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---
:name: sgebd2
:md5sum: e4e4458e28f45673d7327d16a19ea99c
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- d:
:type: real
:intent: output
:dims:
- MIN(m,n)
- e:
:type: real
:intent: output
:dims:
- MIN(m,n)-1
- tauq:
:type: real
:intent: output
:dims:
- MIN(m,n)
- taup:
:type: real
:intent: output
:dims:
- MIN(m,n)
- work:
:type: real
:intent: workspace
:dims:
- MAX(m,n)
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGEBD2 reduces a real general m by n matrix A to upper or lower\n\
* bidiagonal form B by an orthogonal transformation: Q' * A * P = B.\n\
*\n\
* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* M (input) INTEGER\n\
* The number of rows in the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns in the matrix A. N >= 0.\n\
*\n\
* A (input/output) REAL array, dimension (LDA,N)\n\
* On entry, the m by n general matrix to be reduced.\n\
* On exit,\n\
* if m >= n, the diagonal and the first superdiagonal are\n\
* overwritten with the upper bidiagonal matrix B; the\n\
* elements below the diagonal, with the array TAUQ, represent\n\
* the orthogonal matrix Q as a product of elementary\n\
* reflectors, and the elements above the first superdiagonal,\n\
* with the array TAUP, represent the orthogonal matrix P as\n\
* a product of elementary reflectors;\n\
* if m < n, the diagonal and the first subdiagonal are\n\
* overwritten with the lower bidiagonal matrix B; the\n\
* elements below the first subdiagonal, with the array TAUQ,\n\
* represent the orthogonal matrix Q as a product of\n\
* elementary reflectors, and the elements above the diagonal,\n\
* with the array TAUP, represent the orthogonal matrix P as\n\
* a product of elementary reflectors.\n\
* See Further Details.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* D (output) REAL array, dimension (min(M,N))\n\
* The diagonal elements of the bidiagonal matrix B:\n\
* D(i) = A(i,i).\n\
*\n\
* E (output) REAL array, dimension (min(M,N)-1)\n\
* The off-diagonal elements of the bidiagonal matrix B:\n\
* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;\n\
* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.\n\
*\n\
* TAUQ (output) REAL array dimension (min(M,N))\n\
* The scalar factors of the elementary reflectors which\n\
* represent the orthogonal matrix Q. See Further Details.\n\
*\n\
* TAUP (output) REAL array, dimension (min(M,N))\n\
* The scalar factors of the elementary reflectors which\n\
* represent the orthogonal matrix P. See Further Details.\n\
*\n\
* WORK (workspace) REAL array, dimension (max(M,N))\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The matrices Q and P are represented as products of elementary\n\
* reflectors:\n\
*\n\
* If m >= n,\n\
*\n\
* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1)\n\
*\n\
* Each H(i) and G(i) has the form:\n\
*\n\
* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'\n\
*\n\
* where tauq and taup are real scalars, and v and u are real vectors;\n\
* v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);\n\
* u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);\n\
* tauq is stored in TAUQ(i) and taup in TAUP(i).\n\
*\n\
* If m < n,\n\
*\n\
* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m)\n\
*\n\
* Each H(i) and G(i) has the form:\n\
*\n\
* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'\n\
*\n\
* where tauq and taup are real scalars, and v and u are real vectors;\n\
* v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);\n\
* u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);\n\
* tauq is stored in TAUQ(i) and taup in TAUP(i).\n\
*\n\
* The contents of A on exit are illustrated by the following examples:\n\
*\n\
* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):\n\
*\n\
* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )\n\
* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )\n\
* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )\n\
* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )\n\
* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )\n\
* ( v1 v2 v3 v4 v5 )\n\
*\n\
* where d and e denote diagonal and off-diagonal elements of B, vi\n\
* denotes an element of the vector defining H(i), and ui an element of\n\
* the vector defining G(i).\n\
*\n\
* =====================================================================\n\
*\n"
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