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LAPACK
3.9.0
LAPACK: Linear Algebra PACKage
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| subroutine | sggsvp (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO) |
| | SGGSVP More...
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| subroutine | slatzm (SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK) |
| | SLATZM More...
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| subroutine | stzrqf (M, N, A, LDA, TAU, INFO) |
| | STZRQF More...
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| subroutine | sbbcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, WORK, LWORK, INFO) |
| | SBBCSD More...
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| subroutine | sgghd3 (COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, WORK, LWORK, INFO) |
| | SGGHD3 More...
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| subroutine | sgghrd (COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) |
| | SGGHRD More...
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| subroutine | sggqrf (N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) |
| | SGGQRF More...
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| subroutine | sggrqf (M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) |
| | SGGRQF More...
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| subroutine | sggsvp3 (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, LWORK, INFO) |
| | SGGSVP3 More...
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| subroutine | sgsvj0 (JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO) |
| | SGSVJ0 pre-processor for the routine sgesvj. More...
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| subroutine | sgsvj1 (JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO) |
| | SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots. More...
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| subroutine | shsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL, IFAILR, INFO) |
| | SHSEIN More...
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| subroutine | shseqr (JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z, LDZ, WORK, LWORK, INFO) |
| | SHSEQR More...
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| subroutine | sla_lin_berr (N, NZ, NRHS, RES, AYB, BERR) |
| | SLA_LIN_BERR computes a component-wise relative backward error. More...
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| subroutine | sla_wwaddw (N, X, Y, W) |
| | SLA_WWADDW adds a vector into a doubled-single vector. More...
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| subroutine | slals0 (ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO) |
| | SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. More...
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| subroutine | slalsa (ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO) |
| | SLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. More...
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| subroutine | slalsd (UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, IWORK, INFO) |
| | SLALSD uses the singular value decomposition of A to solve the least squares problem. More...
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| real function | slansf (NORM, TRANSR, UPLO, N, A, WORK) |
| | SLANSF More...
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| subroutine | slarscl2 (M, N, D, X, LDX) |
| | SLARSCL2 performs reciprocal diagonal scaling on a vector. More...
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| subroutine | slarz (SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK) |
| | SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. More...
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| subroutine | slarzb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK) |
| | SLARZB applies a block reflector or its transpose to a general matrix. More...
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| subroutine | slarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) |
| | SLARZT forms the triangular factor T of a block reflector H = I - vtvH. More...
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| subroutine | slascl2 (M, N, D, X, LDX) |
| | SLASCL2 performs diagonal scaling on a vector. More...
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| subroutine | slatrz (M, N, L, A, LDA, TAU, WORK) |
| | SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations. More...
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| subroutine | sopgtr (UPLO, N, AP, TAU, Q, LDQ, WORK, INFO) |
| | SOPGTR More...
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| subroutine | sopmtr (SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO) |
| | SOPMTR More...
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| subroutine | sorbdb (TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO) |
| | SORBDB More...
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| subroutine | sorbdb1 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) |
| | SORBDB1 More...
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| subroutine | sorbdb2 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) |
| | SORBDB2 More...
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| subroutine | sorbdb3 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) |
| | SORBDB3 More...
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| subroutine | sorbdb4 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO) |
| | SORBDB4 More...
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| subroutine | sorbdb5 (M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2, WORK, LWORK, INFO) |
| | SORBDB5 More...
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| subroutine | sorbdb6 (M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2, WORK, LWORK, INFO) |
| | SORBDB6 More...
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| recursive subroutine | sorcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, IWORK, INFO) |
| | SORCSD More...
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| subroutine | sorcsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO) |
| | SORCSD2BY1 More...
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| subroutine | sorg2l (M, N, K, A, LDA, TAU, WORK, INFO) |
| | SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). More...
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| subroutine | sorg2r (M, N, K, A, LDA, TAU, WORK, INFO) |
| | SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). More...
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| subroutine | sorghr (N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO) |
| | SORGHR More...
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| subroutine | sorgl2 (M, N, K, A, LDA, TAU, WORK, INFO) |
| | SORGL2 More...
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| subroutine | sorglq (M, N, K, A, LDA, TAU, WORK, LWORK, INFO) |
| | SORGLQ More...
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| subroutine | sorgql (M, N, K, A, LDA, TAU, WORK, LWORK, INFO) |
| | SORGQL More...
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| subroutine | sorgqr (M, N, K, A, LDA, TAU, WORK, LWORK, INFO) |
| | SORGQR More...
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| subroutine | sorgr2 (M, N, K, A, LDA, TAU, WORK, INFO) |
| | SORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). More...
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| subroutine | sorgrq (M, N, K, A, LDA, TAU, WORK, LWORK, INFO) |
| | SORGRQ More...
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| subroutine | sorgtr (UPLO, N, A, LDA, TAU, WORK, LWORK, INFO) |
| | SORGTR More...
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| subroutine | sorm2l (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO) |
| | SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). More...
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| subroutine | sorm2r (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO) |
| | SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm). More...
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| subroutine | sormbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
| | SORMBR More...
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| subroutine | sormhr (SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
| | SORMHR More...
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| subroutine | sorml2 (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO) |
| | SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). More...
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| subroutine | sormlq (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
| | SORMLQ More...
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| subroutine | sormql (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
| | SORMQL More...
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| subroutine | sormqr (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
| | SORMQR More...
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| subroutine | sormr2 (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO) |
| | SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). More...
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| subroutine | sormr3 (SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO) |
| | SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). More...
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| subroutine | sormrq (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
| | SORMRQ More...
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| subroutine | sormrz (SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
| | SORMRZ More...
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| subroutine | sormtr (SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
| | SORMTR More...
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| subroutine | spbcon (UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO) |
| | SPBCON More...
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| subroutine | spbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO) |
| | SPBEQU More...
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| subroutine | spbrfs (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) |
| | SPBRFS More...
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| subroutine | spbstf (UPLO, N, KD, AB, LDAB, INFO) |
| | SPBSTF More...
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| subroutine | spbtf2 (UPLO, N, KD, AB, LDAB, INFO) |
| | SPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm). More...
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| subroutine | spbtrf (UPLO, N, KD, AB, LDAB, INFO) |
| | SPBTRF More...
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| subroutine | spbtrs (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO) |
| | SPBTRS More...
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| subroutine | spftrf (TRANSR, UPLO, N, A, INFO) |
| | SPFTRF More...
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| subroutine | spftri (TRANSR, UPLO, N, A, INFO) |
| | SPFTRI More...
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| subroutine | spftrs (TRANSR, UPLO, N, NRHS, A, B, LDB, INFO) |
| | SPFTRS More...
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| subroutine | sppcon (UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO) |
| | SPPCON More...
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| subroutine | sppequ (UPLO, N, AP, S, SCOND, AMAX, INFO) |
| | SPPEQU More...
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| subroutine | spprfs (UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) |
| | SPPRFS More...
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| subroutine | spptrf (UPLO, N, AP, INFO) |
| | SPPTRF More...
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| subroutine | spptri (UPLO, N, AP, INFO) |
| | SPPTRI More...
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| subroutine | spptrs (UPLO, N, NRHS, AP, B, LDB, INFO) |
| | SPPTRS More...
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| subroutine | spstf2 (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) |
| | SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. More...
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| subroutine | spstrf (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) |
| | SPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. More...
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| subroutine | ssbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO) |
| | SSBGST More...
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| subroutine | ssbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) |
| | SSBTRD More...
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| subroutine | ssfrk (TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C) |
| | SSFRK performs a symmetric rank-k operation for matrix in RFP format. More...
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| subroutine | sspcon (UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, INFO) |
| | SSPCON More...
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| subroutine | sspgst (ITYPE, UPLO, N, AP, BP, INFO) |
| | SSPGST More...
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| subroutine | ssprfs (UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) |
| | SSPRFS More...
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| subroutine | ssptrd (UPLO, N, AP, D, E, TAU, INFO) |
| | SSPTRD More...
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| subroutine | ssptrf (UPLO, N, AP, IPIV, INFO) |
| | SSPTRF More...
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| subroutine | ssptri (UPLO, N, AP, IPIV, WORK, INFO) |
| | SSPTRI More...
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| subroutine | ssptrs (UPLO, N, NRHS, AP, IPIV, B, LDB, INFO) |
| | SSPTRS More...
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| subroutine | sstegr (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO) |
| | SSTEGR More...
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| subroutine | sstein (N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) |
| | SSTEIN More...
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| subroutine | sstemr (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, IWORK, LIWORK, INFO) |
| | SSTEMR More...
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| subroutine | stbcon (NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, IWORK, INFO) |
| | STBCON More...
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| subroutine | stbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) |
| | STBRFS More...
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| subroutine | stbtrs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, INFO) |
| | STBTRS More...
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| subroutine | stfsm (TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) |
| | STFSM solves a matrix equation (one operand is a triangular matrix in RFP format). More...
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| subroutine | stftri (TRANSR, UPLO, DIAG, N, A, INFO) |
| | STFTRI More...
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| subroutine | stfttp (TRANSR, UPLO, N, ARF, AP, INFO) |
| | STFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). More...
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| subroutine | stfttr (TRANSR, UPLO, N, ARF, A, LDA, INFO) |
| | STFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). More...
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| subroutine | stgsen (IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, M, PL, PR, DIF, WORK, LWORK, IWORK, LIWORK, INFO) |
| | STGSEN More...
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| subroutine | stgsja (JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, NCYCLE, INFO) |
| | STGSJA More...
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| subroutine | stgsna (JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, IWORK, INFO) |
| | STGSNA More...
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| subroutine | stpcon (NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK, INFO) |
| | STPCON More...
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| subroutine | stpmqrt (SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) |
| | STPMQRT More...
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| subroutine | stpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO) |
| | STPQRT More...
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| subroutine | stpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO) |
| | STPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. More...
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| subroutine | stprfs (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) |
| | STPRFS More...
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| subroutine | stptri (UPLO, DIAG, N, AP, INFO) |
| | STPTRI More...
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| subroutine | stptrs (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO) |
| | STPTRS More...
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| subroutine | stpttf (TRANSR, UPLO, N, AP, ARF, INFO) |
| | STPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF). More...
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| subroutine | stpttr (UPLO, N, AP, A, LDA, INFO) |
| | STPTTR copies a triangular matrix from the standard packed format (TP) to the standard full format (TR). More...
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| subroutine | strcon (NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, IWORK, INFO) |
| | STRCON More...
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| subroutine | strevc (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) |
| | STREVC More...
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| subroutine | strevc3 (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, LWORK, INFO) |
| | STREVC3 More...
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| subroutine | strexc (COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) |
| | STREXC More...
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| subroutine | strrfs (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) |
| | STRRFS More...
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| subroutine | strsen (JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, WR, WI, M, S, SEP, WORK, LWORK, IWORK, LIWORK, INFO) |
| | STRSEN More...
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| subroutine | strsna (JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, S, SEP, MM, M, WORK, LDWORK, IWORK, INFO) |
| | STRSNA More...
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| subroutine | strti2 (UPLO, DIAG, N, A, LDA, INFO) |
| | STRTI2 computes the inverse of a triangular matrix (unblocked algorithm). More...
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| subroutine | strtri (UPLO, DIAG, N, A, LDA, INFO) |
| | STRTRI More...
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| subroutine | strtrs (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO) |
| | STRTRS More...
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| subroutine | strttf (TRANSR, UPLO, N, A, LDA, ARF, INFO) |
| | STRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF). More...
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| subroutine | strttp (UPLO, N, A, LDA, AP, INFO) |
| | STRTTP copies a triangular matrix from the standard full format (TR) to the standard packed format (TP). More...
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| subroutine | stzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO) |
| | STZRZF More...
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This is the group of real other Computational routines
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.
real function snrm2(N, X, INCX)
SNRM2
subroutine strmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRMM
subroutine sorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGLQ
subroutine slarzt(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
SLARZT forms the triangular factor T of a block reflector H = I - vtvH.
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
subroutine stpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPSV
subroutine strsv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRSV
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
subroutine sorbdb(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO)
SORBDB
subroutine stbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBSV
subroutine slae2(A, B, C, RT1, RT2)
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
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...
real function slamc3(A, B)
SLAMC3
subroutine slabad(SMALL, LARGE)
SLABAD
subroutine stftri(TRANSR, UPLO, DIAG, N, A, INFO)
STFTRI
real function slansf(NORM, TRANSR, UPLO, N, A, WORK)
SLANSF
recursive subroutine sorcsd(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, IWORK, INFO)
SORCSD
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 matri...
subroutine stbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBMV
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
subroutine sorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQL
subroutine slarrj(N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO)
SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.
subroutine slarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
SLARFT forms the triangular factor T of a block reflector H = I - vtvH
subroutine sorml2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sge...
subroutine sormr3(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)
SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stz...
subroutine slatbs(UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
SLATBS solves a triangular banded system of equations.
subroutine slas2(F, G, H, SSMIN, SSMAX)
SLAS2 computes singular values of a 2-by-2 triangular matrix.
subroutine slaev2(A, B, C, RT1, RT2, CS1, SN1)
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
subroutine sspr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
SSPR2
subroutine sspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
SSPMV
subroutine srscl(N, SA, SX, INCX)
SRSCL multiplies a vector by the reciprocal of a real scalar.
subroutine sorgl2(M, N, K, A, LDA, TAU, WORK, INFO)
SORGL2
subroutine slasdq(UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)
SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e....
subroutine spbtrs(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
SPBTRS
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
subroutine spbtf2(UPLO, N, KD, AB, LDAB, INFO)
SPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (un...
subroutine sorbdb6(M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2, WORK, LWORK, INFO)
SORBDB6
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...
subroutine sgeqr2(M, N, A, LDA, TAU, WORK, INFO)
SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
subroutine sormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQR
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 ...
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 iterat...
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.
subroutine sormrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMRQ
subroutine srotm(N, SX, INCX, SY, INCY, SPARAM)
SROTM
subroutine slagtf(N, A, LAMBDA, B, C, TOL, D, IN, INFO)
SLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix,...
subroutine slarzb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
SLARZB applies a block reflector or its transpose to a general matrix.
subroutine stgsyl(TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, IWORK, INFO)
STGSYL
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,...
subroutine strtri(UPLO, DIAG, N, A, LDA, INFO)
STRTRI
subroutine sorbdb1(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
SORBDB1
subroutine slasr(SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
SLASR applies a sequence of plane rotations to a general rectangular matrix.
subroutine slasda(ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)
SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagona...
subroutine spptrs(UPLO, N, NRHS, AP, B, LDB, INFO)
SPPTRS
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.
subroutine slarz(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
subroutine sorbdb4(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO)
SORBDB4
subroutine stgexc(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, WORK, LWORK, INFO)
STGEXC
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
subroutine slapll(N, X, INCX, Y, INCY, SSMIN)
SLAPLL measures the linear dependence of two vectors.
subroutine stfsm(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB)
STFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
subroutine sgeqpf(M, N, A, LDA, JPVT, TAU, WORK, INFO)
SGEQPF
subroutine sspr(UPLO, N, ALPHA, X, INCX, AP)
SSPR
real function slanst(NORM, N, D, E)
SLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
subroutine sorg2l(M, N, K, A, LDA, TAU, WORK, INFO)
SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf ...
integer function isamax(N, SX, INCX)
ISAMAX
subroutine srot(N, SX, INCX, SY, INCY, C, S)
SROT
subroutine slascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
subroutine sorbdb3(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
SORBDB3
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
subroutine slassq(N, X, INCX, SCALE, SUMSQ)
SLASSQ updates a sum of squares represented in scaled form.
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
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...
logical function sisnan(SIN)
SISNAN tests input for NaN.
subroutine slarfg(N, ALPHA, X, INCX, TAU)
SLARFG generates an elementary reflector (Householder matrix).
subroutine spstf2(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)
SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semide...
subroutine ssptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPTRS
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,...
subroutine stpqrt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
STPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix,...
subroutine sormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMLQ
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
subroutine spotrf(UPLO, N, A, LDA, INFO)
SPOTRF
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,...
subroutine sscal(N, SA, SX, INCX)
SSCAL
subroutine sormql(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQL
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 sequ...
subroutine sorbdb5(M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2, WORK, LWORK, INFO)
SORBDB5
subroutine sstemr(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, IWORK, LIWORK, INFO)
SSTEMR
subroutine xerbla(SRNAME, INFO)
XERBLA
real function sdot(N, SX, INCX, SY, INCY)
SDOT
subroutine sgeqrf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGEQRF
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
subroutine sorgr2(M, N, K, A, LDA, TAU, WORK, INFO)
SORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf...
logical function lsame(CA, CB)
LSAME
real function slapy2(X, Y)
SLAPY2 returns sqrt(x2+y2).
subroutine sorg2r(M, N, K, A, LDA, TAU, WORK, INFO)
SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf ...
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
subroutine stpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
subroutine sgghrd(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO)
SGGHRD
subroutine sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
subroutine slarfgp(N, ALPHA, X, INCX, TAU)
SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
subroutine stptri(UPLO, DIAG, N, AP, INFO)
STPTRI
real function slamch(CMACH)
SLAMCH
subroutine sorm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sge...
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.
subroutine ssbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SSBMV
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 sp...
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
subroutine slals0(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO)
SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer...
subroutine spotf2(UPLO, N, A, LDA, INFO)
SPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
subroutine ssyr(UPLO, N, ALPHA, X, INCX, A, LDA)
SSYR
subroutine sorm2l(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sge...
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
subroutine slarrr(N, D, E, INFO)
SLARRR performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive computa...
subroutine strsyl(TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO)
STRSYL
subroutine slartg(F, G, CS, SN, R)
SLARTG generates a plane rotation with real cosine and real sine.
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
subroutine slarrc(JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO)
SLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
subroutine slargv(N, X, INCX, Y, INCY, C, INCC)
SLARGV generates a vector of plane rotations with real cosines and real sines.
subroutine sgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGERQF
subroutine slapmr(FORWRD, M, N, X, LDX, K)
SLAPMR rearranges rows of a matrix as specified by a permutation vector.
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 ...
subroutine slapmt(FORWRD, M, N, X, LDX, K)
SLAPMT performs a forward or backward permutation of the columns of a matrix.
subroutine slalsa(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)
SLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.
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,...
subroutine strti2(UPLO, DIAG, N, A, LDA, INFO)
STRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
subroutine sgeqp3(M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
SGEQP3
subroutine slartgp(F, G, CS, SN, R)
SLARTGP generates a plane rotation so that the diagonal is nonnegative.
subroutine slagts(JOB, N, A, B, C, D, IN, Y, TOL, INFO)
SLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal ma...
subroutine sormr2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sge...
subroutine slasdt(N, LVL, ND, INODE, NDIML, NDIMR, MSUB)
SLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc.
subroutine slartgs(X, Y, SIGMA, CS, SN)
SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bid...
subroutine sorm22(SIDE, TRANS, M, N, N1, N2, Q, LDQ, C, LDC, WORK, LWORK, INFO)
SORM22 multiplies a general matrix by a banded orthogonal matrix.
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
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 ...
subroutine strexc(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO)
STREXC
subroutine sbbcsd(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, WORK, LWORK, INFO)
SBBCSD
subroutine sgerq2(M, N, A, LDA, TAU, WORK, INFO)
SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
subroutine slatrz(M, N, L, A, LDA, TAU, WORK)
SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.
subroutine slasrt(ID, N, D, INFO)
SLASRT sorts numbers in increasing or decreasing order.
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 de...
subroutine slarre(RANGE, N, VL, VU, IL, IU, D, E, E2, RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M, W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN, WORK, IWORK, INFO)
SLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each unreduce...
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 tha...
subroutine sorbdb2(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
SORBDB2
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
1.8.16