SLASD3(3)

🌸 SLASD3(3) — the slasd3.f main character 💅

okay bestie, welcome to the Library Functions Manual page for SLASD3(3) — yes, the page for /home/abui...RC/slasd3.f(3), and the source file is out here living its full path life below. She’s a LAPACK Fortran subroutine, she’s iconic, and she’s about to explain secular-equation square roots and singular-vector updates without making your brain leak. ✨

✨ NAME ✨

SLASD3 — the subroutine chillin’ at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasd3.f. That’s the whole name entry, no cap.

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SLASD3 (nl, nr, sqre, k, d, q, ldq, dsigma, u, ldu, u2, ldu2,
    vt, ldvt, vt2, ldvt2, idxc, ctot, z, info)

SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

💖 Function/Subroutine Documentation 💖

Here’s the full typed signature, character for character, bestie:

subroutine SLASD3 (integer nl, integer nr, integer sqre, integer k, real,
     dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, real,
     dimension( * ) dsigma, real, dimension( ldu, * ) u, integer ldu, real,
     dimension( ldu2, * ) u2, integer ldu2, real, dimension( ldvt, * ) vt,
     integer ldvt, real, dimension( ldvt2, * ) vt2, integer ldvt2, integer,
     dimension( * ) idxc, integer, dimension( * ) ctot, real, dimension( * )
     z, integer info)

SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

Purpose

SLASD3 finds all the square roots of the roots of the secular equation, as defined by the values in D and Z. It makes the appropriate calls to SLASD4 and then updates the singular vectors by matrix multiplication.

SLASD3 is called from SLASD1.

Parameters

• NL — INTEGER. The row dimension of the upper block. NL >= 1.
• NR — INTEGER. The row dimension of the lower block. NR >= 1.
• SQRE — INTEGER. = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.
• K — INTEGER. The size of the secular equation, 1 =< K = < N.
• D — REAL array, dimension(K). On exit the square roots of the roots of the secular equation, in ascending order.
• Q — REAL array, dimension (LDQ,K).
• LDQ — INTEGER. The leading dimension of the array Q. LDQ >= K.
• DSIGMA — REAL array, dimension(K). The first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation.
• U — REAL array, dimension (LDU, N). The last N - K columns of this matrix contain the deflated left singular vectors.
• LDU — INTEGER. The leading dimension of the array U. LDU >= N.
• U2 — REAL array, dimension (LDU2, N). The first K columns of this matrix contain the non-deflated left singular vectors for the split problem.
• LDU2 — INTEGER. The leading dimension of the array U2. LDU2 >= N.
• VT — REAL array, dimension (LDVT, M). The last M - K columns of VT**T contain the deflated right singular vectors.
• LDVT — INTEGER. The leading dimension of the array VT. LDVT >= N.
• VT2 — REAL array, dimension (LDVT2, N). The first K columns of VT2**T contain the non-deflated right singular vectors for the split problem.
• LDVT2 — INTEGER. The leading dimension of the array VT2. LDVT2 >= N.
• IDXC — INTEGER array, dimension (N). The permutation used to arrange the columns of U (and rows of VT) into three groups: the first group contains non-zero entries only at and above (or before) NL +1; the second contains non-zero entries only at and below (or after) NL+2; and the third is dense. The first column of U and the row of VT are treated separately, however. The rows of the singular vectors found by SLASD4 must be likewise permuted before the matrix multiplies can take place.
• CTOT — INTEGER array, dimension (4). A count of the total number of the various types of columns in U (or rows in VT), as described in IDXC. The fourth column type is any column which has been deflated.
• Z — REAL array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating row vector.
• INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value did not converge.

Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Contributors

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 214 of file slasd3.f

Author

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