Section 3: library functions
clange.f – SynopsisFunctions/SubroutinesREAL function clange (NORM, M, N, A, LDA, WORK) CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix. Function/Subroutine DocumentationREAL function clange (characterNORM, integerM, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )WORK)CLANGE returns the value of…
clangb.f – SynopsisFunctions/SubroutinesREAL function clangb (NORM, N, KL, KU, AB, LDAB, WORK) CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Function/Subroutine DocumentationREAL function clangb (characterNORM, integerN, integerKL, integerKU, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK)CLANGB returns the value…
clalsd.f – SynopsisFunctions/Subroutinessubroutine clalsd (UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO) CLALSD uses the singular value decomposition of A to solve the least squares problem. Function/Subroutine Documentationsubroutine clalsd (characterUPLO, integerSMLSIZ, integerN, integerNRHS, real, dimension( * )D, real, dimension( * )E, complex, dimension( ldb, * )B, integerLDB, realRCOND, integerRANK,…
clalsa.f – SynopsisFunctions/Subroutinessubroutine clalsa (ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK, IWORK, INFO) CLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. Function/Subroutine Documentationsubroutine clalsa (integerICOMPQ, integerSMLSIZ, integerN, integerNRHS, complex, dimension( ldb, *…
clals0.f – SynopsisFunctions/Subroutinessubroutine clals0 (ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO) CLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. Function/Subroutine Documentationsubroutine clals0 (integerICOMPQ, integerNL, integerNR, integerSQRE,…
claic1.f – SynopsisFunctions/Subroutinessubroutine claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) CLAIC1 applies one step of incremental condition estimation. Function/Subroutine Documentationsubroutine claic1 (integerJOB, integerJ, complex, dimension( j )X, realSEST, complex, dimension( j )W, complexGAMMA, realSESTPR, complexS, complexC)CLAIC1 applies one step of incremental condition estimation. Purpose: CLAIC1 applies one step of incremental condition estimation…
clahrd.f – SynopsisFunctions/Subroutinessubroutine clahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) CLAHRD 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. Function/Subroutine Documentationsubroutine clahrd…
clahr2.f – SynopsisFunctions/Subroutinessubroutine clahr2 (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) CLAHR2 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. Function/Subroutine…
clahqr.f – SynopsisFunctions/Subroutinessubroutine clahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO) CLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. Function/Subroutine Documentationsubroutine clahqr (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, complex, dimension( ldh, * )H, integerLDH, complex, dimension( * )W, integerILOZ, integerIHIZ, complex,…
clahef.f – SynopsisFunctions/Subroutinessubroutine clahef (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). Function/Subroutine Documentationsubroutine clahef (characterUPLO, integerN, integerNB, integerKB, complex, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex,…
clagtm.f – SynopsisFunctions/Subroutinessubroutine clagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB) CLAGTM 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. Function/Subroutine Documentationsubroutine clagtm…
clags2.f – SynopsisFunctions/Subroutinessubroutine clags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ) CLAGS2 Function/Subroutine Documentationsubroutine clags2 (logicalUPPER, realA1, complexA2, realA3, realB1, complexB2, realB3, realCSU, complexSNU, realCSV, complexSNV, realCSQ, complexSNQ)CLAGS2 Purpose: CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U**H *A*Q = U**H…
clag2z.f – SynopsisFunctions/Subroutinessubroutine clag2z (M, N, SA, LDSA, A, LDA, INFO) CLAG2Z converts a complex single precision matrix to a complex double precision matrix. Function/Subroutine Documentationsubroutine clag2z (integerM, integerN, complex, dimension( ldsa, * )SA, integerLDSA, complex*16, dimension( lda, * )A, integerLDA, integerINFO)CLAG2Z converts a complex single precision matrix to a complex double precision matrix. Purpose:…
claev2.f – SynopsisFunctions/Subroutinessubroutine claev2 (A, B, C, RT1, RT2, CS1, SN1) CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Function/Subroutine Documentationsubroutine claev2 (complexA, complexB, complexC, realRT1, realRT2, realCS1, complexSN1)CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix [ A B…
claesy.f – SynopsisFunctions/Subroutinessubroutine claesy (A, B, C, RT1, RT2, EVSCAL, CS1, SN1) CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix. Function/Subroutine Documentationsubroutine claesy (complexA, complexB, complexC, complexRT1, complexRT2, complexEVSCAL, complexCS1, complexSN1)CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix. Purpose: CLAESY computes the eigendecomposition of a 2-by-2 symmetric…
claein.f – SynopsisFunctions/Subroutinessubroutine claein (RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO) CLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Function/Subroutine Documentationsubroutine claein (logicalRIGHTV, logicalNOINIT, integerN, complex, dimension( ldh, * )H, integerLDH, complexW, complex, dimension( * )V, complex, dimension( ldb, * )B,…
claed8.f – SynopsisFunctions/Subroutinessubroutine claed8 (K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO) CLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. Function/Subroutine Documentationsubroutine claed8 (integerK, integerN, integerQSIZ, complex, dimension( ldq, * )Q, integerLDQ, real,…
claed7.f – SynopsisFunctions/Subroutinessubroutine claed7 (N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO) CLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense. Function/Subroutine Documentationsubroutine claed7…
claed0.f – SynopsisFunctions/Subroutinessubroutine claed0 (QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, IWORK, INFO) CLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Function/Subroutine Documentationsubroutine claed0 (integerQSIZ, integerN, real, dimension( * )D, real, dimension( * )E, complex, dimension( ldq, * )Q,…
cladiv.f – SynopsisFunctions/SubroutinesCOMPLEX function cladiv (X, Y) CLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. Function/Subroutine DocumentationCOMPLEX function cladiv (complexX, complexY)CLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. Purpose: CLADIV := X / Y, where X and Y are complex. The computation of X / Y will not overflow on an…