the array xWSAVE, which is used in both xSINQF and xSINQB. vdsinti vdsinti (3p) - initialize the array xWSAVE, which is used in subroutine xSINT. vdsinti vdsinti (3p) - initialize the array xWSAVE, which is used in subroutine xSINT. vrfftb vrfftb (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. vrfftf vrfftf (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. vrffti vrffti (3p) - initialize the array xWSAVE, which is used in both xFFTF and xFFTB. vsinqb vsinqb (3p) - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 * N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. vsinqf vsinqf (3p) - compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 * N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. vsinqi vsinqi (3p) - initialize the array xWSAVE, which is used in both xSINQF and xSINQB. vsint vsint (3p) - compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 * (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence. vsinti vsinti (3p) - initialize the array xWSAVE, which is used in subroutine xSINT. xerbla xerbla (3p) - error handler for the LAPACK routines zaxpy zaxpy (3p) - Compute y := alpha * x + y zbdsqr zbdsqr (3p) - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B zchdc zchdc (3p) - compute the Cholesky decomposition of a symmetric positive definite matrix A. zchdd zchdd (3p) - downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. zchex zchex (3p) - compute the Cholesky decomposition of a symmetric positive definite matrix A. zchud zchud (3p) - update an augmented Cholesky decomposition of the tria