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---
:name: dsbtrd
:md5sum: f97e07edb1ff5355443723fc32114fa2
:category: :subroutine
:arguments:
- vect:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- ab:
:type: doublereal
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: output
:dims:
- n
- e:
:type: doublereal
:intent: output
:dims:
- n-1
- q:
:type: doublereal
:intent: input/output
:dims:
- ldq
- n
- ldq:
:type: integer
:intent: input
- work:
:type: doublereal
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DSBTRD reduces a real symmetric band matrix A to symmetric\n\
* tridiagonal form T by an orthogonal similarity transformation:\n\
* Q**T * A * Q = T.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* VECT (input) CHARACTER*1\n\
* = 'N': do not form Q;\n\
* = 'V': form Q;\n\
* = 'U': update a matrix X, by forming X*Q.\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of A is stored;\n\
* = 'L': Lower triangle of A is stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KD (input) INTEGER\n\
* The number of superdiagonals of the matrix A if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.\n\
*\n\
* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)\n\
* On entry, the upper or lower triangle of the symmetric band\n\
* matrix A, stored in the first KD+1 rows of the array. The\n\
* j-th column of A is stored in the j-th column of the array AB\n\
* as follows:\n\
* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;\n\
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).\n\
* On exit, the diagonal elements of AB are overwritten by the\n\
* diagonal elements of the tridiagonal matrix T; if KD > 0, the\n\
* elements on the first superdiagonal (if UPLO = 'U') or the\n\
* first subdiagonal (if UPLO = 'L') are overwritten by the\n\
* off-diagonal elements of T; the rest of AB is overwritten by\n\
* values generated during the reduction.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KD+1.\n\
*\n\
* D (output) DOUBLE PRECISION array, dimension (N)\n\
* The diagonal elements of the tridiagonal matrix T.\n\
*\n\
* E (output) DOUBLE PRECISION array, dimension (N-1)\n\
* The off-diagonal elements of the tridiagonal matrix T:\n\
* E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.\n\
*\n\
* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N)\n\
* On entry, if VECT = 'U', then Q must contain an N-by-N\n\
* matrix X; if VECT = 'N' or 'V', then Q need not be set.\n\
*\n\
* On exit:\n\
* if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;\n\
* if VECT = 'U', Q contains the product X*Q;\n\
* if VECT = 'N', the array Q is not referenced.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q.\n\
* LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (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\
* Modified by Linda Kaufman, Bell Labs.\n\
*\n\
* =====================================================================\n\
*\n"
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