real

Collaboration diagram for real:

Functions
subroutine	slahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY)
	SLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. More...
integer function	ilaslc (M, N, A, LDA)
	ILASLC scans a matrix for its last non-zero column. More...
integer function	ilaslr (M, N, A, LDA)
	ILASLR scans a matrix for its last non-zero row. More...
subroutine	slabrd (M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, LDY)
	SLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. More...
subroutine	slacn2 (N, V, X, ISGN, EST, KASE, ISAVE)
	SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. More...
subroutine	slacon (N, V, X, ISGN, EST, KASE)
	SLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. More...
subroutine	sladiv (A, B, C, D, P, Q)
	SLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. More...
subroutine	sladiv1 (A, B, C, D, P, Q)
real function	sladiv2 (A, B, C, D, R, T)
subroutine	slaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO)
	SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. More...
subroutine	slaexc (WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO)
	SLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation. More...
subroutine	slag2 (A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI)
	SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. More...
subroutine	slags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ)
	SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel. More...
subroutine	slagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
	SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. More...
subroutine	slagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR)
	SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. More...
subroutine	slahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, INFO)
	SLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. More...
subroutine	slahr2 (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY)
	SLAHR2 reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. More...
subroutine	slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
	SLAIC1 applies one step of incremental condition estimation. More...
subroutine	slaln2 (LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, LDB, WR, WI, X, LDX, SCALE, XNORM, INFO)
	SLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form. More...
real function	slangt (NORM, N, DL, D, DU)
	SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. More...
real function	slanhs (NORM, N, A, LDA, WORK)
	SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. More...
real function	slansb (NORM, UPLO, N, K, AB, LDAB, WORK)
	SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. More...
real function	slansp (NORM, UPLO, N, AP, WORK)
	SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form. More...
real function	slantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
	SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix. More...
real function	slantp (NORM, UPLO, DIAG, N, AP, WORK)
	SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form. More...
real function	slantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK)
	SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. More...
subroutine	slanv2 (A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN)
	SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. More...
subroutine	slapll (N, X, INCX, Y, INCY, SSMIN)
	SLAPLL measures the linear dependence of two vectors. More...
subroutine	slapmr (FORWRD, M, N, X, LDX, K)
	SLAPMR rearranges rows of a matrix as specified by a permutation vector. More...
subroutine	slapmt (FORWRD, M, N, X, LDX, K)
	SLAPMT performs a forward or backward permutation of the columns of a matrix. More...
subroutine	slaqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK)
	SLAQP2 computes a QR factorization with column pivoting of the matrix block. More...
subroutine	slaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
	SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. More...
subroutine	slaqr0 (WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO)
	SLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. More...
subroutine	slaqr1 (N, H, LDH, SR1, SI1, SR2, SI2, V)
	SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. More...
subroutine	slaqr2 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK)
	SLAQR2 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). More...
subroutine	slaqr3 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK)
	SLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). More...
subroutine	slaqr4 (WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO)
	SLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. More...
subroutine	slaqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH)
	SLAQR5 performs a single small-bulge multi-shift QR sweep. More...
subroutine	slaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
	SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. More...
subroutine	slaqsp (UPLO, N, AP, S, SCOND, AMAX, EQUED)
	SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. More...
subroutine	slaqtr (LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO)
	SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic. More...
subroutine	slar1v (N, B1, BN, LAMBDA, D, L, LD, LLD, PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, R, ISUPPZ, NRMINV, RESID, RQCORR, WORK)
	SLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI. More...
subroutine	slar2v (N, X, Y, Z, INCX, C, S, INCC)
	SLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices. More...
subroutine	slarf (SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
	SLARF applies an elementary reflector to a general rectangular matrix. More...
subroutine	slarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
	SLARFB applies a block reflector or its transpose to a general rectangular matrix. More...
subroutine	slarfg (N, ALPHA, X, INCX, TAU)
	SLARFG generates an elementary reflector (Householder matrix). More...
subroutine	slarfgp (N, ALPHA, X, INCX, TAU)
	SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. More...
subroutine	slarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
	SLARFT forms the triangular factor T of a block reflector H = I - vtvH More...
subroutine	slarfx (SIDE, M, N, V, TAU, C, LDC, WORK)
	SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. More...
subroutine	slarfy (UPLO, N, V, INCV, TAU, C, LDC, WORK)
	SLARFY More...
subroutine	slargv (N, X, INCX, Y, INCY, C, INCC)
	SLARGV generates a vector of plane rotations with real cosines and real sines. More...
subroutine	slarrv (N, VL, VU, D, L, PIVMIN, ISPLIT, M, DOL, DOU, MINRGP, RTOL1, RTOL2, W, WERR, WGAP, IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, WORK, IWORK, INFO)
	SLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. More...
subroutine	slartv (N, X, INCX, Y, INCY, C, S, INCC)
	SLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors. More...
subroutine	slaswp (N, A, LDA, K1, K2, IPIV, INCX)
	SLASWP performs a series of row interchanges on a general rectangular matrix. More...
subroutine	slatbs (UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
	SLATBS solves a triangular banded system of equations. More...
subroutine	slatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
	SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. More...
subroutine	slatps (UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
	SLATPS solves a triangular system of equations with the matrix held in packed storage. More...
subroutine	slatrs (UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
	SLATRS solves a triangular system of equations with the scale factor set to prevent overflow. More...
subroutine	slauu2 (UPLO, N, A, LDA, INFO)
	SLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm). More...
subroutine	slauum (UPLO, N, A, LDA, INFO)
	SLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm). More...
subroutine	srscl (N, SA, SX, INCX)
	SRSCL multiplies a vector by the reciprocal of a real scalar. More...
subroutine	stprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
	STPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks. More...

Detailed Description

This is the group of real other auxiliary routines